diff --git a/benchmarks/curve.bench.ts b/benchmarks/curve.bench.ts
index 1c298d4..3ec1ed9 100644
--- a/benchmarks/curve.bench.ts
+++ b/benchmarks/curve.bench.ts
@@ -3,7 +3,6 @@
 // Copyright (c) A5 contributors
 
 // Benchmarks for the space-filling curve: s -> cell decode, cell -> s encode,
-// and fractional-point location (IJToS).
 //
 // CI runs these same files against both the PR and its merge-base, so they
 // must run on either side of the L-system migration: the adapters below pick
@@ -105,19 +104,3 @@ describe('tripleToS', () => {
     );
   }
 });
-
-describe('IJToS', () => {
-  const values = sampleS(15, N);
-  const ijs: IJ[] = new Array(N);
-  for (let i = 0; i < N; i++) {
-    ijs[i] = centroidIJ(tripleOf(values[i], 15, 'uv'));
-  }
-  let i = 0;
-  bench(
-    'IJToS res 15',
-    () => {
-      lattice.IJToS(ijs[i++ & (N - 1)], 15, 'uv');
-    },
-    BENCH_OPTS
-  );
-});
diff --git a/modules/core/cell.ts b/modules/core/cell.ts
index 1ee590d..cdc20cb 100644
--- a/modules/core/cell.ts
+++ b/modules/core/cell.ts
@@ -7,16 +7,30 @@ glMatrix.setMatrixArrayType(Float64Array as any);
 
 import type {Cartesian, Face, LonLat, Spherical} from './coordinate-systems';
 import {FaceToIJ, fromLonLat, toLonLat, toPolar, normalizeLongitudes} from './coordinate-transforms';
-import {findNearestOrigin, findNearestOriginCartesian, quintantToSegment, segmentToQuintant} from './origin';
+import {
+  findNearestOrigin,
+  findNearestOrigins,
+  QUINTANT_TO_ORIENTATION,
+  QUINTANT_TO_SEGMENT,
+  SEGMENT_TO_ORIENTATION,
+  SEGMENT_TO_QUINTANT
+} from './origin';
 import {DodecahedronProjection} from '../projections/dodecahedron';
-import {A5Cell, OriginId} from './utils';
+import {A5Cell, Origin, OriginId} from './utils';
 import {PentagonShape} from '../geometry/pentagon';
-import {getFaceVertices, getPentagonCenter, getPentagonVertices, getQuintantPolar, getQuintantVertices} from './tiling';
+import {
+  cellMarginScaled,
+  getFaceVertices,
+  getPentagonCenter,
+  getPentagonVertices,
+  getQuintantPolar,
+  getQuintantVertices
+} from './tiling';
 import {PI_OVER_5} from './constants';
-import {IJToS, sToCell} from '../lattice';
-import {deserialize, serialize, FIRST_HILBERT_RESOLUTION, WORLD_CELL} from './serialization';
-import {getGlobalCellNeighbors} from '../traversal/global-neighbors';
-import {Spiral, SPIRAL_SAMPLE_COUNT} from '../utils/spiral';
+import {roundToTriple, sToCell, tripleFlavor, tripleInBounds, tripleToS} from '../lattice';
+import type {Triple} from '../lattice';
+import {deserialize, serialize, FIRST_HILBERT_RESOLUTION, MAX_RESOLUTION, WORLD_CELL} from './serialization';
+import {NEIGHBOR_DELTAS} from '../traversal/neighbors';
 
 // Reuse these objects to avoid allocation
 const rotation = mat2.create();
@@ -34,12 +48,6 @@ let _lastResult: {
   resolution: number;
 } | null = null;
 
-/** Update the single-entry cache with a successful (cell, cellId) pair. */
-function cacheResult(cell: A5Cell, cellId: bigint, resolution: number): bigint {
-  _lastResult = {cellId, pentagon: _getPentagon(cell), originId: cell.origin.id, resolution};
-  return cellId;
-}
-
 export function lonLatToCell(lonLat: LonLat, resolution: number): bigint {
   return sphericalToCell(fromLonLat(lonLat), resolution);
 }
@@ -51,6 +59,9 @@ export function lonLatToCell(lonLat: LonLat, resolution: number): bigint {
  * inverse/forward round-trip in dense-sample loops where the input already
  * comes from the authalic Cartesian space (e.g. polygon-fill boundary slerp).
  */
+// Scratch for the fast path's scaled quintant-frame point
+const _scaledPoint = vec2.create();
+
 export function sphericalToCell(spherical: Spherical, resolution: number): bigint {
   // Resolution -1 represents WORLD_CELL, which covers the entire world
   if (resolution === -1) {
@@ -58,122 +69,182 @@ export function sphericalToCell(spherical: Spherical, resolution: number): bigin
   }
 
   if (resolution < FIRST_HILBERT_RESOLUTION) {
-    // For low resolutions there is no Hilbert curve, so we can just return as the result is exact
-    return serialize(_sphericalToEstimate(spherical, resolution));
+    // For low resolutions there is no Hilbert curve: the cell is determined by
+    // the face (and quintant) alone, so the lookup is exact.
+    const origin = findNearestOrigin(spherical);
+    const dodecPoint = dodecahedron.forward(spherical, origin.id);
+    const quintant = getQuintantPolar(toPolar(dodecPoint));
+    const segment = QUINTANT_TO_SEGMENT[origin.id * 5 + quintant];
+    return serialize({S: 0n, segment, origin, resolution});
   }
 
-  // Try the cached pentagon first — skips the full estimate pipeline when
-  // consecutive calls land in the same cell (common in dense-sample loops).
+  // Try the cached pentagon first — skips the full lookup when consecutive
+  // calls land in the same cell (common in dense-sample loops).
   if (_lastResult && _lastResult.resolution === resolution) {
     const projected = dodecahedron.forward(spherical, _lastResult.originId);
     if (_lastResult.pentagon.containsPoint(projected as Face) > 0) return _lastResult.cellId;
   }
 
-  // Try the original point's projection-based estimate. Common case for
-  // non-boundary points.
-  const firstEstimate = _sphericalToEstimate(spherical, resolution);
-  const firstKey = serialize(firstEstimate);
-  const firstDistance = a5cellContainsPoint(firstEstimate, spherical);
-  if (firstDistance > 0) return cacheResult(firstEstimate, firstKey, resolution);
+  // Fast path: locate the containing pentagon directly. Round to the leaf
+  // triangle, get the closed-form flavor, and test the pentagon geometrically
+  // in the scaled quintant frame; the triangular and pentagonal lattices are
+  // not congruent, but the containing pentagon is always the triangle's cell
+  // or one of its fixed neighbor deltas (verified exhaustively), so at most
+  // one 7-candidate walk resolves it — then a single curve encode.
+  const origin = findNearestOrigin(spherical);
+  const dodecPoint = dodecahedron.forward(spherical, origin.id);
+  const quintant = getQuintantPolar(toPolar(dodecPoint));
+  const best = _lookupInQuintant(dodecPoint, origin, quintant, resolution);
+  if (best !== null && best.margin > 0) return _acceptCandidate(best);
+  // No strictly-containing pentagon in the assigned frame: the point sits on a
+  // cell boundary or within float noise of a quintant/face seam.
+  return _sphericalToCellBoundary(spherical, resolution, origin, quintant, best);
+}
 
-  // Spiral search: perturb the point in the tangent plane to find nearby
-  // estimate cells (see modules/utils/spiral.ts).
-  const hilbertResolution = 1 + resolution - FIRST_HILBERT_RESOLUTION;
-  const scale = SPIRAL_SCALE_RAD / Math.pow(2, hilbertResolution);
-  const estimateSet = new Set<bigint>([firstKey]);
-  const cells: {cellId: bigint; distance: number}[] = [{cellId: firstKey, distance: firstDistance}];
-
-  const spiral = new Spiral(spherical, scale);
-  for (let i = 0; i < SPIRAL_SAMPLE_COUNT; i++) {
-    const estimate = _cartesianToEstimate(spiral.sample(_spiralOut, i), resolution);
-    const estimateKey = serialize(estimate);
-    if (estimateSet.has(estimateKey)) continue;
-    estimateSet.add(estimateKey);
-    const distance = a5cellContainsPoint(estimate, spherical);
-    if (distance > 0) return cacheResult(estimate, estimateKey, resolution);
-    cells.push({cellId: estimateKey, distance});
+// The best cell for `dodecPoint` (face frame of `origin`) within one quintant:
+// round to the leaf triangle, closed-form flavor, geometric margin, and — when
+// the triangle's cell doesn't strictly contain the point — the best of its
+// fixed neighbor deltas. margin > 0 ⇔ the unique strictly-containing pentagon.
+interface CellCandidate {
+  margin: number;
+  cellId: bigint;
+  triple: Triple;
+  flavor: number;
+  quintant: number;
+  hilbertResolution: number;
+  originId: OriginId;
+  resolution: number;
+}
+
+function _lookupInQuintant(
+  dodecPoint: Face,
+  origin: Origin,
+  quintant: number,
+  resolution: number
+): CellCandidate | null {
+  const globalQuintant = origin.id * 5 + quintant;
+  const segment = QUINTANT_TO_SEGMENT[globalQuintant];
+  const orientation = QUINTANT_TO_ORIENTATION[globalQuintant];
+
+  // Res-30 ids can only encode quintants 0-41 (by design: 64 bits cannot fit
+  // res 30 globally, so A5 covers the populous region). In the unsupported
+  // quintants, answer at the finest representable resolution instead — the
+  // res-29 cell CONTAINING the point. (Previously the cap lived only in
+  // serialize, which swapped in the res-29 parent of a res-30 search result —
+  // a cell that fails to contain the query point ~44% of the time there.)
+  if (resolution === MAX_RESOLUTION && 5 * origin.id + ((segment - origin.firstQuintant + 5) % 5) > 41) {
+    resolution = MAX_RESOLUTION - 1;
   }
 
-  // Spiral exhausted without finding a strict container. This is reachable
-  // for points right at the polar singularity at very high resolutions,
-  // where re-projecting any tangent sample snaps back to a small set of
-  // cells while the geometrically-containing cell is offset by one
-  // adjacency step. Fall back to direct neighbours of the closest spiral
-  // candidate, which always finds it.
-  cells.sort((a, b) => b.distance - a.distance);
-  const K = Math.min(3, cells.length);
-  for (let k = 0; k < K; k++) {
-    const neighbors = getGlobalCellNeighbors(cells[k].cellId);
-    for (let n = 0; n < neighbors.length; n++) {
-      const neighborKey = neighbors[n];
-      if (estimateSet.has(neighborKey)) continue;
-      estimateSet.add(neighborKey);
-      const neighborCell = deserialize(neighborKey);
-      const distance = a5cellContainsPoint(neighborCell, spherical);
-      if (distance > 0) return cacheResult(neighborCell, neighborKey, resolution);
-      cells.push({cellId: neighborKey, distance});
+  vec2.copy(_scaledPoint, dodecPoint);
+  if (quintant !== 0) {
+    mat2.fromRotation(rotation, -2 * PI_OVER_5 * quintant);
+    vec2.transformMat2(_scaledPoint, _scaledPoint, rotation);
+  }
+  const hilbertResolution = 1 + resolution - FIRST_HILBERT_RESOLUTION;
+  const scale = 2 ** hilbertResolution;
+  const px = _scaledPoint[0] * scale;
+  const py = _scaledPoint[1] * scale;
+  const ij = FaceToIJ([px, py] as Face);
+
+  const base = roundToTriple(ij, hilbertResolution);
+  let triple = base;
+  let flavor = tripleFlavor(base);
+  let margin = cellMarginScaled(px, py, base.x, base.y, flavor);
+  if (margin <= 0) {
+    // All deltas are relative to the ROUNDED triple (the containing pentagon
+    // is always among its fixed neighbors), not to intermediate best cells.
+    const deltas = NEIGHBOR_DELTAS[flavor].all;
+    const maxRow = scale - 1;
+    for (let i = 0; i < deltas.length; i++) {
+      const d = deltas[i];
+      const neighbor = {x: base.x + d.x, y: base.y + d.y, z: base.z + d.z};
+      if (!tripleInBounds(neighbor, maxRow)) continue;
+      const neighborFlavor = tripleFlavor(neighbor);
+      const neighborMargin = cellMarginScaled(px, py, neighbor.x, neighbor.y, neighborFlavor);
+      if (neighborMargin > margin) {
+        triple = neighbor;
+        flavor = neighborFlavor;
+        margin = neighborMargin;
+        if (margin > 0) break;
+      }
     }
   }
-
-  // True fallback: closest cell wins, even if technically just outside.
-  cells.sort((a, b) => b.distance - a.distance);
-  const fallbackKey = cells[0].cellId;
-  return cacheResult(deserialize(fallbackKey), fallbackKey, resolution);
+  const S = tripleToS(triple, hilbertResolution, orientation);
+  if (S === null) return null;
+  const cellId = serialize({S, segment, origin, resolution});
+  return {margin, cellId, triple, flavor, quintant, hilbertResolution, originId: origin.id, resolution};
 }
 
-// Spiral perturbation radius at hilbertResolution=1 (in radians of tangent
-// offset). For higher resolutions we scale by 1/2^hilbertResolution. Tuned
-// empirically (see SPIRAL_SAMPLE_COUNT in utils/spiral.ts).
-const SPIRAL_SCALE_RAD = (70 * Math.PI) / 180;
-
-// Reusable output buffer for spiral.sample() — written once per iteration,
-// consumed immediately by _cartesianToEstimate. Single-threaded JS makes
-// this safe; ports use stack allocation or per-call locals.
-const _spiralOut = vec3.create() as unknown as Cartesian;
-
-// The IJToS function uses the triangular lattice which only approximates the pentagon lattice
-// Thus these functions only return a cell nearby, and we need to search the neighborhood to find the correct cell
-// TODO: Implement a more accurate function
-
-function _sphericalToEstimate(spherical: Spherical, resolution: number): A5Cell {
-  const origin = {...findNearestOrigin(spherical)};
-  const dodecPoint = dodecahedron.forward(spherical, origin.id);
-  return _faceToEstimate(dodecPoint, origin, resolution);
+/** Cache the winning pentagon for the dense-sample fast accept and return its id. */
+function _acceptCandidate(c: CellCandidate): bigint {
+  _lastResult = {
+    cellId: c.cellId,
+    pentagon: getPentagonVertices(c.hilbertResolution, c.quintant, c.triple, c.flavor),
+    originId: c.originId,
+    resolution: c.resolution
+  };
+  return c.cellId;
 }
 
-function _cartesianToEstimate(cartesian: Cartesian, resolution: number): A5Cell {
-  const origin = {...findNearestOriginCartesian(cartesian)};
-  const dodecPoint = dodecahedron.forwardCartesian(cartesian, origin.id);
-  return _faceToEstimate(dodecPoint, origin, resolution);
-}
+// Tie margin tolerance: containment margins are cross products of unit-scale
+// pentagon edges against coordinates of magnitude up to 2^hilbertResolution,
+// so their float noise is ~2^(hilbertResolution - 52); 2^-44 gives a wide
+// safety factor while staying geometrically negligible (cells are unit-size
+// in the scaled frame).
+const TIE_EPS = 2 ** -44;
 
-function _faceToEstimate(dodecPoint: Face, origin: A5Cell['origin'], resolution: number): A5Cell {
-  const polar = toPolar(dodecPoint);
-  const quintant = getQuintantPolar(polar);
-  const {segment, orientation} = quintantToSegment(quintant, origin);
-  if (resolution < FIRST_HILBERT_RESOLUTION) {
-    // For low resolutions there is no Hilbert curve
-    return {S: 0n, segment, origin, resolution};
+/**
+ * Boundary resolution: the point has no strictly-containing pentagon in its
+ * assigned frame — it lies on a cell edge, or within float noise of a quintant
+ * or face seam (where the containing cell belongs to a neighboring frame).
+ * Deterministically rerun the same lookup in every frame that could own the
+ * point — all 5 quintants of the 3 nearest faces (a dodecahedron vertex joins
+ * 3 faces; a face center joins 5 quintants). A strictly-containing pentagon is
+ * unique, so the first strict hit wins; if none exists the point is exactly on
+ * a boundary shared by the near-best candidates, and the tie-break is the cell
+ * that comes FIRST ALONG THE CURVE — the lowest cell id (origin/segment occupy
+ * the top id bits in curve order, so numeric order is curve order globally).
+ */
+function _sphericalToCellBoundary(
+  spherical: Spherical,
+  resolution: number,
+  firstOrigin: Origin,
+  firstQuintant: number,
+  first: CellCandidate | null
+): bigint {
+  const candidates: CellCandidate[] = first !== null ? [first] : [];
+  for (const origin of findNearestOrigins(spherical, 3)) {
+    const dodecPoint = dodecahedron.forward(spherical, origin.id);
+    // Try this origin's assigned quintant first, then its gamma-adjacent
+    // neighbors: seam points resolve in the adjacent frame, so this order
+    // finds the strict container in 1-2 lookups instead of scanning all 5.
+    const q0 = getQuintantPolar(toPolar(dodecPoint));
+    for (const dq of [0, 1, 4, 2, 3]) {
+      const quintant = (q0 + dq) % 5;
+      if (origin.id === firstOrigin.id && quintant === firstQuintant) continue;
+      const c = _lookupInQuintant(dodecPoint, origin, quintant, resolution);
+      if (c === null) continue;
+      if (c.margin > 0) return _acceptCandidate(c);
+      candidates.push(c);
+    }
   }
-
-  // Rotate into right fifth
-  if (quintant !== 0) {
-    const extraAngle = 2 * PI_OVER_5 * quintant;
-    mat2.fromRotation(rotation, -extraAngle);
-    vec2.transformMat2(dodecPoint, dodecPoint, rotation);
+  let best = -Infinity;
+  for (const c of candidates) if (c.margin > best) best = c.margin;
+  const eps = TIE_EPS * 2 ** (1 + resolution - FIRST_HILBERT_RESOLUTION);
+  let winner: CellCandidate | null = null;
+  for (const c of candidates) {
+    if (c.margin >= best - eps && (winner === null || c.cellId < winner.cellId)) winner = c;
   }
-
-  const hilbertResolution = 1 + resolution - FIRST_HILBERT_RESOLUTION;
-  vec2.scale(dodecPoint, dodecPoint, 2 ** hilbertResolution);
-
-  const ij = FaceToIJ(dodecPoint);
-  let S = IJToS(ij, hilbertResolution, orientation);
-  return {S, segment, origin, resolution};
+  if (winner === null) throw new Error('sphericalToCell: no candidate cell found');
+  return _acceptCandidate(winner);
 }
 
 // TODO move into tiling.ts
 export function _getPentagon({S, segment, origin, resolution}: A5Cell): PentagonShape {
-  const {quintant, orientation} = segmentToQuintant(segment, origin);
+  const globalQuintant = origin.id * 5 + segment;
+  const quintant = SEGMENT_TO_QUINTANT[globalQuintant];
+  const orientation = SEGMENT_TO_ORIENTATION[globalQuintant];
   if (resolution === FIRST_HILBERT_RESOLUTION - 1) {
     const out = getQuintantVertices(quintant);
     return out;
@@ -191,7 +262,9 @@ export function cellToSpherical(cell: bigint): Spherical {
   if (resolution >= FIRST_HILBERT_RESOLUTION) {
     // Fast path: the pentagon center is O(1) from (triple, flavor) — no need
     // to construct the pentagon itself.
-    const {quintant, orientation} = segmentToQuintant(segment, origin);
+    const globalQuintant = origin.id * 5 + segment;
+    const quintant = SEGMENT_TO_QUINTANT[globalQuintant];
+    const orientation = SEGMENT_TO_ORIENTATION[globalQuintant];
     const hilbertResolution = resolution - FIRST_HILBERT_RESOLUTION + 1;
     const {triple, flavor} = sToCell(S, hilbertResolution, orientation);
     const center = getPentagonCenter(hilbertResolution, quintant, triple, flavor);
diff --git a/modules/core/origin.ts b/modules/core/origin.ts
index 004c7c9..b872780 100644
--- a/modules/core/origin.ts
+++ b/modules/core/origin.ts
@@ -114,6 +114,38 @@ export function segmentToQuintant(segment: number, origin: Origin): {quintant: n
   return {quintant, orientation};
 }
 
+// Lookup tables for the two mappings above, built once at startup — there are
+// only 60 (origin, quintant) pairs. Indexed by origin.id * 5 + quintant
+// (resp. + segment, the global quintant number as encoded in serialized cell
+// ids). Call sites read these directly: a pair of flat array loads that V8
+// cannot pessimize, unlike the object-returning functions (a cold second call
+// site to quintantToSegment measurably degraded the optimized hot path).
+export const QUINTANT_TO_SEGMENT = new Uint8Array(60);
+export const QUINTANT_TO_ORIENTATION: Orientation[] = new Array(60);
+export const SEGMENT_TO_QUINTANT = new Uint8Array(60);
+export const SEGMENT_TO_ORIENTATION: Orientation[] = new Array(60);
+for (const origin of origins) {
+  for (let i = 0; i < 5; i++) {
+    const {segment, orientation} = quintantToSegment(i, origin);
+    QUINTANT_TO_SEGMENT[origin.id * 5 + i] = segment;
+    QUINTANT_TO_ORIENTATION[origin.id * 5 + i] = orientation;
+    const s2q = segmentToQuintant(i, origin);
+    SEGMENT_TO_QUINTANT[origin.id * 5 + i] = s2q.quintant;
+    SEGMENT_TO_ORIENTATION[origin.id * 5 + i] = s2q.orientation;
+  }
+}
+
+/**
+ * The `count` origins nearest to a point, by haversine distance, nearest first.
+ * Used by the boundary resolution in sphericalToCell: a point on (or within
+ * float noise of) a face seam or dodecahedron vertex may belong to a cell of
+ * the 2nd- or 3rd-nearest face.
+ */
+export function findNearestOrigins(point: Spherical, count: number): Origin[] {
+  const sorted = [...origins].sort((a, b) => haversine(point, a.axis) - haversine(point, b.axis));
+  return sorted.slice(0, count);
+}
+
 /**
  * Find the nearest origin to a point on the sphere
  * Uses haversine formula to calculate great-circle distance
@@ -136,25 +168,6 @@ export function isNearestOrigin(point: Spherical, origin: Origin): boolean {
   return haversine(point, origin.axis) > 0.49999999;
 }
 
-/**
- * Same as `findNearestOrigin` but takes a Cartesian unit vector. The
- * argmin of `1 − a·b` matches the argmin of haversine, so this returns
- * the same origin without any spherical-trig conversions.
- */
-export function findNearestOriginCartesian(c: Cartesian): Origin {
-  let minDistance = Infinity;
-  let nearest = origins[0];
-  for (const origin of origins) {
-    const ax = origin.axisCartesian;
-    const distance = 1 - (c[0] * ax[0] + c[1] * ax[1] + c[2] * ax[2]);
-    if (distance < minDistance) {
-      minDistance = distance;
-      nearest = origin;
-    }
-  }
-  return nearest;
-}
-
 /**
  * Modified haversine formula to calculate great-circle distance.
  * Retruns the "angle" between the two points. We need to minimize this to find the nearest origin
diff --git a/modules/core/tiling.ts b/modules/core/tiling.ts
index 38e93b6..37a0286 100644
--- a/modules/core/tiling.ts
+++ b/modules/core/tiling.ts
@@ -36,6 +36,51 @@ const FLAVOR_CENTERS = [0, 1, 2, 3].map(flavor => {
   return p.getCenter();
 });
 
+// The base PENTAGON under each flavor's orientation ops, flattened to
+// [x0,y0,...,x4,y4] for the allocation-free containment test below.
+const FLAVOR_PENTAGONS = [0, 1, 2, 3].map(flavor => {
+  const p = PENTAGON.clone();
+  if (flavor & 1) p.rotate180();
+  if (flavor & 2) p.reflectY();
+  const verts = p.getVertices();
+  const flat = new Float64Array(10);
+  for (let i = 0; i < 5; i++) {
+    flat[i * 2] = verts[i][0];
+    flat[i * 2 + 1] = verts[i][1];
+  }
+  return flat;
+});
+
+/**
+ * Signed containment margin of a point in the pentagon of (triple, flavor)
+ * (> 0 ⇔ strictly inside; the most-violated-edge cross product otherwise),
+ * tested in the SCALED quintant-0 frame (face coords rotated into quintant 0 and scaled
+ * by 2^resolution — the frame `_faceToEstimate` works in). In this frame the
+ * cell's pentagon is the flavor-oriented base pentagon translated by
+ * BASIS·(x+y, -x+(flavor&1)), so the test needs no curve decode, no
+ * re-projection, and — pentagons being unit-size here — stays well-conditioned
+ * at every resolution.
+ */
+export function cellMarginScaled(px: number, py: number, x: number, y: number, flavor: number): number {
+  const rx = x + y;
+  const ry = -x + (flavor & 1);
+  const tx = BASIS[0] * rx + BASIS[2] * ry;
+  const ty = BASIS[1] * rx + BASIS[3] * ry;
+  const pent = FLAVOR_PENTAGONS[flavor];
+  let margin = Infinity;
+  for (let i = 0; i < 5; i++) {
+    const j = i === 4 ? 0 : i + 1;
+    const v1x = pent[i * 2] + tx;
+    const v1y = pent[i * 2 + 1] + ty;
+    const v2x = pent[j * 2] + tx;
+    const v2y = pent[j * 2 + 1] + ty;
+    // (v1 - v2) × (p - v1): < 0 ⇒ strictly outside this edge
+    const cross = (v1x - v2x) * (py - v1y) - (v1y - v2y) * (px - v1x);
+    if (cross < margin) margin = cross;
+  }
+  return margin;
+}
+
 /**
  * Get pentagon vertices for a cell.
  *
diff --git a/modules/lattice/compat.ts b/modules/lattice/compat.ts
index f21d38f..727a42b 100644
--- a/modules/lattice/compat.ts
+++ b/modules/lattice/compat.ts
@@ -228,7 +228,7 @@ export function compatTripleToS(t: Triple, resolution: number, orientation: Orie
     raw = {x: raw.z, y: raw.y, z: raw.x};
   }
   const ab = tripleToAB(raw);
-  const sGeo = axiomTargetToS(ORIGINAL, ab.a, ab.b, resolution, AXIOM_W, true)[0];
+  const sGeo = axiomTargetToS(ORIGINAL, ab.a, ab.b, resolution, AXIOM_W)[0];
   const digits = digitsOf(sGeo, resolution);
   inverseShift(digits, rec.invertJ, rec.flipIJ);
   const v = packDigits(digits);
diff --git a/modules/lattice/curve.ts b/modules/lattice/curve.ts
index 12bf81d..9f4826b 100644
--- a/modules/lattice/curve.ts
+++ b/modules/lattice/curve.ts
@@ -7,17 +7,43 @@
 // (sToCell / sToTriple) and triple.ts (tripleToS).
 
 import type {IJ} from '../core/coordinate-systems';
-import type {Orientation} from './types';
-import {sumPointToS} from './lsystem';
+import type {Orientation, Triple} from './types';
+import {tripleToSLattice} from './lsystem';
+import {POW2} from './lsystem/tables';
 
 /**
- * Fractional IJ point -> curve position `s` of the containing cell, by direct
- * L-system descent. The IJ plane maps onto the L-system's corner-sum frame by
- * the exact affine map target = (12*(i+j), -12*j) — derived by matching cell
- * centroids across the two frames (parity-0 cell (x,y,z): centroid (x+y+1/3,
- * -x+1/3) in IJ, corner sum (12y+8, 12x-4); parity-1: (x+y-1/3, -x+2/3) and
- * (12y+4, 12x-8); both fit sum = (12(i+j), -12j) exactly), and validated
- * against the old-engine discretization over all resolutions and orientations.
+ * Locate the lattice triangle containing a fractional IJ point, as a triple.
+ *
+ * The triples tile the IJ plane as triangles: the unit square (m, n) =
+ * (floor(i), floor(j)) splits along the diagonal u+v = 1 into a lower triangle
+ * (the parity-0 cell (-n, m+n, -m), centroid (m+1/3, n+1/3)) and an upper
+ * triangle (the parity-1 cell (-n, m+n+1, -m), centroid (m+2/3, n+2/3)) — the
+ * centroid correspondences were derived from the exact IJ <-> corner-sum
+ * affine map target = (12*(i+j), -12*j) and validated against the old-engine
+ * discretization over all resolutions and orientations. Point location is two floors + one
+ * diagonal comparison. Points exactly on a triangle edge have no unique cell;
+ * the >= tie-break below is the fixed convention.
+ *
+ * The result is clamped into quintant bounds (m >= 0, n >= 0, m+n+parity <=
+ * maxRow, equivalent to tripleInBounds): a point slightly outside the quintant
+ * (as the estimate path can produce near quintant edges) must still map to a
+ * valid cell for the exact encode.
  */
-export const IJToS = (ij: IJ, resolution: number, orientation: Orientation = 'uv'): bigint =>
-  sumPointToS(12 * (ij[0] + ij[1]), -12 * ij[1], resolution, orientation);
+export function roundToTriple(ij: IJ, resolution: number): Triple {
+  const maxRow = POW2[resolution] - 1;
+  let m = Math.floor(ij[0]);
+  let n = Math.floor(ij[1]);
+  let parity = ij[0] - m + (ij[1] - n) >= 1 ? 1 : 0;
+  if (m < 0) m = 0;
+  if (n < 0) n = 0;
+  if (m + n + parity > maxRow) {
+    parity = 0;
+    if (m + n > maxRow) {
+      const over = m + n - maxRow;
+      const dm = Math.min(m, over);
+      m -= dm;
+      n -= over - dm;
+    }
+  }
+  return {x: -n, y: m + n + parity, z: -m};
+}
diff --git a/modules/lattice/index.ts b/modules/lattice/index.ts
index 2ddb067..c94ba8c 100644
--- a/modules/lattice/index.ts
+++ b/modules/lattice/index.ts
@@ -2,28 +2,21 @@
 // SPDX-License-Identifier: Apache-2.0
 // Copyright (c) A5 contributors
 
-// The canonical A5 curve is currently the ORIGINAL construction (compat.ts):
-// the two-motif quaternary L-system with the shiftDigits recode on top, so
-// cell IDs remain bit-identical to previous releases. The non-self-intersecting
-// L-system curve (lsystem.ts / curve.ts) powers the machinery underneath and is
-// fully implemented and pinned by fixtures (tests/lattice/lsystem.test.ts);
-// making it canonical is a planned follow-up — a breaking change of all cell
-// IDs that swaps the exports below to lsystem.ts/curve.ts and regenerates the
-// fixtures.
+// The canonical A5 curve is the non-self-intersecting L-system curve
+// (lsystem/ + curve.ts): point location via roundToTriple, s <-> cell mappings via
+// sToCell / sToTriple / tripleToS. This is a breaking change from previous
+// releases — cell IDs differ from the original construction. The original curve
+// remains available bit-for-bit via the compat* exports below for migration.
 
 export type {Orientation} from './types';
 
-export {
-  compatSToCell as sToCell,
-  compatSToTriple as sToTriple,
-  compatTripleToS as tripleToS,
-  compatIJToS as IJToS
-} from './compat';
+export {roundToTriple} from './curve';
+export {sToCell, sToTriple} from './lsystem';
 export type {Cell} from './lsystem';
 
 export type {Triple} from './triple';
-export {tripleParity, tripleInBounds} from './triple';
+export {tripleParity, tripleInBounds, tripleFlavor, tripleToS} from './triple';
 
-// Also exported under their own names, so the old-curve behavior stays pinned
-// explicitly (tests/lattice/compat.test.ts) across the future canonical swap.
+// The ORIGINAL (pre-L-system) curve, bit-for-bit, for the migration path —
+// same cells, same pentagon flavors, old visiting order (tests/lattice/compat.test.ts).
 export {compatSToCell, compatSToTriple, compatTripleToS, compatIJToS} from './compat';
diff --git a/modules/lattice/lsystem/index.ts b/modules/lattice/lsystem/index.ts
index 8af19d9..406f7e9 100644
--- a/modules/lattice/lsystem/index.ts
+++ b/modules/lattice/lsystem/index.ts
@@ -133,61 +133,16 @@ export function axiomLeafCell(
   };
 }
 
-// ---------- inverse: descend by which child's convex footprint contains the target ----------
-// `ta`/`tb` is the target in the corner-sum frame (= 3x the (a,b) point frame):
-// a cell's corner sum for the exact triple path, or 3x a fractional point for
-// direct point location. For each footprint edge we cross the UNIT edge direction
-// with (target - corner); > 0 for every edge means the target is inside.
-//
-// Early exits (exact for both target kinds): the children tile the parent, so a
-// strictly-inside child (min cross > 0) is unique and ends the scan; and an edge
-// cross that is both <= 0 and <= the best score so far can neither be strictly
-// inside nor win the argmax fallback, so the edge loop aborts. Targets on a
-// boundary (fractional points only) fall through to the argmax, matching the
-// exhaustive scan.
-function insideScore(
-  t: CurveTables,
-  motif: number,
-  flip: number,
-  lvl: number,
-  posA: number,
-  posB: number,
-  ta: number,
-  tb: number,
-  best: number
-): number {
-  const scale = POW2[lvl - 1];
-  const edges = t.fpEdges[motif * 2 + flip];
-  // posA/posB are fixed across this hull; fold 3*pos into the target once.
-  const ra = ta - 3 * posA;
-  const rb = tb - 3 * posB;
-  let minCross = Infinity;
-  for (let e = 0; e < edges.length; e += 4) {
-    const dta = ra - edges[e] * scale;
-    const dtb = rb - edges[e + 1] * scale;
-    const cross = edges[e + 2] * dtb - edges[e + 3] * dta;
-    if (cross < minCross) {
-      minCross = cross;
-      if (minCross <= 0 && minCross <= best) return minCross;
-    }
-  }
-  return minCross;
-}
-
-// Shared descent for both leaf modes. `exact` targets are corner sums of real
-// cells (leaf resolved by exact sum match); fractional targets resolve the leaf
-// by point-in-cell over the 4 level-1 triangles. Internal; also used by compat.ts.
+// ---------- inverse: descend by the branchless child classifier ----------
+// Shared descent: the target is the corner sum of a real cell, which is
+// strictly interior at every level, so the branchless classifier is provably
+// the containing child (and the leaf resolves by exact sum match). Fractional
+// point location no longer descends at all — sphericalToCell rounds to a triple
+// (see curve.ts roundToTriple). Internal; also used by compat.ts.
 //
 // Returns [s, leafFlavor]. Callers that only need `s` take [0].
-export function axiomTargetToS(
-  t: CurveTables,
-  ta: number,
-  tb: number,
-  R: number,
-  axiom: number,
-  exact: boolean
-): [bigint, number] {
-  const {childToken, childFlip, childOffA, childOffB, leafSum, leafTri} = t;
+export function axiomTargetToS(t: CurveTables, ta: number, tb: number, R: number, axiom: number): [bigint, number] {
+  const {childToken, childFlip, childOffA, childOffB, leafSum} = t;
   let motif = axiom,
     flip = 0;
   let posA = 0,
@@ -197,37 +152,7 @@ export function axiomTargetToS(
   for (let L = R; L >= 2; L--) {
     const scale = POW2[L - 2];
     const sign = flip ? -scale : scale;
-    // Exact targets (real cell corner sums) are strictly interior at every level,
-    // so the branchless classifier is provably the containing child. Fractional
-    // targets can sit on a child boundary, where the classifier's tie-break can
-    // differ from the argmax, so keep the exact argmax scan for that path
-    // (only sumPointToS uses it — compat locates points via the old sign tests).
-    let bestD: number;
-    if (exact) {
-      bestD = classify(t, motif * 2 + flip, ta - 3 * posA, tb - 3 * posB, scale);
-    } else {
-      bestD = 0;
-      let bestScore = -Infinity;
-      for (let d = 0; d < 4; d++) {
-        const ci = motif * 4 + d;
-        const score = insideScore(
-          t,
-          childToken[ci],
-          flip ^ childFlip[ci],
-          L - 1,
-          posA + childOffA[ci] * sign,
-          posB + childOffB[ci] * sign,
-          ta,
-          tb,
-          bestScore
-        );
-        if (score > bestScore) {
-          bestScore = score;
-          bestD = d;
-          if (score > 0) break; // strictly inside: the unique containing child
-        }
-      }
-    }
+    const bestD = classify(t, motif * 2 + flip, ta - 3 * posA, tb - 3 * posB, scale);
     const ci = motif * 4 + bestD;
     posA += childOffA[ci] * sign;
     posB += childOffB[ci] * sign;
@@ -237,40 +162,18 @@ export function axiomTargetToS(
     if (idx < LO_DIGITS) sLo += bestD * POW4[idx];
     else sHi += bestD * POW4[idx - LO_DIGITS];
   }
-  // level 1: pick the leaf cell, by exact corner-sum match or point-in-cell
+  // level 1: pick the leaf cell by exact corner-sum match
   const base = motif * 2 + flip;
-  let d0 = 0;
-  if (exact) {
-    const relA = ta - 3 * posA,
-      relB = tb - 3 * posB;
-    d0 = -1;
-    for (let d = 0; d < 4; d++) {
-      if (leafSum[base * 8 + d * 2] === relA && leafSum[base * 8 + d * 2 + 1] === relB) {
-        d0 = d;
-        break;
-      }
-    }
-    if (d0 < 0) throw new Error(`lsystem inverse: no leaf match for corner sum (${ta},${tb})`);
-  } else {
-    const ra = ta - 3 * posA,
-      rb = tb - 3 * posB;
-    let bestScore = -Infinity;
-    for (let d = 0; d < 4; d++) {
-      let minCross = Infinity;
-      for (let e = 0; e < 3; e++) {
-        const o = base * 48 + d * 12 + e * 4;
-        const dta = ra - leafTri[o];
-        const dtb = rb - leafTri[o + 1];
-        const cross = leafTri[o + 2] * dtb - leafTri[o + 3] * dta;
-        if (cross < minCross) minCross = cross;
-      }
-      if (minCross > bestScore) {
-        bestScore = minCross;
-        d0 = d;
-        if (minCross > 0) break;
-      }
+  const relA = ta - 3 * posA,
+    relB = tb - 3 * posB;
+  let d0 = -1;
+  for (let d = 0; d < 4; d++) {
+    if (leafSum[base * 8 + d * 2] === relA && leafSum[base * 8 + d * 2 + 1] === relB) {
+      d0 = d;
+      break;
     }
   }
+  if (d0 < 0) throw new Error(`lsystem inverse: no leaf match for corner sum (${ta},${tb})`);
   sLo += d0;
   const s = R > LO_DIGITS ? (BigInt(sHi) << LO_BITS) | BigInt(sLo) : BigInt(sLo);
   return [s, t.leafFlavor[base * 4 + d0]];
@@ -330,20 +233,6 @@ export function tripleToSLattice(triple: Triple, resolution: number, orientation
   const rec = ORIENT[orientation];
   const ab = tripleToAB(triple);
   const tauSum = rec.isB ? 12 * POW2[resolution] : 0;
-  const sAxiom = axiomTargetToS(A5, ab.a - tauSum, ab.b + tauSum, resolution, rec.axiom, true)[0];
-  return rec.reverse ? N - 1n - sAxiom : sAxiom;
-}
-
-/**
- * Fractional point -> the curve position `s` of the containing cell, by direct
- * descent. The target is given in the corner-sum frame (= 3x the L-system (a,b)
- * point frame); callers map their coordinate system into it (for the IJ plane
- * the exact affine map is target = (12*(i+j), -12*j), see curve.ts).
- */
-export function sumPointToS(ta: number, tb: number, resolution: number, orientation: Orientation = 'uv'): bigint {
-  const N = 1n << BigInt(2 * resolution);
-  const rec = ORIENT[orientation];
-  const tauSum = rec.isB ? 12 * POW2[resolution] : 0;
-  const sAxiom = axiomTargetToS(A5, ta - tauSum, tb + tauSum, resolution, rec.axiom, false)[0];
+  const sAxiom = axiomTargetToS(A5, ab.a - tauSum, ab.b + tauSum, resolution, rec.axiom)[0];
   return rec.reverse ? N - 1n - sAxiom : sAxiom;
 }
diff --git a/modules/lattice/lsystem/tables.ts b/modules/lattice/lsystem/tables.ts
index 785ec80..c0b2613 100644
--- a/modules/lattice/lsystem/tables.ts
+++ b/modules/lattice/lsystem/tables.ts
@@ -34,10 +34,8 @@ export interface CurveTables {
   childOffB: Float64Array;
   // footprint hulls per (motif, flip): edge list [3*c0.a, 3*c0.b, d.a, d.b]*E
   fpEdges: Float64Array[];
-  // leaf tables per (motif, flip): 4 host cells as corner sums, point-in-cell
-  // triangle edges, and pentagon flavors
+  // leaf tables per (motif, flip): 4 host cells as corner sums and pentagon flavors
   leafSum: Float64Array;
-  leafTri: Float64Array;
   leafFlavor: Uint8Array;
   // Branchless child classifier per state k = motif*2+flip: 3 separating lines
   // (classSep[k*9 ..] = [nx0,ny0,c0, nx1,ny1,c1, nx2,ny2,c2]) evaluated against
@@ -242,11 +240,8 @@ export function compileGrammar(rules: Record<string, string>, draws: Record<stri
 
   // ---------- leaf tables: per (motif, flip = heading 0|3) the 4 level-1 host cells ----------
   //  - corner sums relative to the descent position: sum = 3*pos + leafSum[..]
-  //  - triangle edges [3*c0.a, 3*c0.b, d.a, d.b]*3 for point-in-cell tests,
-  //    winding-normalized to CCW so "inside" is cross > 0 on every edge
   //  - the cell's pentagon flavor
   const leafSum = new Float64Array(motifCount * 2 * 8);
-  const leafTri = new Float64Array(motifCount * 2 * 48);
   const leafFlavor = new Uint8Array(motifCount * 2 * 4);
   for (const m of allMotifs) {
     const drawStr = toDraws(m, 1);
@@ -260,18 +255,6 @@ export function compileGrammar(rules: Record<string, string>, draws: Record<stri
         const upper = sym.toUpperCase();
         if (FLAVOR_BASE[upper] === undefined) throw new Error(`lsystem: no pentagon flavor for draw symbol ${sym}`);
         leafFlavor[base * 4 + d] = FLAVOR_BASE[upper] ^ (sym === upper ? 0 : 1) ^ (hh & 1);
-        let c = hostCorners(sym, from, hh);
-        const area = (c[1].a - c[0].a) * (c[2].b - c[0].b) - (c[1].b - c[0].b) * (c[2].a - c[0].a);
-        if (area < 0) c = [c[0], c[2], c[1]];
-        for (let e = 0; e < 3; e++) {
-          const c0 = c[e],
-            c1 = c[(e + 1) % 3];
-          const o = base * 48 + d * 12 + e * 4;
-          leafTri[o] = 3 * c0.a;
-          leafTri[o + 1] = 3 * c0.b;
-          leafTri[o + 2] = c1.a - c0.a;
-          leafTri[o + 3] = c1.b - c0.b;
-        }
         d++;
       });
     }
@@ -285,7 +268,6 @@ export function compileGrammar(rules: Record<string, string>, draws: Record<stri
     childOffB,
     fpEdges,
     leafSum,
-    leafTri,
     leafFlavor,
     classSep: new Float64Array(motifCount * 2 * 9),
     classLut: new Uint8Array(motifCount * 2 * 8)
diff --git a/modules/lattice/triple.ts b/modules/lattice/triple.ts
index 40d08f8..ef2e027 100644
--- a/modules/lattice/triple.ts
+++ b/modules/lattice/triple.ts
@@ -12,6 +12,18 @@ export function tripleParity(t: Triple): number {
   return t.x + t.y + t.z;
 }
 
+// The pentagon flavor is a CLOSED FORM of the triple: it depends only on the
+// parity and y mod 2 (the Cairo-like tiling repeats its four orientations with
+// period 2). Verified exhaustively against the descent's flavor over all cells
+// (see tests/lattice/curve.test.ts); the descent's leaf flavor agrees because
+// both describe the same fixed tiling.
+const FLAVOR_LUT = [0, 2, 3, 1]; // index = parity << 1 | (y & 1)
+
+/** The pentagon flavor (0-3) of a triple's cell — orientation-independent. */
+export function tripleFlavor(t: Triple): number {
+  return FLAVOR_LUT[((t.x + t.y + t.z) << 1) | (t.y & 1)];
+}
+
 /** Check if a triple is within valid quintant bounds. */
 export function tripleInBounds(t: Triple, maxRow: number): boolean {
   const sum = t.x + t.y + t.z;
diff --git a/modules/projections/dodecahedron.ts b/modules/projections/dodecahedron.ts
index 4b71d32..d9be3a8 100644
--- a/modules/projections/dodecahedron.ts
+++ b/modules/projections/dodecahedron.ts
@@ -44,7 +44,7 @@ export class DodecahedronProjection {
   /**
    * Same as `forward` but takes a Cartesian unit vector — skips the
    * `toCartesian` round-trip when the caller already has the Cartesian
-   * form (e.g. in the spiral-search path inside `sphericalToCell`).
+   * form.
    */
   forwardCartesian(unprojected: Cartesian, originId: OriginId): Face {
     const origin = origins[originId];
diff --git a/modules/test-index.ts b/modules/test-index.ts
index e4b131f..b8243ff 100644
--- a/modules/test-index.ts
+++ b/modules/test-index.ts
@@ -30,7 +30,7 @@ export {getPentagonVertices, getQuintantVertices, getFaceVertices, getQuintantPo
 export {NEIGHBOR_DELTAS} from './traversal/neighbors';
 
 // Export curve / lattice functions for testing
-export {IJToS, sToCell, sToTriple, tripleParity, tripleInBounds, tripleToS} from './lattice';
+export {roundToTriple, sToCell, sToTriple, tripleParity, tripleInBounds, tripleToS} from './lattice';
 export {compatSToCell, compatSToTriple, compatTripleToS, compatIJToS} from './lattice';
 export type {Cell, Triple} from './lattice';
 
@@ -41,7 +41,6 @@ export {
   sToTriple as lsystemSToTriple,
   tripleToSLattice as lsystemTripleToS
 } from './lattice/lsystem';
-export {IJToS as lsystemIJToS} from './lattice/curve';
 
 // Export neighbor functions for testing
 export {getCellNeighbors} from './traversal/quintant-neighbors';
@@ -53,9 +52,6 @@ export {metersToH, estimateCellRadius, pickCoarseResolution} from './traversal/c
 // Export great-circle helpers for testing
 export {greatCircleDistance, sampleGreatCircleArc} from './utils/great-circle';
 
-// Export spiral helper for testing
-export {Spiral, SPIRAL_SAMPLE_COUNT} from './utils/spiral';
-
 // Export lattice neighbor / flood-fill for testing
 export {getLatticeNeighbors} from './traversal/lattice-neighbors';
 export {tripleSpaceFloodFill} from './traversal/lattice-flood-fill';
diff --git a/modules/traversal/global-neighbors.ts b/modules/traversal/global-neighbors.ts
index 4e4cd67..66deaf3 100644
--- a/modules/traversal/global-neighbors.ts
+++ b/modules/traversal/global-neighbors.ts
@@ -5,7 +5,7 @@
 import {sToCell, tripleParity} from '../lattice';
 import type {Origin} from '../core/utils';
 import {deserialize, serialize, FIRST_HILBERT_RESOLUTION} from '../core/serialization';
-import {segmentToQuintant, quintantToSegment, origins} from '../core/origin';
+import {origins, QUINTANT_TO_SEGMENT, SEGMENT_TO_ORIENTATION, SEGMENT_TO_QUINTANT} from '../core/origin';
 import {FACE_ADJACENCY} from '../core/face-adjacency';
 import {compareBigint} from '../utils/bigint';
 import {findQuintantNeighborS} from './quintant-neighbors';
@@ -13,7 +13,7 @@ import {getBoundaryNeighbors} from './lattice-boundary';
 
 /** Serialize a res 1 cell from origin and quintant. */
 function serializeRes1(origin: Origin, quintant: number): bigint {
-  const {segment} = quintantToSegment(quintant, origin);
+  const segment = QUINTANT_TO_SEGMENT[origin.id * 5 + quintant];
   return serialize({origin, segment, S: 0n, resolution: 1});
 }
 
@@ -33,7 +33,7 @@ function getRes0Neighbors(origin: Origin): bigint[] {
  * Get neighbors of a resolution 1 cell (quintant).
  */
 function getRes1Neighbors(origin: Origin, segment: number, edgeOnly: boolean): bigint[] {
-  const {quintant} = segmentToQuintant(segment, origin);
+  const quintant = SEGMENT_TO_QUINTANT[origin.id * 5 + segment];
   const neighborSet = new Set<bigint>();
 
   // Left and right quintant on the same face (A, B)
@@ -89,7 +89,9 @@ export function getGlobalCellNeighbors(cellId: bigint, options?: {edgeOnly?: boo
   if (resolution === 1) return getRes1Neighbors(origin, segment, edgeOnly);
 
   const hilbertRes = resolution - FIRST_HILBERT_RESOLUTION + 1;
-  const {quintant: sourceQuintant, orientation: sourceOrientation} = segmentToQuintant(segment, origin);
+  const globalQuintant = origin.id * 5 + segment;
+  const sourceQuintant = SEGMENT_TO_QUINTANT[globalQuintant];
+  const sourceOrientation = SEGMENT_TO_ORIENTATION[globalQuintant];
 
   // Triple coordinates are orientation-independent
   const {triple, flavor} = sToCell(S, hilbertRes, sourceOrientation);
diff --git a/modules/traversal/lattice-boundary.ts b/modules/traversal/lattice-boundary.ts
index 4b3cd9e..c8858ff 100644
--- a/modules/traversal/lattice-boundary.ts
+++ b/modules/traversal/lattice-boundary.ts
@@ -6,7 +6,7 @@ import type {Orientation, Triple} from '../lattice';
 import {tripleToS, tripleInBounds} from '../lattice';
 import type {Origin} from '../core/utils';
 import {serialize} from '../core/serialization';
-import {quintantToSegment, origins} from '../core/origin';
+import {origins, QUINTANT_TO_ORIENTATION, QUINTANT_TO_SEGMENT} from '../core/origin';
 import {FACE_ADJACENCY} from '../core/face-adjacency';
 
 /** Neighbor delta: [dx, dy, dz, isEdgeSharing] */
@@ -113,7 +113,9 @@ export function getBoundaryNeighbors(ctx: BoundaryContext, edgeOnly: boolean, sk
   // Left edge (z=0): neighbor in previous quintant at swapped [0, y, x]
   if (triple.z === 0) {
     const targetQuintant = (sourceQuintant - 1 + 5) % 5;
-    const {segment, orientation} = quintantToSegment(targetQuintant, origin);
+    const globalQuintant = origin.id * 5 + targetQuintant;
+    const segment = QUINTANT_TO_SEGMENT[globalQuintant];
+    const orientation = QUINTANT_TO_ORIENTATION[globalQuintant];
     pushDeltas(
       out,
       {x: 0, y: triple.y, z: triple.x},
@@ -129,7 +131,9 @@ export function getBoundaryNeighbors(ctx: BoundaryContext, edgeOnly: boolean, sk
   // Right edge (x=0): neighbor in next quintant at swapped [z, y, 0]
   if (triple.x === 0) {
     const targetQuintant = (sourceQuintant + 1) % 5;
-    const {segment, orientation} = quintantToSegment(targetQuintant, origin);
+    const globalQuintant = origin.id * 5 + targetQuintant;
+    const segment = QUINTANT_TO_SEGMENT[globalQuintant];
+    const orientation = QUINTANT_TO_ORIENTATION[globalQuintant];
     pushDeltas(
       out,
       {x: triple.z, y: triple.y, z: 0},
@@ -146,7 +150,9 @@ export function getBoundaryNeighbors(ctx: BoundaryContext, edgeOnly: boolean, sk
   if (triple.y === maxRow) {
     const [adjFaceId, adjQuintant] = FACE_ADJACENCY[origin.id][sourceQuintant];
     const adjOrigin = origins[adjFaceId];
-    const {segment, orientation} = quintantToSegment(adjQuintant, adjOrigin);
+    const globalQuintant = adjOrigin.id * 5 + adjQuintant;
+    const segment = QUINTANT_TO_SEGMENT[globalQuintant];
+    const orientation = QUINTANT_TO_ORIENTATION[globalQuintant];
     pushDeltas(
       out,
       {x: triple.z, y: maxRow, z: triple.x},
@@ -165,7 +171,9 @@ export function getBoundaryNeighbors(ctx: BoundaryContext, edgeOnly: boolean, sk
       if (q === sourceQuintant) continue;
       const distance = Math.min((q - sourceQuintant + 5) % 5, (sourceQuintant - q + 5) % 5);
       if (edgeOnly && distance !== 1) continue;
-      const {segment, orientation} = quintantToSegment(q, origin);
+      const globalQuintant = origin.id * 5 + q;
+      const segment = QUINTANT_TO_SEGMENT[globalQuintant];
+      const orientation = QUINTANT_TO_ORIENTATION[globalQuintant];
       pushTriple(out, triple, orientation, origin, segment, ctx);
     }
   }
@@ -178,17 +186,18 @@ export function getBoundaryNeighbors(ctx: BoundaryContext, edgeOnly: boolean, sk
     const prevQuintant = (sourceQuintant - 1 + 5) % 5;
     const [prevAdjFaceId, prevAdjQuintant] = FACE_ADJACENCY[origin.id][prevQuintant];
     const prevAdjOrigin = origins[prevAdjFaceId];
-    const {segment: prevAdjSegment, orientation: prevAdjOrientation} = quintantToSegment(
-      prevAdjQuintant,
-      prevAdjOrigin
-    );
+    const prevAdjGlobalQuintant = prevAdjOrigin.id * 5 + prevAdjQuintant;
+    const prevAdjSegment = QUINTANT_TO_SEGMENT[prevAdjGlobalQuintant];
+    const prevAdjOrientation = QUINTANT_TO_ORIENTATION[prevAdjGlobalQuintant];
     pushTriple(out, triple, prevAdjOrientation, prevAdjOrigin, prevAdjSegment, ctx);
 
     // Vertex neighbor 2: adjacent quintant on the primary cross-face
     const [crossFaceId, crossQuintant] = FACE_ADJACENCY[origin.id][sourceQuintant];
     const crossOrigin = origins[crossFaceId];
     const nextCrossQuintant = (crossQuintant + 1) % 5;
-    const {segment: crossSegment, orientation: crossOrientation} = quintantToSegment(nextCrossQuintant, crossOrigin);
+    const crossGlobalQuintant = crossOrigin.id * 5 + nextCrossQuintant;
+    const crossSegment = QUINTANT_TO_SEGMENT[crossGlobalQuintant];
+    const crossOrientation = QUINTANT_TO_ORIENTATION[crossGlobalQuintant];
     pushTriple(out, triple, crossOrientation, crossOrigin, crossSegment, ctx);
   }
 
diff --git a/modules/traversal/lattice-flood-fill.ts b/modules/traversal/lattice-flood-fill.ts
index ec9bb3e..ede211d 100644
--- a/modules/traversal/lattice-flood-fill.ts
+++ b/modules/traversal/lattice-flood-fill.ts
@@ -6,7 +6,7 @@ import type {Orientation} from '../lattice';
 import {sToTriple, tripleToS} from '../lattice';
 import type {Origin} from '../core/utils';
 import {deserialize, serialize, FIRST_HILBERT_RESOLUTION} from '../core/serialization';
-import {segmentToQuintant} from '../core/origin';
+import {SEGMENT_TO_ORIENTATION} from '../core/origin';
 
 /** Per-quintant context needed to convert triples back to cell IDs. */
 interface QuintantCtx {
@@ -67,7 +67,7 @@ function cellToQuintantKey(
   yStride: number
 ): {quintantIdx: number; key: number; ctx: QuintantCtx} {
   const {origin, segment, S} = deserialize(cellId);
-  const {orientation} = segmentToQuintant(segment, origin);
+  const orientation = SEGMENT_TO_ORIENTATION[origin.id * 5 + segment];
   const triple = sToTriple(S, hilbertRes, orientation);
   const parity = triple.x + triple.y + triple.z; // 0 or 1
   return {
diff --git a/modules/traversal/lattice-neighbors.ts b/modules/traversal/lattice-neighbors.ts
index 7546193..1963791 100644
--- a/modules/traversal/lattice-neighbors.ts
+++ b/modules/traversal/lattice-neighbors.ts
@@ -6,7 +6,7 @@ import type {Orientation, Triple} from '../lattice';
 import {sToTriple, tripleToS, tripleParity, tripleInBounds} from '../lattice';
 import type {Origin} from '../core/utils';
 import {deserialize, serialize, FIRST_HILBERT_RESOLUTION} from '../core/serialization';
-import {segmentToQuintant} from '../core/origin';
+import {SEGMENT_TO_ORIENTATION, SEGMENT_TO_QUINTANT} from '../core/origin';
 import {getGlobalCellNeighbors} from './global-neighbors';
 import {type BoundaryContext, getBoundaryNeighbors} from './lattice-boundary';
 
@@ -30,7 +30,9 @@ function decodeSource(cellId: bigint): LatticeSource | null {
   if (resolution < FIRST_HILBERT_RESOLUTION) return null;
 
   const hilbertRes = resolution - FIRST_HILBERT_RESOLUTION + 1;
-  const {quintant, orientation} = segmentToQuintant(segment, origin);
+  const globalQuintant = origin.id * 5 + segment;
+  const quintant = SEGMENT_TO_QUINTANT[globalQuintant];
+  const orientation = SEGMENT_TO_ORIENTATION[globalQuintant];
   const triple = sToTriple(S, hilbertRes, orientation);
 
   return {
diff --git a/modules/utils/spiral.ts b/modules/utils/spiral.ts
deleted file mode 100644
index 6d81edf..0000000
--- a/modules/utils/spiral.ts
+++ /dev/null
@@ -1,91 +0,0 @@
-// A5
-// SPDX-License-Identifier: Apache-2.0
-// Copyright (c) A5 contributors
-
-import {vec3, quat, glMatrix} from 'gl-matrix';
-glMatrix.setMatrixArrayType(Float64Array as any);
-
-import type {Cartesian, Spherical} from '../core/coordinate-systems';
-import {toCartesian} from '../core/coordinate-transforms';
-
-/**
- * Number of perturbed sample points the spiral can produce. Tuned on a
- * corpus of ~3500 spherical points × 8 resolutions, such that the spiral
- * hits a strictly-containing cell within these many iterations for all
- * but a handful of points right at the polar singularity at very high
- * resolutions.
- */
-export const SPIRAL_SAMPLE_COUNT = 24;
-
-/**
- * Azimuthal step between consecutive samples in the rotated tangent plane.
- * 1.4 rad (~80°) sits on a flat plateau of the parameter sweep.
- */
-const ANGLE_STEP_RAD = 1.4;
-
-// Precomputed unit-direction spiral at the canonical pole's tangent plane
-// (z=0). Each entry is the tangent direction of one sample. The pattern
-// is independent of resolution; per spiral the directions are rotated to
-// the input point's tangent plane via a single quaternion.
-const POLE: vec3 = vec3.fromValues(0, 0, 1);
-const SPIRAL_DIRECTIONS: vec3[] = (() => {
-  const out: vec3[] = [];
-  for (let i = 0; i < SPIRAL_SAMPLE_COUNT; i++) {
-    const a = (i + 1) * ANGLE_STEP_RAD;
-    out.push(vec3.fromValues(Math.cos(a), Math.sin(a), 0));
-  }
-  return out;
-})();
-
-/**
- * Lazy spiral sampler around a center point on the unit sphere — used by
- * `sphericalToCell` to discover nearby cells when the projection-based
- * estimate lands in the wrong one.
- *
- * Construction precomputes the pole→center quaternion. `sample(i)`
- * rotates the i-th cached direction into the tangent plane at `center`,
- * scales by the appropriate radius, and returns a Cartesian point near
- * the unit sphere — the consumer of the spiral (the dodecahedron
- * projection) wants Cartesian anyway, so we skip the spherical
- * round-trip entirely. The point is slightly off the unit sphere by
- * O(R²); downstream callers either tolerate this or normalise.
- *
- * All state is per-instance (no module-level mutable scratch), so each
- * thread/task can hold its own without locking.
- */
-export class Spiral {
-  private c0: Cartesian;
-  private q: quat;
-  private scaleRad: number;
-  private scratch: vec3;
-
-  /**
-   * Initialise a spiral around `center` on the unit sphere. The
-   * tangent-plane radius of the outermost sample is `scaleRad`;
-   * intermediate samples scale linearly between 0 and that.
-   * `quat.rotationTo` handles the antipode case internally.
-   */
-  constructor(center: Spherical, scaleRad: number) {
-    this.c0 = toCartesian(center);
-    this.q = quat.create();
-    quat.rotationTo(this.q, POLE, this.c0 as unknown as vec3);
-    this.scaleRad = scaleRad;
-    this.scratch = vec3.create();
-  }
-
-  /**
-   * Write the i-th spiral sample (0 ≤ i < SPIRAL_SAMPLE_COUNT) into
-   * `out` and return it. Sample i sits at tangent-plane offset of
-   * magnitude `(i+1)/(SPIRAL_SAMPLE_COUNT+1) · scaleRad` from `center`,
-   * rotated by azimuth `(i+1) · 1.4 rad` in `center`'s tangent frame.
-   *
-   * `out` is supplied by the caller so the same buffer can be reused
-   * across all samples in a search, avoiding per-iteration allocation.
-   */
-  sample(out: Cartesian, i: number): Cartesian {
-    vec3.transformQuat(this.scratch, SPIRAL_DIRECTIONS[i], this.q);
-    const R = ((i + 1) / (SPIRAL_SAMPLE_COUNT + 1)) * this.scaleRad;
-    vec3.scaleAndAdd(out as unknown as vec3, this.c0 as unknown as vec3, this.scratch, R);
-    return out;
-  }
-}
diff --git a/scripts/fixtures/lattice/curve.cjs b/scripts/fixtures/lattice/curve.cjs
index a7a0515..24c1746 100644
--- a/scripts/fixtures/lattice/curve.cjs
+++ b/scripts/fixtures/lattice/curve.cjs
@@ -1,6 +1,6 @@
 const fs = require('fs');
 const path = require('path');
-const {sToCell, tripleToS, tripleParity, tripleInBounds, IJToS} = require('../../a5-test.cjs');
+const {sToCell, tripleToS, tripleParity, tripleInBounds, roundToTriple} = require('../../a5-test.cjs');
 
 const outputDir = path.join(__dirname, '../../../tests/fixtures/lattice');
 const outputPath = path.join(outputDir, 'curve.json');
@@ -46,7 +46,7 @@ for (const resolution of resolutions) {
 }
 console.log(`  sToCell: ${sToCellFixtures.length} cases (all round-trips verified)`);
 
-// --- IJToS: fractional IJ point -> s of the containing cell ---
+// --- pointToS: fractional IJ point -> s of the containing cell (roundToTriple + encode) ---
 // Deterministic sample points, as fractions of the quintant triangle
 // (i >= 0, j >= 0, i + j <= 2^resolution)
 const pointFractions = [
@@ -67,9 +67,9 @@ for (const resolution of resolutions) {
     for (const [fi, fj] of pointFractions) {
       const i = fi * n;
       const j = fj * n;
-      const s = IJToS([i, j], resolution, orientation);
+      const s = tripleToS(roundToTriple([i, j], resolution), resolution, orientation);
       if (s < 0n || s >= BigInt(numCells)) {
-        console.error(`  ERROR: IJToS(${i},${j}) out of range for res=${resolution}, ori=${orientation}: ${s}`);
+        console.error(`  ERROR: pointToS(${i},${j}) out of range for res=${resolution}, ori=${orientation}: ${s}`);
         process.exit(1);
       }
       // Cross-check: the containing cell's centroid must map back to the same s
@@ -78,10 +78,10 @@ for (const resolution of resolutions) {
       const parity = tripleParity(triple);
       const ci = triple.x + triple.y + (parity === 0 ? 1 / 3 : -1 / 3);
       const cj = -triple.x + (parity === 0 ? 1 / 3 : 2 / 3);
-      const sCentroid = IJToS([ci, cj], resolution, orientation);
+      const sCentroid = tripleToS(roundToTriple([ci, cj], resolution), resolution, orientation);
       if (sCentroid !== s) {
         console.error(
-          `  ERROR: IJToS centroid cross-check failed for (${i},${j}) res=${resolution}, ori=${orientation}: ${s} vs ${sCentroid}`
+          `  ERROR: pointToS centroid cross-check failed for (${i},${j}) res=${resolution}, ori=${orientation}: ${s} vs ${sCentroid}`
         );
         process.exit(1);
       }
@@ -89,7 +89,7 @@ for (const resolution of resolutions) {
     }
   }
 }
-console.log(`  IJToS: ${ijToSFixtures.length} cases (all centroid cross-checks verified)`);
+console.log(`  pointToS: ${ijToSFixtures.length} cases (all centroid cross-checks verified)`);
 
 // --- tripleInBounds ---
 const maxRow = 15; // resolution 4: 2^4 - 1
@@ -118,7 +118,7 @@ console.log(`  tripleInBounds: ${boundsCases.length} cases (all verified)`);
 
 const fixtures = {
   sToCell: sToCellFixtures,
-  IJToS: ijToSFixtures,
+  pointToS: ijToSFixtures,
   tripleInBounds: boundsCases
 };
 
diff --git a/scripts/fixtures/lattice/lsystem.cjs b/scripts/fixtures/lattice/lsystem.cjs
index 4fd4c66..baf8e3b 100644
--- a/scripts/fixtures/lattice/lsystem.cjs
+++ b/scripts/fixtures/lattice/lsystem.cjs
@@ -1,6 +1,6 @@
 const fs = require('fs');
 const path = require('path');
-const {lsystemSToCell, lsystemTripleToS, lsystemIJToS, tripleParity} = require('../../a5-test.cjs');
+const {lsystemSToCell, lsystemTripleToS, roundToTriple, tripleParity} = require('../../a5-test.cjs');
 
 const outputDir = path.join(__dirname, '../../../tests/fixtures/lattice');
 const outputPath = path.join(outputDir, 'lsystem.json');
@@ -50,7 +50,7 @@ for (const resolution of resolutions) {
 }
 console.log(`  lsystemSToCell: ${sToCellFixtures.length} cases (all round-trips verified)`);
 
-// --- IJToS: fractional IJ point -> s of the containing cell ---
+// --- pointToS: fractional IJ point -> s of the containing cell (roundToTriple + encode) ---
 // Deterministic sample points, as fractions of the quintant triangle
 // (i >= 0, j >= 0, i + j <= 2^resolution)
 const pointFractions = [
@@ -71,9 +71,9 @@ for (const resolution of resolutions) {
     for (const [fi, fj] of pointFractions) {
       const i = fi * n;
       const j = fj * n;
-      const s = lsystemIJToS([i, j], resolution, orientation);
+      const s = lsystemTripleToS(roundToTriple([i, j], resolution), resolution, orientation);
       if (s < 0n || s >= BigInt(numCells)) {
-        console.error(`  ERROR: lsystemIJToS(${i},${j}) out of range for res=${resolution}, ori=${orientation}: ${s}`);
+        console.error(`  ERROR: pointToS(${i},${j}) out of range for res=${resolution}, ori=${orientation}: ${s}`);
         process.exit(1);
       }
       // Cross-check: the containing cell's centroid must map back to the same s
@@ -82,10 +82,10 @@ for (const resolution of resolutions) {
       const parity = tripleParity(triple);
       const ci = triple.x + triple.y + (parity === 0 ? 1 / 3 : -1 / 3);
       const cj = -triple.x + (parity === 0 ? 1 / 3 : 2 / 3);
-      const sCentroid = lsystemIJToS([ci, cj], resolution, orientation);
+      const sCentroid = lsystemTripleToS(roundToTriple([ci, cj], resolution), resolution, orientation);
       if (sCentroid !== s) {
         console.error(
-          `  ERROR: lsystemIJToS centroid cross-check failed for (${i},${j}) res=${resolution}, ori=${orientation}: ${s} vs ${sCentroid}`
+          `  ERROR: pointToS centroid cross-check failed for (${i},${j}) res=${resolution}, ori=${orientation}: ${s} vs ${sCentroid}`
         );
         process.exit(1);
       }
@@ -93,8 +93,8 @@ for (const resolution of resolutions) {
     }
   }
 }
-console.log(`  lsystemIJToS: ${ijToSFixtures.length} cases (all centroid cross-checks verified)`);
+console.log(`  pointToS: ${ijToSFixtures.length} cases (all centroid cross-checks verified)`);
 
 fs.mkdirSync(outputDir, {recursive: true});
-fs.writeFileSync(outputPath, JSON.stringify({sToCell: sToCellFixtures, IJToS: ijToSFixtures}, null, 2));
+fs.writeFileSync(outputPath, JSON.stringify({sToCell: sToCellFixtures, pointToS: ijToSFixtures}, null, 2));
 console.log(`  Wrote fixtures to ${outputPath}`);
diff --git a/scripts/fixtures/utils/spiral.cjs b/scripts/fixtures/utils/spiral.cjs
deleted file mode 100644
index 34809df..0000000
--- a/scripts/fixtures/utils/spiral.cjs
+++ /dev/null
@@ -1,64 +0,0 @@
-const fs = require('fs');
-const path = require('path');
-const {Spiral, SPIRAL_SAMPLE_COUNT} = require('../../a5-test.cjs');
-
-const outputDir = path.join(__dirname, '../../../tests/fixtures/utils');
-const outputPath = path.join(outputDir, 'spiral.json');
-
-// Each case: a center point in spherical (theta, phi) and a scale (radians).
-// Scales mimic those used by sphericalToCell at various hilbertResolutions:
-// scale = (70° in rad) / 2^hilbertResolution.
-const SCALE_BASE = (70 * Math.PI) / 180;
-const cases = [
-  // Equator-ish point (no degenerate orientation).
-  {name: 'equator_low_res', center: [0.5, Math.PI / 2], scaleRad: SCALE_BASE},
-  {name: 'equator_high_res', center: [0.5, Math.PI / 2], scaleRad: SCALE_BASE / 64},
-  // Mid-latitudes.
-  {name: 'midlat_north', center: [1.0, Math.PI / 4], scaleRad: SCALE_BASE / 4},
-  {name: 'midlat_south', center: [-2.5, (3 * Math.PI) / 4], scaleRad: SCALE_BASE / 16},
-  // Canonical pole — quat.rotationTo identity case.
-  {name: 'north_pole', center: [0, 0.001], scaleRad: SCALE_BASE / 8},
-  // Antipode of canonical pole — quat.rotationTo's special-case path.
-  {name: 'south_pole', center: [0, Math.PI - 0.001], scaleRad: SCALE_BASE / 8},
-  // Right at the pole (numerically): exercises the antipode branch precisely.
-  {name: 'south_pole_exact', center: [0, Math.PI], scaleRad: SCALE_BASE / 1024}
-];
-
-const fixtures = cases.map(c => {
-  const spiral = new Spiral(c.center, c.scaleRad);
-  const out = new Float64Array(3);
-  const samples = [];
-  for (let i = 0; i < SPIRAL_SAMPLE_COUNT; i++) {
-    spiral.sample(out, i);
-    samples.push([out[0], out[1], out[2]]);
-  }
-  return {
-    name: c.name,
-    center: c.center,
-    scaleRad: c.scaleRad,
-    sampleCount: samples.length,
-    samples
-  };
-});
-
-console.log('Generating utils/spiral fixtures...');
-console.log(`  SPIRAL_SAMPLE_COUNT = ${SPIRAL_SAMPLE_COUNT}`);
-for (const f of fixtures) {
-  console.log(
-    `  ${f.name}: center=[${f.center[0].toFixed(4)}, ${f.center[1].toFixed(4)}] scale=${f.scaleRad.toExponential(2)} samples=${f.sampleCount}`
-  );
-}
-
-fs.mkdirSync(outputDir, {recursive: true});
-fs.writeFileSync(
-  outputPath,
-  JSON.stringify(
-    {
-      sampleCount: SPIRAL_SAMPLE_COUNT,
-      spiral: fixtures
-    },
-    null,
-    2
-  )
-);
-console.log(`  Wrote fixtures to ${outputPath}`);
diff --git a/scripts/generate-fixtures.cjs b/scripts/generate-fixtures.cjs
index f4bd908..2f8da64 100644
--- a/scripts/generate-fixtures.cjs
+++ b/scripts/generate-fixtures.cjs
@@ -26,7 +26,6 @@ require('./fixtures/core/compact.cjs');
 
 // Utils generators
 require('./fixtures/utils/great-circle.cjs');
-require('./fixtures/utils/spiral.cjs');
 
 // Region generators
 require('./fixtures/regions/polygon.cjs');
diff --git a/scripts/sync_fixtures.py b/scripts/sync_fixtures.py
index 5e2d698..b6f14f9 100644
--- a/scripts/sync_fixtures.py
+++ b/scripts/sync_fixtures.py
@@ -50,6 +50,10 @@
         (PY_ROOT, "tests/core/fixtures/tiling.json"),
         (RS_ROOT, "tests/fixtures/tiling.json"),
     ],
+    "tests/fixtures/serialization.json": [
+        (PY_ROOT, "tests/core/fixtures/serialization.json"),
+        (RS_ROOT, "tests/fixtures/serialization.json"),
+    ],
 
     # Lattice fixtures
     "tests/fixtures/lattice/curve.json": [
@@ -82,6 +86,18 @@
         (PY_ROOT, "tests/traversal/fixtures/quintant-neighbors.json"),
         (RS_ROOT, "tests/fixtures/traversal/quintant-neighbors.json"),
     ],
+    "tests/fixtures/traversal/lattice-flood-fill.json": [
+        (PY_ROOT, "tests/traversal/fixtures/lattice-flood-fill.json"),
+        (RS_ROOT, "tests/fixtures/traversal/lattice-flood-fill.json"),
+    ],
+    "tests/fixtures/traversal/lattice-neighbors.json": [
+        (PY_ROOT, "tests/traversal/fixtures/lattice-neighbors.json"),
+        (RS_ROOT, "tests/fixtures/traversal/lattice-neighbors.json"),
+    ],
+    "tests/fixtures/traversal/line.json": [
+        (PY_ROOT, "tests/traversal/fixtures/line.json"),
+        (RS_ROOT, "tests/fixtures/traversal/line.json"),
+    ],
 
     # Geometry fixtures
     "tests/geometry/fixtures/pentagon.json": [
@@ -98,9 +114,8 @@
     ],
 
     # Region fixtures
-    # NOTE: not yet synced to PY_ROOT — the Python port still uses the old
-    # single-ring polygon_to_cells; add the PY entry when porting hole support.
     "tests/fixtures/regions/polygon.json": [
+        (PY_ROOT, "tests/regions/fixtures/polygon.json"),
         (RS_ROOT, "tests/fixtures/regions/polygon.json"),
     ],
 
diff --git a/tests/fixtures/cell-to-lonlat.json b/tests/fixtures/cell-to-lonlat.json
index 72001e9..93d1c25 100644
--- a/tests/fixtures/cell-to-lonlat.json
+++ b/tests/fixtures/cell-to-lonlat.json
@@ -17,7 +17,7 @@
       35.677369792795794
     ],
     "resolution": 8,
-    "cell_id": "872f880000000000",
+    "cell_id": "872fb80000000000",
     "center_lonlat": [
       139.62350637919997,
       35.63157147255161
@@ -29,7 +29,7 @@
       35.677369792795794
     ],
     "resolution": 12,
-    "cell_id": "872f937800000000",
+    "cell_id": "872fae1800000000",
     "center_lonlat": [
       139.76867809739872,
       35.67600097803834
@@ -41,7 +41,7 @@
       35.677369792795794
     ],
     "resolution": 16,
-    "cell_id": "872f938388000000",
+    "cell_id": "872fae73b8000000",
     "center_lonlat": [
       139.76297049600976,
       35.6775299174842
@@ -53,7 +53,7 @@
       35.677369792795794
     ],
     "resolution": 20,
-    "cell_id": "872f938393780000",
+    "cell_id": "872fae73ae180000",
     "center_lonlat": [
       139.76240307455004,
       35.67735665532112
@@ -65,7 +65,7 @@
       35.677369792795794
     ],
     "resolution": 4,
-    "cell_id": "75b8000000000000",
+    "cell_id": "75f8000000000000",
     "center_lonlat": [
       78.76278431609035,
       35.245063054446746
@@ -77,7 +77,7 @@
       35.677369792795794
     ],
     "resolution": 8,
-    "cell_id": "76dd780000000000",
+    "cell_id": "76e2780000000000",
     "center_lonlat": [
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diff --git a/tests/fixtures/lattice/curve.json b/tests/fixtures/lattice/curve.json
index 4713785..8b53433 100644
--- a/tests/fixtures/lattice/curve.json
+++ b/tests/fixtures/lattice/curve.json
@@ -16,9 +16,9 @@
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@@ -154,9 +154,9 @@
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@@ -196,9 +196,9 @@
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@@ -1795,19 +1795,19 @@
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@@ -1856,14 +1856,14 @@
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@@ -1912,7 +1912,7 @@
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@@ -1926,35 +1926,35 @@
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@@ -1968,7 +1968,7 @@
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@@ -1982,35 +1982,35 @@
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@@ -2038,7 +2038,7 @@
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@@ -2066,7 +2066,7 @@
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@@ -2094,7 +2094,7 @@
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@@ -2122,7 +2122,7 @@
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@@ -2136,14 +2136,14 @@
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@@ -2157,7 +2157,7 @@
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@@ -2171,14 +2171,14 @@
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@@ -2192,14 +2192,14 @@
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@@ -2213,7 +2213,7 @@
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@@ -2227,14 +2227,14 @@
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@@ -2248,49 +2248,49 @@
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@@ -2304,49 +2304,49 @@
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@@ -2360,7 +2360,7 @@
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@@ -2374,7 +2374,7 @@
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@@ -2388,7 +2388,7 @@
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@@ -2402,7 +2402,7 @@
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@@ -2416,7 +2416,7 @@
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@@ -2430,7 +2430,7 @@
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@@ -2444,7 +2444,7 @@
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@@ -2458,7 +2458,7 @@
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@@ -2472,161 +2472,161 @@
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@@ -2640,49 +2640,49 @@
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@@ -2696,7 +2696,7 @@
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@@ -2710,7 +2710,7 @@
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@@ -2724,21 +2724,21 @@
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@@ -2752,7 +2752,7 @@
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@@ -2766,7 +2766,7 @@
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@@ -2780,21 +2780,21 @@
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@@ -2808,7 +2808,7 @@
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diff --git a/tests/fixtures/lattice/lsystem.json b/tests/fixtures/lattice/lsystem.json
index fb11015..89a8c31 100644
--- a/tests/fixtures/lattice/lsystem.json
+++ b/tests/fixtures/lattice/lsystem.json
@@ -1801,7 +1801,7 @@
       "flavor": 2
     }
   ],
-  "IJToS": [
+  "pointToS": [
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       "j": 1.6,
@@ -1968,7 +1968,7 @@
       "j": 2,
       "resolution": 3,
       "orientation": "uw",
-      "s": 33
+      "s": 45
     },
     {
       "i": 0.8,
@@ -2024,7 +2024,7 @@
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       "resolution": 3,
       "orientation": "wu",
-      "s": 30
+      "s": 18
     },
     {
       "i": 0.8,
@@ -2080,7 +2080,7 @@
       "j": 2,
       "resolution": 3,
       "orientation": "vw",
-      "s": 9
+      "s": 7
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     {
       "i": 0.8,
@@ -2136,7 +2136,7 @@
       "j": 2,
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+      "s": 56
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     {
       "i": 3.2,
@@ -2304,7 +2304,7 @@
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       "orientation": "uw",
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+      "s": 725
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     {
       "i": 3.2,
@@ -2360,7 +2360,7 @@
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       "resolution": 5,
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-      "s": 480
+      "s": 298
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     {
       "i": 3.2,
@@ -2416,7 +2416,7 @@
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+      "s": 116
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     {
       "i": 3.2,
@@ -2472,7 +2472,7 @@
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+      "s": 907
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     {
       "i": 12.8,
@@ -2640,7 +2640,7 @@
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+      "s": 11610
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     {
       "i": 12.8,
@@ -2696,7 +2696,7 @@
       "j": 32,
       "resolution": 7,
       "orientation": "wu",
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+      "s": 4773
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     {
       "i": 12.8,
@@ -2752,7 +2752,7 @@
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       "resolution": 7,
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+      "s": 1871
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     {
       "i": 12.8,
@@ -2808,7 +2808,7 @@
       "j": 32,
       "resolution": 7,
       "orientation": "wv",
-      "s": 13835
+      "s": 14512
     }
   ]
 }
\ No newline at end of file
diff --git a/tests/fixtures/regions/polygon.json b/tests/fixtures/regions/polygon.json
index 5fd4a24..5c2eea6 100644
--- a/tests/fixtures/regions/polygon.json
+++ b/tests/fixtures/regions/polygon.json
@@ -20,12 +20,12 @@
       ],
       "resolution": 5,
       "cells": [
-        "3ede000000000000",
+        "3eee000000000000",
         "3ef2000000000000",
         "3ef6000000000000",
         "3efa000000000000",
-        "3f6e000000000000",
-        "3f7a000000000000",
+        "3f5e000000000000",
+        "3f62000000000000",
         "3f86000000000000",
         "3f8a000000000000",
         "3f8e000000000000",
@@ -40,11 +40,11 @@
         "3fb6000000000000",
         "3fba000000000000",
         "3fbe000000000000",
+        "3fc2000000000000",
         "3fc6000000000000",
         "3fca000000000000",
-        "3fce000000000000",
-        "3fd2000000000000",
         "3fda000000000000",
+        "3fde000000000000",
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         "3fe6000000000000",
         "3fea000000000000",
@@ -74,15 +74,15 @@
       ],
       "resolution": 5,
       "cells": [
-        "4912000000000000",
-        "491a000000000000",
-        "491e000000000000",
+        "4916000000000000",
+        "4926000000000000",
         "492a000000000000",
+        "492e000000000000",
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         "4936000000000000",
         "493a000000000000",
         "493e000000000000",
-        "4946000000000000",
+        "494a000000000000",
         "496a000000000000",
         "496e000000000000",
         "4976000000000000",
@@ -97,9 +97,6 @@
         "499a000000000000",
         "499e000000000000",
         "49a2000000000000",
-        "49a6000000000000",
-        "49aa000000000000",
-        "49ae000000000000",
         "49b2000000000000",
         "49b6000000000000",
         "49ba000000000000",
@@ -117,18 +114,21 @@
         "49ea000000000000",
         "49ee000000000000",
         "49f2000000000000",
-        "4b06000000000000",
+        "49f6000000000000",
+        "49fa000000000000",
+        "49fe000000000000",
+        "4b1e000000000000",
         "4b22000000000000",
-        "4b2a000000000000",
+        "4b26000000000000",
         "4b2e000000000000",
-        "4b3a000000000000",
-        "4f6a000000000000",
-        "4f7e000000000000",
-        "4fc2000000000000",
-        "4fc6000000000000",
-        "4fca000000000000",
-        "4fce000000000000",
+        "4b36000000000000",
+        "4f8e000000000000",
+        "4f92000000000000",
         "4fd2000000000000",
+        "4fd6000000000000",
+        "4fda000000000000",
+        "4fde000000000000",
+        "4fe2000000000000",
         "6cd6000000000000",
         "6cee000000000000"
       ]
@@ -172,35 +172,35 @@
         "5176000000000000",
         "517a000000000000",
         "517e000000000000",
-        "51c2000000000000",
-        "51ca000000000000",
-        "51ce000000000000",
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-        "635a000000000000",
-        "635e000000000000",
-        "6362000000000000",
-        "6366000000000000",
-        "636a000000000000",
-        "636e000000000000",
-        "6372000000000000",
+        "5182000000000000",
+        "5186000000000000",
+        "518a000000000000",
+        "5196000000000000",
+        "519e000000000000",
         "6376000000000000",
-        "637a000000000000",
         "637e000000000000",
+        "6382000000000000",
+        "6386000000000000",
+        "638a000000000000",
+        "638e000000000000",
+        "6392000000000000",
+        "6396000000000000",
+        "639a000000000000",
+        "639e000000000000",
         "63a2000000000000",
+        "63a6000000000000",
         "63aa000000000000",
-        "63c2000000000000",
-        "63c6000000000000",
-        "63ca000000000000",
+        "63b2000000000000",
+        "63b6000000000000",
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         "63d2000000000000",
         "63d6000000000000",
         "63da000000000000",
         "63de000000000000",
         "63e2000000000000",
+        "63e6000000000000",
+        "63ea000000000000",
+        "63ee000000000000",
         "63f2000000000000",
         "63f6000000000000",
         "63fa000000000000",
@@ -246,29 +246,13 @@
         "517d800000000000",
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         "517f800000000000",
-        "634f800000000000",
-        "6360800000000000",
-        "6362800000000000",
-        "6363800000000000",
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-        "63cb800000000000",
-        "63cc800000000000",
-        "63cd800000000000",
-        "63ce800000000000",
-        "63cf800000000000",
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+        "6394800000000000",
+        "6395800000000000",
+        "6396800000000000",
+        "63b3800000000000",
         "63d0800000000000",
         "63d1800000000000",
         "63d2800000000000",
@@ -283,9 +267,25 @@
         "63db800000000000",
         "63dc800000000000",
         "63dd800000000000",
-        "63f9800000000000",
-        "63fa800000000000",
-        "63fb800000000000"
+        "63de800000000000",
+        "63df800000000000",
+        "63e0800000000000",
+        "63e1800000000000",
+        "63e2800000000000",
+        "63e3800000000000",
+        "63e4800000000000",
+        "63e5800000000000",
+        "63e6800000000000",
+        "63e7800000000000",
+        "63e8800000000000",
+        "63e9800000000000",
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+        "63eb800000000000",
+        "63ec800000000000",
+        "63ed800000000000",
+        "63f5800000000000",
+        "63f6800000000000",
+        "63f7800000000000"
       ]
     },
     {
@@ -323,7 +323,7 @@
         "c38000000000000",
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         "ca8000000000000",
-        "5118000000000000",
+        "5128000000000000",
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         "5148000000000000",
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@@ -337,12 +337,12 @@
         "51d8000000000000",
         "51e8000000000000",
         "51f8000000000000",
-        "5308000000000000",
         "5328000000000000",
-        "5358000000000000",
+        "5338000000000000",
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         "6318000000000000",
-        "6338000000000000",
+        "6328000000000000",
         "6348000000000000",
         "6358000000000000",
         "6368000000000000",
@@ -419,7 +419,7 @@
         "8d18000000000000",
         "8d28000000000000",
         "8d38000000000000",
-        "8db8000000000000",
+        "8df8000000000000",
         "8e08000000000000",
         "8e18000000000000",
         "8e28000000000000",
@@ -436,9 +436,9 @@
         "8ed8000000000000",
         "8ee8000000000000",
         "8ef8000000000000",
+        "8f08000000000000",
         "8f18000000000000",
         "8f28000000000000",
-        "8f38000000000000",
         "8f48000000000000",
         "8f58000000000000",
         "8f68000000000000",
@@ -450,16 +450,16 @@
         "9098000000000000",
         "90a8000000000000",
         "90b8000000000000",
+        "90c8000000000000",
         "90d8000000000000",
-        "90e8000000000000",
         "90f8000000000000",
-        "9208000000000000",
-        "9218000000000000",
-        "9228000000000000",
-        "9238000000000000",
+        "9248000000000000",
+        "9258000000000000",
+        "9268000000000000",
+        "9278000000000000",
         "9288000000000000",
+        "a0c8000000000000",
         "a0d8000000000000",
-        "a0e8000000000000",
         "a0f8000000000000",
         "a108000000000000",
         "a118000000000000",
@@ -470,12 +470,12 @@
         "a168000000000000",
         "a178000000000000",
         "a188000000000000",
-        "a198000000000000",
-        "a1a8000000000000",
         "a1c8000000000000",
+        "a1d8000000000000",
+        "a1e8000000000000",
         "a208000000000000",
-        "a218000000000000",
-        "a248000000000000"
+        "a248000000000000",
+        "a258000000000000"
       ]
     },
     {
@@ -530,9 +530,9 @@
         "ece0000000000000",
         "ed20000000000000",
         "ed60000000000000",
-        "eda0000000000000",
-        "ee20000000000000",
-        "efa0000000000000"
+        "ede0000000000000",
+        "ee60000000000000",
+        "ef60000000000000"
       ]
     },
     {
@@ -567,11 +567,11 @@
       ],
       "resolution": 6,
       "cells": [
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+        "5143800000000000",
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         "5146800000000000",
-        "5147800000000000",
+        "5148800000000000",
         "5149800000000000",
         "514a800000000000",
         "514b800000000000",
@@ -583,10 +583,10 @@
         "5151800000000000",
         "5152800000000000",
         "5153800000000000",
-        "5158800000000000",
-        "515a800000000000",
         "515b800000000000",
+        "515d800000000000",
         "515e800000000000",
+        "515f800000000000",
         "5160800000000000",
         "5161800000000000",
         "5162800000000000",
@@ -619,108 +619,108 @@
         "517d800000000000",
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         "517f800000000000",
-        "5190800000000000",
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-        "636d800000000000",
-        "636e800000000000",
-        "636f800000000000",
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         "637d800000000000",
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+        "639e800000000000",
+        "639f800000000000",
         "63a0800000000000",
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         "63a2800000000000",
-        "63a3800000000000",
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+        "63a5800000000000",
+        "63a6800000000000",
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         "63a8800000000000",
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-        "63c3800000000000",
-        "63c4800000000000",
-        "63c5800000000000",
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-        "63c7800000000000",
+        "63af800000000000",
+        "63b0800000000000",
+        "63b1800000000000",
+        "63b2800000000000",
+        "63b3800000000000",
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+        "63b5800000000000",
+        "63b6800000000000",
+        "63b7800000000000",
+        "63b8800000000000",
         "63c8800000000000",
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-        "63ca800000000000",
-        "63cb800000000000",
-        "63cc800000000000",
         "63cd800000000000",
         "63ce800000000000",
         "63cf800000000000",
+        "63d0800000000000",
         "63d1800000000000",
         "63d2800000000000",
         "63d3800000000000",
+        "63d4800000000000",
+        "63d5800000000000",
+        "63d6800000000000",
+        "63d7800000000000",
         "63d8800000000000",
+        "63d9800000000000",
+        "63da800000000000",
         "63db800000000000",
-        "63e0800000000000",
+        "63dc800000000000",
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+        "63de800000000000",
+        "63df800000000000",
         "63e1800000000000",
         "63e2800000000000",
-        "63e4800000000000"
+        "63e3800000000000",
+        "63e8800000000000",
+        "63eb800000000000"
       ]
     },
     {
@@ -772,27 +772,27 @@
         "515e000000000000",
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         "5166000000000000",
-        "5192000000000000",
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-        "635e000000000000",
-        "6362000000000000",
-        "6366000000000000",
-        "636e000000000000",
-        "6372000000000000",
+        "519e000000000000",
+        "51ce000000000000",
         "6376000000000000",
-        "637a000000000000",
+        "637e000000000000",
+        "6382000000000000",
+        "6386000000000000",
+        "638a000000000000",
+        "6396000000000000",
+        "639a000000000000",
+        "639e000000000000",
         "63a2000000000000",
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         "63aa000000000000",
-        "63ca000000000000",
+        "63b2000000000000",
+        "63b6000000000000",
         "63ce000000000000",
+        "63d2000000000000",
         "63d6000000000000",
-        "63da000000000000",
-        "63de000000000000",
-        "63e2000000000000",
+        "63e6000000000000",
+        "63ea000000000000",
+        "63ee000000000000",
         "63f2000000000000",
         "63f6000000000000",
         "63fa000000000000",
@@ -831,56 +831,56 @@
       ],
       "resolution": 6,
       "cells": [
+        "5159800000000000",
+        "515a800000000000",
         "515b800000000000",
-        "515d800000000000",
-        "515e800000000000",
         "515f800000000000",
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         "5169800000000000",
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-        "516d800000000000",
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         "5174800000000000",
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-        "63cc800000000000",
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         "63ce800000000000",
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         "63d0800000000000",
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-        "63de800000000000",
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+        "63ec800000000000",
+        "63ed800000000000",
+        "63ee800000000000",
         "63f1800000000000",
         "63f2800000000000",
         "63f3800000000000",
@@ -892,7 +892,7 @@
         "63f9800000000000",
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         "63fb800000000000",
-        "63fc800000000000"
+        "63fd800000000000"
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     {
@@ -930,216 +930,216 @@
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-        "637b200000000000",
-        "637b600000000000",
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-        "637c200000000000",
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@@ -1183,7 +1183,7 @@
       ],
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+        "a1a0000000000000"
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@@ -1226,16 +1226,16 @@
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@@ -1248,62 +1248,53 @@
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@@ -1322,19 +1313,28 @@
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@@ -1377,16 +1377,16 @@
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@@ -1408,13 +1408,13 @@
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@@ -1444,139 +1444,86 @@
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@@ -1606,21 +1553,12 @@
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@@ -1630,22 +1568,84 @@
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@@ -1688,8 +1688,8 @@
       ],
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@@ -1716,60 +1716,60 @@
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@@ -1796,64 +1796,64 @@
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@@ -1967,28 +1967,28 @@
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@@ -2002,109 +2002,109 @@
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@@ -2209,15 +2209,15 @@
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@@ -2261,14 +2261,14 @@
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@@ -2366,9 +2366,9 @@
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@@ -2416,11 +2416,11 @@
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@@ -2465,109 +2465,109 @@
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@@ -2675,11 +2675,18 @@
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+        "518e000000000000",
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@@ -2687,29 +2694,26 @@
         "51d2000000000000",
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-        "51de000000000000",
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-        "51fa000000000000",
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-        "6136000000000000",
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@@ -2717,14 +2721,10 @@
         "6382000000000000",
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-        "6396000000000000",
-        "639a000000000000",
-        "639e000000000000",
+        "638e000000000000",
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-        "63b2000000000000",
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@@ -2741,7 +2741,7 @@
         "63ea000000000000",
         "63ee000000000000",
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-        "63f6000000000000",
+        "63fa000000000000",
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@@ -2820,35 +2820,35 @@
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-        "636a000000000000",
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         "6376000000000000",
-        "637a000000000000",
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+        "639a000000000000",
+        "639e000000000000",
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         "63aa000000000000",
-        "63c2000000000000",
-        "63c6000000000000",
-        "63ca000000000000",
+        "63b2000000000000",
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         "63d2000000000000",
         "63d6000000000000",
         "63da000000000000",
         "63de000000000000",
         "63e2000000000000",
+        "63e6000000000000",
+        "63ea000000000000",
+        "63ee000000000000",
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@@ -2905,11 +2905,11 @@
       ],
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       "cells": [
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-        "5147800000000000",
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@@ -2921,10 +2921,10 @@
         "5151800000000000",
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         "5153800000000000",
-        "5158800000000000",
-        "515a800000000000",
         "515b800000000000",
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@@ -2957,95 +2957,95 @@
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@@ -3090,39 +3090,39 @@
       ],
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       "cells": [
-        "515f800000000000",
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@@ -3205,13 +3205,13 @@
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@@ -3407,11 +3407,11 @@
         "516c600000000000",
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@@ -3439,52 +3439,27 @@
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@@ -3497,12 +3472,18 @@
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@@ -3527,21 +3508,6 @@
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@@ -3559,11 +3525,6 @@
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@@ -3578,22 +3539,122 @@
         "51a0600000000000",
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@@ -3613,11 +3674,19 @@
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@@ -3626,6 +3695,7 @@
         "51cd600000000000",
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@@ -3650,6 +3720,21 @@
         "51d3a00000000000",
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@@ -3659,63 +3744,32 @@
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@@ -3723,78 +3777,24 @@
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@@ -3815,68 +3815,63 @@
         "6143600000000000",
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@@ -3942,18 +3937,6 @@
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@@ -3972,10 +3955,6 @@
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@@ -3996,18 +3975,54 @@
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@@ -4019,13 +4034,33 @@
         "6370a00000000000",
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@@ -4039,14 +4074,30 @@
         "637aa00000000000",
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@@ -4060,7 +4111,6 @@
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@@ -4069,39 +4119,7 @@
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@@ -4113,23 +4131,12 @@
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@@ -4250,7 +4257,6 @@
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@@ -4262,15 +4268,23 @@
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@@ -4284,7 +4298,6 @@
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@@ -4312,7 +4325,12 @@
         "63d0e00000000000",
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@@ -4333,35 +4351,9 @@
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@@ -4370,11 +4362,6 @@
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@@ -4396,11 +4383,24 @@
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@@ -4535,11 +4535,11 @@
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@@ -4584,109 +4584,109 @@
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+        "63b8800000000000",
+        "63b9800000000000",
+        "63c7800000000000",
         "63c8800000000000",
-        "63ca800000000000",
-        "63cb800000000000",
-        "63cc800000000000",
+        "63c9800000000000",
         "63cd800000000000",
         "63ce800000000000",
         "63cf800000000000",
+        "63d0800000000000",
+        "63d1800000000000",
+        "63d2800000000000",
+        "63d3800000000000",
+        "63d4800000000000",
         "63d5800000000000",
-        "63d6800000000000",
         "63d7800000000000",
-        "63d8800000000000",
-        "63d9800000000000",
-        "63da800000000000",
-        "63db800000000000",
-        "63dc800000000000",
-        "63dd800000000000",
-        "63de800000000000",
-        "63df800000000000",
-        "63e0800000000000",
-        "63e1800000000000",
-        "63e2800000000000",
-        "63e4800000000000",
         "63e5800000000000",
+        "63e6800000000000",
+        "63e7800000000000",
+        "63e8800000000000",
+        "63e9800000000000",
+        "63ea800000000000",
+        "63eb800000000000",
+        "63ec800000000000",
+        "63ed800000000000",
         "63ee800000000000",
+        "63ef800000000000",
         "63f1800000000000",
         "63f2800000000000",
         "63f3800000000000",
diff --git a/tests/fixtures/serialization.json b/tests/fixtures/serialization.json
index 5b0323c..a9c643e 100644
--- a/tests/fixtures/serialization.json
+++ b/tests/fixtures/serialization.json
@@ -51,295 +51,295 @@
     "1a80000000000000",
     "5320000000000000",
     "2aa0000000000000",
-    "c1e0000000000000",
+    "c1a0000000000000",
     "6c20000000000000",
     "23a0000000000000",
     "d2e0000000000000",
     "76a0000000000000",
     "41e0000000000000",
-    "2db8000000000000",
+    "2da8000000000000",
     "e098000000000000",
-    "7518000000000000",
+    "7528000000000000",
     "9f08000000000000",
-    "9518000000000000",
-    "9d88000000000000",
-    "c348000000000000",
-    "3a58000000000000",
+    "9508000000000000",
+    "9dd8000000000000",
+    "c378000000000000",
+    "3a18000000000000",
     "64d6000000000000",
-    "dfa6000000000000",
+    "dfaa000000000000",
     "8ffa000000000000",
     "b13e000000000000",
-    "51aa000000000000",
+    "51e6000000000000",
     "3d2000000000000",
     "bc6000000000000",
-    "5912000000000000",
+    "590e000000000000",
     "2156800000000000",
-    "272c800000000000",
-    "2a4d800000000000",
-    "8811800000000000",
-    "ee66800000000000",
-    "58e6800000000000",
-    "305f800000000000",
-    "aece800000000000",
+    "273c800000000000",
+    "2a0a800000000000",
+    "8812800000000000",
+    "ee39800000000000",
+    "58e9800000000000",
+    "3050800000000000",
+    "aec8800000000000",
     "80b1600000000000",
-    "d9fa200000000000",
-    "a038a00000000000",
-    "9ca3200000000000",
-    "7799600000000000",
-    "d433600000000000",
-    "1bb5a00000000000",
+    "d9ad600000000000",
+    "a020a00000000000",
+    "9cb3a00000000000",
+    "775da00000000000",
+    "d42d600000000000",
+    "1bbb600000000000",
     "3222a00000000000",
     "66cbc80000000000",
-    "26dde80000000000",
-    "3322b80000000000",
-    "9280880000000000",
-    "ebb6180000000000",
+    "26e2e80000000000",
+    "3322a80000000000",
+    "9280a80000000000",
+    "eb96180000000000",
     "66dd980000000000",
-    "8f67580000000000",
+    "8f68b80000000000",
     "6fae880000000000",
-    "c072860000000000",
-    "75678a0000000000",
-    "2dacf20000000000",
-    "bd5fea0000000000",
+    "c0be720000000000",
+    "7577360000000000",
+    "2db1060000000000",
+    "bd703e0000000000",
     "11ddda0000000000",
-    "a15620000000000",
-    "ccba1a0000000000",
+    "a141e0000000000",
+    "ccba160000000000",
     "4662ce0000000000",
-    "3b2c1f8000000000",
+    "3b3c208000000000",
     "59d1d48000000000",
-    "35fdcb8000000000",
-    "90a8548000000000",
-    "5647af8000000000",
+    "35a9c88000000000",
+    "90be248000000000",
+    "5607f08000000000",
     "6c03628000000000",
     "d352e88000000000",
-    "2b5df48000000000",
-    "ae53de2000000000",
-    "1b75b0a000000000",
-    "30aea0a000000000",
-    "bd6d01a000000000",
-    "45d3b56000000000",
-    "4e1d622000000000",
+    "2b4d648000000000",
+    "ae13ee2000000000",
+    "1b7545e000000000",
+    "30a9b66000000000",
+    "bd52ab6000000000",
+    "45d3bbe000000000",
+    "4e426a2000000000",
     "654c48e000000000",
     "a652e46000000000",
     "1a90fa0800000000",
-    "51941c3800000000",
-    "91b249b800000000",
-    "1bf6271800000000",
-    "a2942a1800000000",
+    "51c8333800000000",
+    "91f5ba0800000000",
+    "1bf6277800000000",
+    "a284ea3800000000",
     "5b33154800000000",
-    "94586cd800000000",
-    "826d650800000000",
-    "b6ba6e3200000000",
-    "c89f623a00000000",
-    "504fd23200000000",
-    "52dd57a00000000",
-    "7b82607200000000",
-    "82a79a5e00000000",
-    "48475cbe00000000",
-    "61c274c200000000",
-    "ab096cdf80000000",
+    "945814d800000000",
+    "826d64f800000000",
+    "b6b896ee00000000",
+    "c89f61e200000000",
+    "509c192e00000000",
+    "519197a00000000",
+    "7b82af4200000000",
+    "828a248a00000000",
+    "4890b37e00000000",
+    "618c872600000000",
+    "ab09512080000000",
     "8551d93380000000",
-    "266ce26980000000",
-    "d76e771f80000000",
-    "c7ded57f80000000",
-    "7404106580000000",
+    "2631325680000000",
+    "d762570f80000000",
+    "c7eed97f80000000",
+    "74042ae580000000",
     "e967369d80000000",
-    "53b22c3b80000000",
-    "d25451e920000000",
-    "c21d138be0000000",
-    "2923b23660000000",
-    "68e4def9e0000000",
-    "7d798a65e0000000",
-    "1dc3070220000000",
-    "4d6a31d4a0000000",
-    "573d2048a0000000",
-    "3597d03cf8000000",
-    "309b87b4e8000000",
-    "3f8bbff058000000",
-    "4fcc3d2228000000",
-    "7006f1bd48000000",
-    "c3e131e438000000",
+    "53b12eb480000000",
+    "d254793ea0000000",
+    "c242278820000000",
+    "291e313a20000000",
+    "68e4decf20000000",
+    "7d528b45e0000000",
+    "1dc3046920000000",
+    "4d7ab7db60000000",
+    "57169fbb60000000",
+    "35ca6fc368000000",
+    "309a44ca28000000",
+    "3f8b555f78000000",
+    "4fd27ed5d8000000",
+    "700aac8c48000000",
+    "c3e1131b38000000",
     "1390dc1308000000",
-    "ed6d00a9c8000000",
-    "58c31e9f32000000",
-    "ddeb3d1aa2000000",
-    "c963436b7a000000",
-    "1e4aca5896000000",
-    "431842c5ae000000",
-    "eac29e9fea000000",
-    "663b87e0da000000",
+    "ed7d0076c8000000",
+    "58c31e29f2000000",
+    "ddb47dd612000000",
+    "c962ab6b7a000000",
+    "1e4ad7f562000000",
+    "431842c772000000",
+    "eac29e2942000000",
+    "6621b24f82000000",
     "6ad3ece636000000",
-    "41f6fcbb6b800000",
-    "ceb80a3ac4800000",
-    "ca9dac0644800000",
-    "736f331827800000",
-    "a43d082fe800000",
-    "97d576e988800000",
-    "2bfd13799e800000",
-    "79e6e97ac8800000",
-    "13206d7c20200000",
-    "9bfa99542fa00000",
-    "516d4e5565600000",
-    "85adcb6d54a00000",
-    "6a316b169f600000",
-    "28e1cda6f3e00000",
-    "a7d1a0390a600000",
-    "724c3e96caa00000",
-    "b6d3fedfc780000",
-    "eae3017cdd980000",
-    "21d9af61f5580000",
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-    "1563a4c56c180000",
-    "35da6065dfc80000",
-    "51860de25b080000",
-    "671d8de9c6fe0000",
-    "b3afe78e4cea0000",
-    "11389813a1a20000",
-    "3e87e905565a0000",
-    "67d4de98bcea0000",
-    "7738b286d4660000",
-    "1a70b79947560000",
-    "8ad557bdea1e0000",
-    "bbe1886535868000",
-    "634f6302f8948000",
-    "ab5f73a4030d8000",
-    "551f5983e9868000",
-    "a85db0bf34d38000",
-    "c8c0962b23258000",
-    "ce3fda45b1878000",
+    "41c9565363800000",
+    "ceb80a3abb800000",
+    "ca9da40658800000",
+    "7360713563800000",
+    "a43d372fe800000",
+    "97d429bd88800000",
+    "2bfdd8b9a1800000",
+    "79b9295d1a800000",
+    "1323057c23e00000",
+    "9bf82603d7a00000",
+    "516e38502d200000",
+    "85adcb6d53600000",
+    "6a315c6de0a00000",
+    "28dcc5a2f2600000",
+    "a7d176890a600000",
+    "720bc29639a00000",
+    "b6d3fe5fc780000",
+    "eaeec17cdd980000",
+    "2198d0530bf80000",
+    "667670f1e8180000",
+    "627ac93a3c580000",
+    "15620bb014180000",
+    "359a20a1d6880000",
+    "51d1f11d58f80000",
+    "671d8de2b6fe0000",
+    "b373caf082c20000",
+    "112367ce0c4e0000",
+    "3eae4a52fd260000",
+    "67d4aea75cea0000",
+    "77114c79249a0000",
+    "1a765fe6e4be0000",
+    "8aea5716b4e20000",
+    "bbe15465b55d8000",
+    "63b39496f3648000",
+    "ab5c83a4030d8000",
+    "5523a67cde798000",
+    "a85245c044d38000",
+    "c8c091d123248000",
+    "ce3fdba746478000",
     "5dde7034279f8000",
-    "7bdb44111fc9a000",
-    "c32c6bbd9a61e000",
-    "252f8d8345d12000",
-    "16733bba751ca000",
-    "64e4f1cba9696000",
-    "9204289709caa000",
-    "e21cb034e52e6000",
-    "1fe4510b596ae000",
-    "2d1bc307239ce800",
-    "a85f8007146a5800",
-    "54c23d6ffc404800",
-    "de5c7d2401b59800",
-    "653eedbc7562a800",
-    "c124debe43fe7800",
-    "981ee36493483800",
-    "d0ff6e1e3157d800",
-    "e73fdd61a71a7600",
-    "a14bab871e652e00",
-    "b468c9f595ddf600",
-    "76d2ce572c9dfe00",
-    "36e6df6410c44a00",
-    "a7032a27aa58ae00",
-    "cd5648ea53963e00",
-    "a527150815d86600",
-    "8755cebd9ded7180",
-    "c9af50737ccd980",
-    "cf8c699a0f4c6d80",
-    "6b5f80b2089f1780",
-    "19f93389a77b0d80",
-    "d03ac1e46584ed80",
-    "728414fa09a18980",
-    "403256edb701b480",
-    "9347e04aebf168e0",
-    "b6b9a4b9789d40e0",
-    "e7e8dd655066e760",
-    "bf6b45850f69a1a0",
-    "271ce8dc66c87ee0",
-    "a3bd80e70258b2a0",
-    "8be89b55b18ac5e0",
-    "1c8fc2d4c126cf60",
-    "3f5d823ebdbf7f68",
-    "c6a59952cfff2008",
-    "3d336c31673b858",
-    "1fb48397e3065ca8",
-    "562cc7091f266958",
-    "54a2e7ca58a791d8",
-    "123b63f3b88252c8",
-    "a16c36e19cfbf0c8",
-    "1f9e9a08dfee05c2",
-    "a4e0ea690e7de712",
-    "3e6d2ce1e273e72a",
-    "b8e12843725a328e",
-    "8c3f35d7a0210a8a",
-    "3615ee35e7a1c9f2",
-    "b8e51075b7e31e76",
-    "b44fc77997ef86e6",
-    "37bd3d1d431532a4",
-    "cc608c17aeb4b41b",
-    "93a2995410129469",
-    "9e5b9fbbb97ae00d",
-    "aa8937c3f4cc50ff"
+    "7bd86cdb0fca6000",
+    "c32325d672ace000",
+    "251af28375d2a000",
+    "16733998a8cba000",
+    "64e4f1cb82122000",
+    "9253c76766776000",
+    "e2439c38c96ba000",
+    "1fe4798b5990e000",
+    "2d141807239d2800",
+    "a850e0047e5fb800",
+    "54e6316c023f4800",
+    "de1c3de7fc886800",
+    "653ee5bc756d0800",
+    "c118cd4242547800",
+    "981e6e9491c81800",
+    "d0ff6e13417c2800",
+    "e73fdd6c4ada7600",
+    "a1445b870e65ee00",
+    "b468b9f5aa220a00",
+    "76edc49853210200",
+    "36d9ecd6b3136600",
+    "a7032a27afb57200",
+    "cd567b15ac69c200",
+    "a52717881725da00",
+    "8754be9d9de57180",
+    "c990acec8332680",
+    "cf8c6995f0b39280",
+    "6b50e0b2089f1c80",
+    "19cfb389a78c5280",
+    "d03ac1e45b5eee80",
+    "72ac3cf5f56f5880",
+    "4032569e4801b480",
+    "93b81fb8fc0d1520",
+    "b6ba4b52236a3fa0",
+    "e7ebad6aaf99caa0",
+    "bf6caf5f8f6e7760",
+    "2722c11365178120",
+    "a3bc80873ea4b9a0",
+    "8bc16065b8744a20",
+    "1c8fc2eec126cf60",
+    "3f4dbddb41558fa8",
+    "c6a1d5827fff3008",
+    "3d336c3168c44f8",
+    "1fb483973b065178",
+    "566c78f2df357968",
+    "54b22bce54879228",
+    "123b63f39b7d8d48",
+    "a16c32dcbc6c0f18",
+    "1f9fe764dc33871a",
+    "a4e0eb9e8e72277a",
+    "3e319481e2bdb8da",
+    "b8e1a863725b428e",
+    "8c25d596dfeec57a",
+    "364b1215b85cca0e",
+    "b8e5184b48e31e7a",
+    "b449777997e7b16a",
+    "37bd507018e84c1c",
+    "cc588c6ac2b489f1",
+    "93247734100af473",
+    "9e7ba024272c8d5d",
+    "aa96d65c6f33a701"
   ],
   "res30Locations": [
     {
       "lon": -0.1276,
       "lat": 51.5074,
       "name": "London",
-      "hex": "c6c233d3108a860f",
+      "hex": "c72e4dd2eb957921",
       "resolution": 30
     },
     {
       "lon": -73.9857,
       "lat": 40.7484,
       "name": "New York",
-      "hex": "4c20ec50870a8987",
+      "hex": "4c9ef458823b764f",
       "resolution": 30
     },
     {
       "lon": 139.6917,
       "lat": 35.6895,
       "name": "Tokyo",
-      "hex": "397c21a383a22934",
+      "hex": "397d9f569c5dd434",
       "resolution": 30
     },
     {
       "lon": -155.5,
       "lat": 19.9,
       "name": "Hawaii Big Island",
-      "hex": "e034b8a6996e5f9a",
+      "hex": "e03790b496a45f56",
       "resolution": 29
     },
     {
       "lon": -157.8,
       "lat": 21.3,
       "name": "Oahu",
-      "hex": "e03bc1fbb7bc4d52",
+      "hex": "e03e81fbe717b1ba",
       "resolution": 29
     },
     {
       "lon": 0,
       "lat": -85,
       "name": "Antarctica Weddell Sea",
-      "hex": "b80eff0c12648c86",
+      "hex": "b80ec051ba648c8a",
       "resolution": 29
     },
     {
       "lon": 90,
       "lat": -80,
       "name": "Antarctica East",
-      "hex": "b7b9a407b85f146a",
+      "hex": "b79a4bf19b09d5a6",
       "resolution": 29
     },
     {
       "lon": -75,
       "lat": -80,
       "name": "Antarctica West",
-      "hex": "be76922a668ac4b6",
+      "hex": "be79ea2b99d71eb6",
       "resolution": 29
     },
     {
       "lon": 180,
       "lat": -75,
       "name": "Antarctica Ross",
-      "hex": "c511c2098ec7797a",
+      "hex": "c52e3cf2bc48b906",
       "resolution": 29
     },
     {
       "lon": -135,
       "lat": -78,
       "name": "Antarctica Pacific",
-      "hex": "c39210cdc12df6aa",
+      "hex": "c392ece2bd963256",
       "resolution": 29
     }
   ]
diff --git a/tests/fixtures/traversal/cap.json b/tests/fixtures/traversal/cap.json
index 34d5158..d19712c 100644
--- a/tests/fixtures/traversal/cap.json
+++ b/tests/fixtures/traversal/cap.json
@@ -44,19 +44,20 @@
       "cellId": "620000000000000",
       "radius": 1000000,
       "cells": [
-        "1a0000000000000",
-        "1e0000000000000",
         "4e0000000000000",
+        "5e0000000000000",
         "620000000000000",
         "660000000000000",
-        "6a0000000000000"
+        "6a0000000000000",
+        "6e0000000000000",
+        "8320000000000000"
       ]
     },
     {
       "cellId": "7e0000000000000",
       "radius": 1000000,
       "cells": [
-        "760000000000000",
+        "7a0000000000000",
         "7e0000000000000",
         "820000000000000",
         "6560000000000000",
@@ -70,7 +71,7 @@
       "cells": [
         "1fe0000000000000",
         "2020000000000000",
-        "20a0000000000000",
+        "2060000000000000",
         "2960000000000000",
         "2ea0000000000000",
         "d420000000000000"
@@ -82,9 +83,9 @@
       "cellId": "402000000000000",
       "radius": 500000,
       "compactedCells": [
-        "38e000000000000",
-        "3e2000000000000",
-        "3e6000000000000",
+        "3ba000000000000",
+        "3ea000000000000",
+        "3ee000000000000",
         "3f6000000000000",
         "3fa000000000000",
         "3fe000000000000",
@@ -113,14 +114,14 @@
         "2156000000000000",
         "215a000000000000",
         "215e000000000000",
-        "27de000000000000",
+        "27c6000000000000",
         "27ee000000000000",
         "27f2000000000000",
         "27f6000000000000",
         "27fa000000000000",
         "27fe000000000000",
         "2802000000000000",
-        "280a000000000000",
+        "2806000000000000",
         "3aaa000000000000",
         "5bf2000000000000",
         "5bf6000000000000",
@@ -144,10 +145,10 @@
         "715a000000000000",
         "715e000000000000",
         "77f2000000000000",
-        "77f6000000000000",
+        "77fa000000000000",
         "77fe000000000000",
         "7802000000000000",
-        "780a000000000000",
+        "7806000000000000",
         "780e000000000000",
         "7ea2000000000000",
         "7ea6000000000000",
@@ -169,14 +170,14 @@
       "cellId": "402000000000000",
       "radius": 1000000,
       "compactedCells": [
-        "23e000000000000",
-        "382000000000000",
-        "386000000000000",
-        "38a000000000000",
-        "38e000000000000",
-        "392000000000000",
-        "396000000000000",
-        "39a000000000000",
+        "226000000000000",
+        "39e000000000000",
+        "3a2000000000000",
+        "3a6000000000000",
+        "3ae000000000000",
+        "3b2000000000000",
+        "3b6000000000000",
+        "3ba000000000000",
         "3be000000000000",
         "3c2000000000000",
         "3d2000000000000",
@@ -191,19 +192,19 @@
         "426000000000000",
         "42a000000000000",
         "42e000000000000",
+        "432000000000000",
         "436000000000000",
-        "43a000000000000",
         "43e000000000000",
         "442000000000000",
         "446000000000000",
         "44a000000000000",
         "44e000000000000",
         "452000000000000",
-        "456000000000000",
+        "45a000000000000",
         "45e000000000000",
         "462000000000000",
         "982000000000000",
-        "986000000000000",
+        "98e000000000000",
         "992000000000000",
         "996000000000000",
         "99a000000000000",
@@ -229,7 +230,7 @@
         "dc2000000000000",
         "dc6000000000000",
         "dca000000000000",
-        "1196000000000000",
+        "1192000000000000",
         "119a000000000000",
         "119e000000000000",
         "11a8000000000000",
@@ -247,7 +248,7 @@
       "cellId": "5c02000000000000",
       "radius": 1000000,
       "compactedCells": [
-        "2146000000000000",
+        "214a000000000000",
         "214e000000000000",
         "2158000000000000",
         "2162000000000000",
@@ -257,26 +258,26 @@
         "2176000000000000",
         "217a000000000000",
         "217e000000000000",
-        "2742000000000000",
-        "274a000000000000",
-        "274e000000000000",
-        "2762000000000000",
+        "2796000000000000",
+        "27b2000000000000",
+        "27b6000000000000",
+        "27be000000000000",
         "27c2000000000000",
         "27c6000000000000",
         "27ca000000000000",
         "27ce000000000000",
-        "27d8000000000000",
-        "27e2000000000000",
-        "27e6000000000000",
-        "27ea000000000000",
-        "27ee000000000000",
+        "27d2000000000000",
+        "27d6000000000000",
+        "27da000000000000",
+        "27de000000000000",
+        "27e8000000000000",
         "27f8000000000000",
         "2808000000000000",
         "2812000000000000",
+        "2816000000000000",
+        "281a000000000000",
+        "281e000000000000",
         "2822000000000000",
-        "2826000000000000",
-        "282a000000000000",
-        "282e000000000000",
         "283a000000000000",
         "3a8a000000000000",
         "3a8e000000000000",
@@ -285,7 +286,7 @@
         "3a9e000000000000",
         "3aa8000000000000",
         "3ab2000000000000",
-        "3aba000000000000",
+        "3ab6000000000000",
         "5b92000000000000",
         "5b96000000000000",
         "5bc2000000000000",
@@ -308,11 +309,11 @@
         "5c36000000000000",
         "5c3a000000000000",
         "5c3e000000000000",
+        "5c42000000000000",
         "5c46000000000000",
         "5c4a000000000000",
-        "5c4e000000000000",
-        "5ca2000000000000",
-        "5ca6000000000000",
+        "5caa000000000000",
+        "5cae000000000000",
         "5cba000000000000"
       ]
     },
@@ -333,15 +334,15 @@
         "7176000000000000",
         "717a000000000000",
         "717e000000000000",
-        "7192000000000000",
+        "71ce000000000000",
         "77c6000000000000",
         "77ca000000000000",
-        "77ce000000000000",
         "77d2000000000000",
         "77d6000000000000",
-        "77da000000000000",
         "77de000000000000",
+        "77e2000000000000",
         "77e6000000000000",
+        "77ea000000000000",
         "77ee000000000000",
         "77f8000000000000",
         "7808000000000000",
@@ -350,12 +351,12 @@
         "781a000000000000",
         "781e000000000000",
         "7822000000000000",
-        "7826000000000000",
         "782a000000000000",
         "782e000000000000",
         "7832000000000000",
         "7836000000000000",
         "783a000000000000",
+        "783e000000000000",
         "7e86000000000000",
         "7e8a000000000000",
         "7e8e000000000000",
@@ -364,11 +365,11 @@
         "7e9e000000000000",
         "7ea8000000000000",
         "7eb2000000000000",
-        "7eba000000000000",
-        "a75e000000000000",
-        "a7b2000000000000",
+        "7eb6000000000000",
+        "a752000000000000",
         "a7b6000000000000",
         "a7ba000000000000",
+        "a7be000000000000",
         "a7c2000000000000",
         "a7c6000000000000",
         "a7ca000000000000",
diff --git a/tests/fixtures/traversal/global-neighbors.json b/tests/fixtures/traversal/global-neighbors.json
index a70fdab..db0a31b 100644
--- a/tests/fixtures/traversal/global-neighbors.json
+++ b/tests/fixtures/traversal/global-neighbors.json
@@ -126,7 +126,7 @@
         "fe0000000000000",
         "1020000000000000",
         "15a0000000000000",
-        "2620000000000000",
+        "2660000000000000",
         "26a0000000000000",
         "5d60000000000000"
       ],
@@ -188,20 +188,20 @@
     },
     "output": {
       "neighbors": [
-        "1628000000000000",
-        "1638000000000000",
-        "1648000000000000",
+        "15f8000000000000",
+        "1618000000000000",
         "1658000000000000",
-        "1668000000000000",
-        "1798000000000000",
-        "17a8000000000000"
+        "24a8000000000000",
+        "24b8000000000000",
+        "24c8000000000000",
+        "2658000000000000"
       ],
       "edgeNeighbors": [
-        "1628000000000000",
-        "1638000000000000",
+        "15f8000000000000",
+        "1618000000000000",
         "1658000000000000",
-        "1668000000000000",
-        "17a8000000000000"
+        "24b8000000000000",
+        "24c8000000000000"
       ]
     }
   },
@@ -217,7 +217,7 @@
         "2420000000000000",
         "24a0000000000000",
         "24e0000000000000",
-        "2620000000000000"
+        "2660000000000000"
       ],
       "edgeNeighbors": [
         "15e0000000000000",
@@ -332,7 +332,7 @@
         "17e8000000000000",
         "1808000000000000",
         "1818000000000000",
-        "1878000000000000",
+        "1848000000000000",
         "1e58000000000000",
         "23f8000000000000",
         "2408000000000000"
@@ -558,15 +558,15 @@
     "output": {
       "neighbors": [
         "2156000000000000",
-        "215e000000000000",
-        "27f6000000000000",
+        "215a000000000000",
+        "27fa000000000000",
         "2802000000000000",
         "5bfe000000000000",
         "5c02000000000000"
       ],
       "edgeNeighbors": [
         "2156000000000000",
-        "27f6000000000000",
+        "27fa000000000000",
         "2802000000000000",
         "5bfe000000000000",
         "5c02000000000000"
@@ -581,15 +581,15 @@
       "neighbors": [
         "2156000000000000",
         "27fe000000000000",
-        "280a000000000000",
-        "3aa2000000000000",
+        "2806000000000000",
+        "3aa6000000000000",
         "3aaa000000000000",
         "5bfe000000000000"
       ],
       "edgeNeighbors": [
         "2156000000000000",
         "27fe000000000000",
-        "280a000000000000",
+        "2806000000000000",
         "3aaa000000000000",
         "5bfe000000000000"
       ]
@@ -789,7 +789,7 @@
       "neighbors": [
         "2020000000000000",
         "2960000000000000",
-        "29e0000000000000",
+        "29a0000000000000",
         "2e60000000000000",
         "d3e0000000000000",
         "d420000000000000"
@@ -930,20 +930,20 @@
     },
     "output": {
       "neighbors": [
-        "3548000000000000",
         "3558000000000000",
         "3568000000000000",
+        "3c08000000000000",
         "3c28000000000000",
         "3c38000000000000",
-        "3c98000000000000",
-        "3cb8000000000000"
+        "4e88000000000000",
+        "4ea8000000000000"
       ],
       "edgeNeighbors": [
-        "3548000000000000",
-        "3568000000000000",
+        "3558000000000000",
+        "3c08000000000000",
         "3c28000000000000",
         "3c38000000000000",
-        "3cb8000000000000"
+        "4e88000000000000"
       ]
     }
   },
@@ -953,20 +953,20 @@
     },
     "output": {
       "neighbors": [
+        "3560000000000000",
+        "35e0000000000000",
+        "3c20000000000000",
         "3ca0000000000000",
         "3ce0000000000000",
-        "3e20000000000000",
-        "3ea0000000000000",
-        "3ee0000000000000",
-        "4ce0000000000000",
-        "4e20000000000000"
+        "4e60000000000000",
+        "4ea0000000000000"
       ],
       "edgeNeighbors": [
+        "3560000000000000",
+        "3c20000000000000",
         "3ca0000000000000",
         "3ce0000000000000",
-        "3ea0000000000000",
-        "3ee0000000000000",
-        "4e20000000000000"
+        "4e60000000000000"
       ]
     }
   },
@@ -1024,20 +1024,20 @@
     },
     "output": {
       "neighbors": [
-        "3d6e000000000000",
-        "3d7a000000000000",
-        "3d7e000000000000",
+        "3d8a000000000000",
+        "3d8e000000000000",
+        "3d92000000000000",
+        "3dbe000000000000",
+        "3dc6000000000000",
         "3dca000000000000",
-        "3dd6000000000000",
-        "427a000000000000",
-        "4282000000000000"
+        "3dee000000000000"
       ],
       "edgeNeighbors": [
-        "3d7a000000000000",
-        "3d7e000000000000",
+        "3d8e000000000000",
+        "3d92000000000000",
+        "3dc6000000000000",
         "3dca000000000000",
-        "3dd6000000000000",
-        "427a000000000000"
+        "3dee000000000000"
       ]
     }
   },
@@ -1095,7 +1095,7 @@
     },
     "output": {
       "neighbors": [
-        "3e2000000000000",
+        "3ee000000000000",
         "3fa000000000000",
         "3fe000000000000",
         "406000000000000",
@@ -1119,7 +1119,7 @@
     },
     "output": {
       "neighbors": [
-        "388000000000000",
+        "3b8000000000000",
         "3e8000000000000",
         "3f8000000000000",
         "418000000000000",
@@ -1215,20 +1215,20 @@
     },
     "output": {
       "neighbors": [
-        "446000000000000",
+        "44a000000000000",
         "452000000000000",
-        "52e000000000000",
+        "51a000000000000",
         "97e000000000000",
-        "986000000000000",
-        "992000000000000",
+        "982000000000000",
+        "996000000000000",
         "99e000000000000"
       ],
       "edgeNeighbors": [
-        "446000000000000",
+        "44a000000000000",
         "452000000000000",
-        "52e000000000000",
-        "986000000000000",
-        "992000000000000"
+        "51a000000000000",
+        "982000000000000",
+        "996000000000000"
       ]
     }
   },
@@ -1267,7 +1267,7 @@
         "4a0000000000000",
         "520000000000000",
         "560000000000000",
-        "5a0000000000000",
+        "5e0000000000000",
         "960000000000000",
         "9a0000000000000"
       ],
@@ -1410,20 +1410,20 @@
     },
     "output": {
       "neighbors": [
-        "50d8000000000000",
-        "50f8000000000000",
         "5108000000000000",
+        "5118000000000000",
+        "5128000000000000",
+        "51f8000000000000",
         "5218000000000000",
-        "5228000000000000",
-        "6958000000000000",
-        "6b08000000000000"
+        "5248000000000000",
+        "5318000000000000"
       ],
       "edgeNeighbors": [
-        "50f8000000000000",
-        "5108000000000000",
+        "5118000000000000",
+        "5128000000000000",
         "5218000000000000",
-        "5228000000000000",
-        "6b08000000000000"
+        "5248000000000000",
+        "5318000000000000"
       ]
     }
   },
@@ -1433,20 +1433,20 @@
     },
     "output": {
       "neighbors": [
-        "5060000000000000",
-        "50e0000000000000",
         "5120000000000000",
+        "51e0000000000000",
         "5260000000000000",
         "52a0000000000000",
-        "6960000000000000",
-        "6b20000000000000"
+        "5320000000000000",
+        "5360000000000000",
+        "53a0000000000000"
       ],
       "edgeNeighbors": [
-        "50e0000000000000",
         "5120000000000000",
         "5260000000000000",
         "52a0000000000000",
-        "6b20000000000000"
+        "5320000000000000",
+        "5360000000000000"
       ]
     }
   },
@@ -1503,18 +1503,18 @@
     },
     "output": {
       "neighbors": [
-        "52c2000000000000",
-        "52ca000000000000",
-        "52ce000000000000",
-        "52e2000000000000",
-        "548e000000000000",
+        "5432000000000000",
+        "5436000000000000",
+        "5496000000000000",
+        "549a000000000000",
+        "549e000000000000",
         "54a6000000000000",
         "54aa000000000000"
       ],
       "edgeNeighbors": [
-        "52ca000000000000",
-        "52ce000000000000",
-        "548e000000000000",
+        "5432000000000000",
+        "549a000000000000",
+        "549e000000000000",
         "54a6000000000000",
         "54aa000000000000"
       ]
@@ -1648,7 +1648,7 @@
         "53f8000000000000",
         "5408000000000000",
         "59a8000000000000",
-        "5f88000000000000",
+        "5fb8000000000000",
         "5fe8000000000000",
         "5ff8000000000000",
         "6018000000000000",
@@ -1767,15 +1767,15 @@
         "be0000000000000",
         "c20000000000000",
         "5160000000000000",
-        "51e0000000000000",
-        "6360000000000000",
+        "51a0000000000000",
+        "63a0000000000000",
         "6aa0000000000000"
       ],
       "edgeNeighbors": [
         "be0000000000000",
         "c20000000000000",
         "5160000000000000",
-        "6360000000000000",
+        "63a0000000000000",
         "6aa0000000000000"
       ]
     }
@@ -1790,14 +1790,14 @@
         "c08000000000000",
         "5158000000000000",
         "5178000000000000",
-        "63d8000000000000",
+        "63e8000000000000",
         "6aa8000000000000"
       ],
       "edgeNeighbors": [
         "bf8000000000000",
         "c08000000000000",
         "5158000000000000",
-        "63d8000000000000",
+        "63e8000000000000",
         "6aa8000000000000"
       ]
     }
@@ -1811,15 +1811,15 @@
         "bfe000000000000",
         "c02000000000000",
         "5156000000000000",
-        "515e000000000000",
-        "63f6000000000000",
+        "515a000000000000",
+        "63fa000000000000",
         "6aaa000000000000"
       ],
       "edgeNeighbors": [
         "bfe000000000000",
         "c02000000000000",
         "5156000000000000",
-        "63f6000000000000",
+        "63fa000000000000",
         "6aaa000000000000"
       ]
     }
@@ -1908,14 +1908,14 @@
         "4802000000000000",
         "6ff2000000000000",
         "6ffe000000000000",
-        "700a000000000000",
+        "7006000000000000",
         "abfe000000000000",
         "ac02000000000000"
       ],
       "edgeNeighbors": [
         "4802000000000000",
         "6ffe000000000000",
-        "700a000000000000",
+        "7006000000000000",
         "abfe000000000000",
         "ac02000000000000"
       ]
@@ -1952,7 +1952,7 @@
     },
     "output": {
       "neighbors": [
-        "6788000000000000",
+        "67b8000000000000",
         "67e8000000000000",
         "67f8000000000000",
         "6808000000000000",
@@ -2072,15 +2072,15 @@
     "output": {
       "neighbors": [
         "7160000000000000",
-        "71e0000000000000",
-        "7760000000000000",
+        "71a0000000000000",
+        "77a0000000000000",
         "7820000000000000",
         "7ea0000000000000",
         "a820000000000000"
       ],
       "edgeNeighbors": [
         "7160000000000000",
-        "7760000000000000",
+        "77a0000000000000",
         "7820000000000000",
         "7ea0000000000000",
         "a820000000000000"
@@ -2095,14 +2095,14 @@
       "neighbors": [
         "7158000000000000",
         "7178000000000000",
-        "77d8000000000000",
+        "77e8000000000000",
         "7808000000000000",
         "7ea8000000000000",
         "a808000000000000"
       ],
       "edgeNeighbors": [
         "7158000000000000",
-        "77d8000000000000",
+        "77e8000000000000",
         "7808000000000000",
         "7ea8000000000000",
         "a808000000000000"
@@ -2187,7 +2187,7 @@
     },
     "output": {
       "neighbors": [
-        "760000000000000",
+        "7a0000000000000",
         "820000000000000",
         "8e0000000000000",
         "6560000000000000",
@@ -2195,7 +2195,7 @@
         "8020000000000000"
       ],
       "edgeNeighbors": [
-        "760000000000000",
+        "7a0000000000000",
         "820000000000000",
         "6560000000000000",
         "7fe0000000000000",
@@ -2209,7 +2209,7 @@
     },
     "output": {
       "neighbors": [
-        "7d8000000000000",
+        "7e8000000000000",
         "808000000000000",
         "818000000000000",
         "6558000000000000",
@@ -2217,7 +2217,7 @@
         "8008000000000000"
       ],
       "edgeNeighbors": [
-        "7d8000000000000",
+        "7e8000000000000",
         "808000000000000",
         "6558000000000000",
         "7ff8000000000000",
@@ -2231,7 +2231,7 @@
     },
     "output": {
       "neighbors": [
-        "7f6000000000000",
+        "7fa000000000000",
         "802000000000000",
         "80e000000000000",
         "6556000000000000",
@@ -2239,7 +2239,7 @@
         "8002000000000000"
       ],
       "edgeNeighbors": [
-        "7f6000000000000",
+        "7fa000000000000",
         "802000000000000",
         "6556000000000000",
         "7ffe000000000000",
@@ -2491,20 +2491,20 @@
     },
     "output": {
       "neighbors": [
-        "8cd8000000000000",
-        "8cf8000000000000",
         "8d08000000000000",
+        "8d18000000000000",
+        "8d28000000000000",
+        "8df8000000000000",
         "8e18000000000000",
-        "8e28000000000000",
-        "a108000000000000",
-        "a208000000000000"
+        "8e48000000000000",
+        "8f18000000000000"
       ],
       "edgeNeighbors": [
-        "8cf8000000000000",
-        "8d08000000000000",
+        "8d18000000000000",
+        "8d28000000000000",
         "8e18000000000000",
-        "8e28000000000000",
-        "a108000000000000"
+        "8e48000000000000",
+        "8f18000000000000"
       ]
     }
   },
@@ -2514,20 +2514,20 @@
     },
     "output": {
       "neighbors": [
-        "8c60000000000000",
-        "8ce0000000000000",
         "8d20000000000000",
+        "8de0000000000000",
         "8e60000000000000",
         "8ea0000000000000",
-        "a120000000000000",
-        "a220000000000000"
+        "8f20000000000000",
+        "8f60000000000000",
+        "8fa0000000000000"
       ],
       "edgeNeighbors": [
-        "8ce0000000000000",
         "8d20000000000000",
         "8e60000000000000",
         "8ea0000000000000",
-        "a120000000000000"
+        "8f20000000000000",
+        "8f60000000000000"
       ]
     }
   },
@@ -2634,17 +2634,17 @@
     },
     "output": {
       "neighbors": [
-        "921e000000000000",
-        "922e000000000000",
-        "9232000000000000",
-        "923a000000000000",
+        "8c72000000000000",
+        "8c76000000000000",
+        "8c7a000000000000",
+        "8c8e000000000000",
         "925e000000000000",
         "9266000000000000",
         "926a000000000000"
       ],
       "edgeNeighbors": [
-        "922e000000000000",
-        "923a000000000000",
+        "8c76000000000000",
+        "8c7a000000000000",
         "925e000000000000",
         "9266000000000000",
         "926a000000000000"
@@ -2730,7 +2730,7 @@
     "output": {
       "neighbors": [
         "99a0000000000000",
-        "9e20000000000000",
+        "9e60000000000000",
         "9ea0000000000000",
         "c7e0000000000000",
         "c820000000000000",
@@ -3134,15 +3134,15 @@
       "neighbors": [
         "4420000000000000",
         "ad60000000000000",
-        "ade0000000000000",
-        "b360000000000000",
+        "ada0000000000000",
+        "b3a0000000000000",
         "b420000000000000",
         "baa0000000000000"
       ],
       "edgeNeighbors": [
         "4420000000000000",
         "ad60000000000000",
-        "b360000000000000",
+        "b3a0000000000000",
         "b420000000000000",
         "baa0000000000000"
       ]
@@ -3157,14 +3157,14 @@
         "4408000000000000",
         "ad58000000000000",
         "ad78000000000000",
-        "b3d8000000000000",
+        "b3e8000000000000",
         "b408000000000000",
         "baa8000000000000"
       ],
       "edgeNeighbors": [
         "4408000000000000",
         "ad58000000000000",
-        "b3d8000000000000",
+        "b3e8000000000000",
         "b408000000000000",
         "baa8000000000000"
       ]
@@ -3176,7 +3176,7 @@
     },
     "output": {
       "neighbors": [
-        "b3d8000000000000",
+        "b3c8000000000000",
         "b3e8000000000000",
         "b3f8000000000000",
         "b428000000000000",
@@ -3185,7 +3185,7 @@
         "baa8000000000000"
       ],
       "edgeNeighbors": [
-        "b3d8000000000000",
+        "b3e8000000000000",
         "b3f8000000000000",
         "b428000000000000",
         "b438000000000000",
@@ -3200,7 +3200,7 @@
     "output": {
       "neighbors": [
         "b320000000000000",
-        "b360000000000000",
+        "b3a0000000000000",
         "b3e0000000000000",
         "b460000000000000",
         "b4a0000000000000",
@@ -3208,7 +3208,7 @@
         "baa0000000000000"
       ],
       "edgeNeighbors": [
-        "b360000000000000",
+        "b3a0000000000000",
         "b3e0000000000000",
         "b460000000000000",
         "b4a0000000000000",
@@ -3274,7 +3274,7 @@
         "b7fa000000000000",
         "b802000000000000",
         "b806000000000000",
-        "b81e000000000000",
+        "b812000000000000",
         "be56000000000000",
         "c3fe000000000000",
         "c402000000000000"
@@ -3370,14 +3370,14 @@
         "3002000000000000",
         "bff2000000000000",
         "bffe000000000000",
-        "c00a000000000000",
+        "c006000000000000",
         "cffe000000000000",
         "d002000000000000"
       ],
       "edgeNeighbors": [
         "3002000000000000",
         "bffe000000000000",
-        "c00a000000000000",
+        "c006000000000000",
         "cffe000000000000",
         "d002000000000000"
       ]
@@ -3414,7 +3414,7 @@
     },
     "output": {
       "neighbors": [
-        "b788000000000000",
+        "b7b8000000000000",
         "b7e8000000000000",
         "b7f8000000000000",
         "b808000000000000",
@@ -3536,15 +3536,15 @@
         "9960000000000000",
         "9ea0000000000000",
         "c160000000000000",
-        "c1e0000000000000",
-        "c760000000000000",
+        "c1a0000000000000",
+        "c7a0000000000000",
         "cea0000000000000"
       ],
       "edgeNeighbors": [
         "9960000000000000",
         "9ea0000000000000",
         "c160000000000000",
-        "c760000000000000",
+        "c7a0000000000000",
         "cea0000000000000"
       ]
     }
@@ -3559,14 +3559,14 @@
         "9ea8000000000000",
         "c158000000000000",
         "c178000000000000",
-        "c7d8000000000000",
+        "c7e8000000000000",
         "cea8000000000000"
       ],
       "edgeNeighbors": [
         "9958000000000000",
         "9ea8000000000000",
         "c158000000000000",
-        "c7d8000000000000",
+        "c7e8000000000000",
         "cea8000000000000"
       ]
     }
@@ -3602,20 +3602,20 @@
     },
     "output": {
       "neighbors": [
+        "ca32000000000000",
+        "ca3e000000000000",
         "cb82000000000000",
         "cb86000000000000",
         "cb8e000000000000",
-        "cb92000000000000",
-        "cb9a000000000000",
-        "d822000000000000",
-        "d82a000000000000"
+        "cb96000000000000",
+        "cb9a000000000000"
       ],
       "edgeNeighbors": [
+        "ca32000000000000",
         "cb82000000000000",
         "cb86000000000000",
         "cb8e000000000000",
-        "cb92000000000000",
-        "d822000000000000"
+        "cb9a000000000000"
       ]
     }
   },
@@ -3750,20 +3750,20 @@
     },
     "output": {
       "neighbors": [
-        "c988000000000000",
-        "c9e8000000000000",
-        "c9f8000000000000",
-        "ca18000000000000",
-        "d8f8000000000000",
+        "d8c8000000000000",
+        "d8d8000000000000",
+        "d8e8000000000000",
+        "d9f8000000000000",
         "da18000000000000",
-        "da28000000000000"
+        "da48000000000000",
+        "dad8000000000000"
       ],
       "edgeNeighbors": [
-        "c9e8000000000000",
-        "c9f8000000000000",
-        "d8f8000000000000",
+        "d8d8000000000000",
+        "d8e8000000000000",
         "da18000000000000",
-        "da28000000000000"
+        "da48000000000000",
+        "dad8000000000000"
       ]
     }
   },
@@ -3773,20 +3773,20 @@
     },
     "output": {
       "neighbors": [
-        "c960000000000000",
-        "c9a0000000000000",
-        "c9e0000000000000",
-        "ca20000000000000",
         "d8e0000000000000",
+        "d9e0000000000000",
         "da60000000000000",
-        "daa0000000000000"
+        "daa0000000000000",
+        "dae0000000000000",
+        "e320000000000000",
+        "e3a0000000000000"
       ],
       "edgeNeighbors": [
-        "c9a0000000000000",
-        "c9e0000000000000",
         "d8e0000000000000",
         "da60000000000000",
-        "daa0000000000000"
+        "daa0000000000000",
+        "dae0000000000000",
+        "e320000000000000"
       ]
     }
   },
diff --git a/tests/fixtures/traversal/grid-disk.json b/tests/fixtures/traversal/grid-disk.json
index 2c52f36..8028b2d 100644
--- a/tests/fixtures/traversal/grid-disk.json
+++ b/tests/fixtures/traversal/grid-disk.json
@@ -461,16 +461,16 @@
     "cellId": "620000000000000",
     "k": 1,
     "cells": [
-      "1a0000000000000",
-      "1e0000000000000",
       "4e0000000000000",
       "620000000000000",
       "660000000000000",
-      "6a0000000000000"
+      "6a0000000000000",
+      "6e0000000000000",
+      "8320000000000000"
     ],
     "extraVertexCells": [
-      "160000000000000",
-      "220000000000000"
+      "5e0000000000000",
+      "83a0000000000000"
     ]
   },
   {
@@ -508,7 +508,7 @@
     "cellId": "5c20000000000000",
     "k": 1,
     "cells": [
-      "2760000000000000",
+      "27a0000000000000",
       "27e0000000000000",
       "5be0000000000000",
       "5c20000000000000",
@@ -533,7 +533,7 @@
     ],
     "extraVertexCells": [
       "6020000000000000",
-      "6220000000000000"
+      "6260000000000000"
     ]
   },
   {
@@ -565,7 +565,7 @@
     ],
     "extraVertexCells": [
       "8820000000000000",
-      "8a20000000000000"
+      "8a60000000000000"
     ]
   },
   {
@@ -645,7 +645,7 @@
       "4e0000000000000",
       "520000000000000",
       "560000000000000",
-      "5a0000000000000",
+      "5e0000000000000",
       "960000000000000",
       "9a0000000000000",
       "9e0000000000000",
@@ -656,7 +656,7 @@
     "extraVertexCells": [
       "1e0000000000000",
       "2e0000000000000",
-      "620000000000000",
+      "660000000000000",
       "a20000000000000",
       "d60000000000000",
       "de0000000000000",
@@ -669,30 +669,31 @@
     "cellId": "620000000000000",
     "k": 2,
     "cells": [
-      "120000000000000",
       "160000000000000",
       "1a0000000000000",
       "1e0000000000000",
       "220000000000000",
-      "260000000000000",
       "4a0000000000000",
       "4e0000000000000",
       "5a0000000000000",
+      "5e0000000000000",
       "620000000000000",
       "660000000000000",
       "6a0000000000000",
       "6e0000000000000",
+      "82e0000000000000",
       "8320000000000000",
+      "8360000000000000",
       "83a0000000000000",
-      "83e0000000000000",
-      "eea0000000000000"
+      "83e0000000000000"
     ],
     "extraVertexCells": [
-      "2a0000000000000",
-      "3a0000000000000",
-      "420000000000000",
-      "e960000000000000",
-      "ee60000000000000"
+      "460000000000000",
+      "560000000000000",
+      "8060000000000000",
+      "8260000000000000",
+      "8420000000000000",
+      "8460000000000000"
     ]
   },
   {
@@ -710,7 +711,7 @@
       "bf60000000000000",
       "bfe0000000000000",
       "c020000000000000",
-      "c0a0000000000000",
+      "c060000000000000",
       "cfe0000000000000",
       "d020000000000000",
       "d060000000000000"
@@ -759,7 +760,7 @@
     "k": 2,
     "cells": [
       "2160000000000000",
-      "21e0000000000000",
+      "21a0000000000000",
       "2720000000000000",
       "2760000000000000",
       "27a0000000000000",
@@ -777,8 +778,8 @@
     ],
     "extraVertexCells": [
       "2560000000000000",
-      "25e0000000000000",
-      "3a60000000000000",
+      "25a0000000000000",
+      "3a20000000000000",
       "5a20000000000000",
       "5b20000000000000",
       "5ee0000000000000"
@@ -802,7 +803,7 @@
       "6060000000000000",
       "60a0000000000000",
       "60e0000000000000",
-      "61a0000000000000",
+      "61e0000000000000",
       "6220000000000000",
       "6260000000000000"
     ],
@@ -834,11 +835,11 @@
       "e960000000000000",
       "e9a0000000000000",
       "e9e0000000000000",
-      "ee20000000000000",
+      "ee60000000000000",
       "eea0000000000000"
     ],
     "extraVertexCells": [
-      "660000000000000",
+      "620000000000000",
       "8220000000000000",
       "8320000000000000",
       "86e0000000000000",
@@ -864,7 +865,7 @@
       "8860000000000000",
       "88a0000000000000",
       "88e0000000000000",
-      "89a0000000000000",
+      "89e0000000000000",
       "8a20000000000000",
       "8a60000000000000"
     ],
@@ -885,10 +886,10 @@
       "7160000000000000",
       "71a0000000000000",
       "71e0000000000000",
-      "7760000000000000",
+      "77a0000000000000",
       "77e0000000000000",
       "7820000000000000",
-      "78a0000000000000",
+      "7860000000000000",
       "7ea0000000000000",
       "a760000000000000",
       "a7a0000000000000",
@@ -900,7 +901,7 @@
     ],
     "extraVertexCells": [
       "78e0000000000000",
-      "7e20000000000000",
+      "7e60000000000000",
       "a4e0000000000000",
       "a9e0000000000000"
     ]
@@ -948,7 +949,7 @@
       "3060000000000000",
       "bfe0000000000000",
       "c020000000000000",
-      "c0a0000000000000",
+      "c060000000000000",
       "cf60000000000000",
       "cfa0000000000000",
       "cfe0000000000000",
diff --git a/tests/fixtures/traversal/lattice-flood-fill.json b/tests/fixtures/traversal/lattice-flood-fill.json
index 94693f0..5d8f8d4 100644
--- a/tests/fixtures/traversal/lattice-flood-fill.json
+++ b/tests/fixtures/traversal/lattice-flood-fill.json
@@ -7,15 +7,15 @@
         "5172000000000000"
       ],
       "firewallCells": [
-        "5146000000000000",
+        "514a000000000000",
         "514e000000000000",
         "5152000000000000",
         "5156000000000000",
         "516e000000000000",
         "517e000000000000",
-        "63c2000000000000",
-        "63ca000000000000",
+        "63d6000000000000",
         "63da000000000000",
+        "63ea000000000000",
         "63f2000000000000",
         "63fe000000000000",
         "6aae000000000000",
@@ -40,16 +40,16 @@
         "5172000000000000"
       ],
       "firewallCells": [
-        "5182000000000000",
-        "518a000000000000",
+        "518e000000000000",
         "519a000000000000",
         "51c6000000000000",
+        "51d6000000000000",
         "51da000000000000",
-        "634a000000000000",
-        "635a000000000000",
-        "636e000000000000",
-        "6376000000000000",
-        "63e6000000000000",
+        "638a000000000000",
+        "639e000000000000",
+        "63a6000000000000",
+        "63b6000000000000",
+        "63ca000000000000",
         "640a000000000000",
         "6432000000000000",
         "6a56000000000000",
@@ -73,8 +73,8 @@
         "517a000000000000"
       ],
       "frontierCells": [
-        "515a000000000000",
-        "5162000000000000",
+        "515e000000000000",
+        "5166000000000000",
         "516a000000000000",
         "517a000000000000"
       ]
@@ -84,21 +84,21 @@
       "resolution": 5,
       "seedCells": [
         "5172000000000000",
-        "515e000000000000",
+        "515a000000000000",
         "5172000000000000"
       ],
       "firewallCells": [
         "5152000000000000",
         "5156000000000000",
-        "515a000000000000",
+        "515e000000000000",
         "5162000000000000",
         "5166000000000000",
         "516a000000000000",
         "5176000000000000",
         "517a000000000000",
-        "63c6000000000000",
-        "63d2000000000000",
-        "63d6000000000000",
+        "63de000000000000",
+        "63e2000000000000",
+        "63e6000000000000",
         "63f2000000000000",
         "63f6000000000000",
         "63fa000000000000",
@@ -113,19 +113,19 @@
       "name": "res3_small_ring",
       "resolution": 3,
       "seedCells": [
-        "4de0000000000000"
+        "4da0000000000000"
       ],
       "firewallCells": [
         "4ce0000000000000",
         "4d60000000000000",
-        "4e60000000000000",
-        "4f60000000000000",
-        "55e0000000000000",
-        "5660000000000000",
+        "4e20000000000000",
+        "4fa0000000000000",
+        "55a0000000000000",
+        "5620000000000000",
         "5720000000000000"
       ],
       "interiorCells": [
-        "4da0000000000000",
+        "4de0000000000000",
         "4ee0000000000000",
         "4f20000000000000"
       ],
diff --git a/tests/fixtures/traversal/lattice-neighbors.json b/tests/fixtures/traversal/lattice-neighbors.json
index f42c1cf..68fc185 100644
--- a/tests/fixtures/traversal/lattice-neighbors.json
+++ b/tests/fixtures/traversal/lattice-neighbors.json
@@ -785,7 +785,7 @@
       ],
       "supersetNeighbors": [
         "11a8000000000000",
-        "388000000000000",
+        "3b8000000000000",
         "3e8000000000000",
         "3f8000000000000",
         "3f8000000000000",
@@ -801,30 +801,30 @@
       "cell": "608000000000000",
       "resolution": 4,
       "edgeOnlyNeighbors": [
-        "1e8000000000000",
-        "1f8000000000000",
-        "4f8000000000000",
-        "618000000000000"
+        "4e8000000000000",
+        "618000000000000",
+        "648000000000000"
       ],
       "supersetNeighbors": [
-        "188000000000000",
-        "1e8000000000000",
-        "1f8000000000000",
-        "218000000000000",
-        "4a8000000000000",
         "4c8000000000000",
         "4d8000000000000",
-        "4f8000000000000",
+        "4e8000000000000",
+        "5e8000000000000",
+        "5f8000000000000",
         "618000000000000",
-        "628000000000000",
-        "648000000000000"
+        "638000000000000",
+        "648000000000000",
+        "658000000000000",
+        "668000000000000",
+        "678000000000000",
+        "6d8000000000000"
       ]
     },
     {
       "cell": "7f8000000000000",
       "resolution": 4,
       "edgeOnlyNeighbors": [
-        "7d8000000000000",
+        "7e8000000000000",
         "8008000000000000",
         "808000000000000"
       ],
@@ -844,7 +844,7 @@
       "resolution": 4,
       "edgeOnlyNeighbors": [
         "1ff8000000000000",
-        "2028000000000000",
+        "2018000000000000",
         "2958000000000000"
       ],
       "supersetNeighbors": [
@@ -862,23 +862,23 @@
       "cell": "2208000000000000",
       "resolution": 4,
       "edgeOnlyNeighbors": [
-        "20f8000000000000",
-        "2108000000000000",
+        "2128000000000000",
         "2218000000000000",
-        "2908000000000000"
+        "2248000000000000"
       ],
       "supersetNeighbors": [
-        "20d8000000000000",
-        "20e8000000000000",
-        "20f8000000000000",
         "2108000000000000",
         "2118000000000000",
         "2128000000000000",
+        "21e8000000000000",
+        "21f8000000000000",
         "2218000000000000",
-        "2228000000000000",
+        "2238000000000000",
         "2248000000000000",
-        "2908000000000000",
-        "2a08000000000000"
+        "2258000000000000",
+        "2268000000000000",
+        "2278000000000000",
+        "2318000000000000"
       ]
     },
     {
@@ -931,10 +931,10 @@
       "edgeOnlyNeighbors": [
         "31f8000000000000",
         "3218000000000000",
-        "32a8000000000000"
+        "32b8000000000000"
       ],
       "supersetNeighbors": [
-        "3158000000000000",
+        "3178000000000000",
         "3188000000000000",
         "31d8000000000000",
         "31e8000000000000",
@@ -944,8 +944,8 @@
         "3278000000000000",
         "3288000000000000",
         "3298000000000000",
-        "32a8000000000000",
-        "32f8000000000000"
+        "32b8000000000000",
+        "32c8000000000000"
       ]
     },
     {
@@ -962,7 +962,7 @@
         "33d8000000000000",
         "33e8000000000000",
         "3408000000000000",
-        "3428000000000000",
+        "3418000000000000",
         "bc08000000000000",
         "bc18000000000000",
         "bc38000000000000"
@@ -973,7 +973,7 @@
       "resolution": 4,
       "edgeOnlyNeighbors": [
         "3558000000000000",
-        "3c28000000000000",
+        "3c18000000000000",
         "4ea8000000000000"
       ],
       "supersetNeighbors": [
@@ -991,23 +991,23 @@
       "cell": "3e08000000000000",
       "resolution": 4,
       "edgeOnlyNeighbors": [
-        "3508000000000000",
-        "3cf8000000000000",
-        "3d08000000000000",
-        "3e18000000000000"
+        "3d28000000000000",
+        "3e18000000000000",
+        "3e48000000000000"
       ],
       "supersetNeighbors": [
-        "3508000000000000",
-        "3608000000000000",
-        "3cd8000000000000",
-        "3ce8000000000000",
-        "3cf8000000000000",
         "3d08000000000000",
         "3d18000000000000",
         "3d28000000000000",
+        "3de8000000000000",
+        "3df8000000000000",
         "3e18000000000000",
-        "3e28000000000000",
-        "3e48000000000000"
+        "3e38000000000000",
+        "3e48000000000000",
+        "3e58000000000000",
+        "3e68000000000000",
+        "3e78000000000000",
+        "3f18000000000000"
       ]
     },
     {
@@ -1028,7 +1028,7 @@
         "4008000000000000",
         "4008000000000000",
         "4018000000000000",
-        "4078000000000000",
+        "4048000000000000",
         "4658000000000000",
         "4bf8000000000000",
         "4c08000000000000",
@@ -1039,13 +1039,13 @@
       "cell": "5c08000000000000",
       "resolution": 4,
       "edgeOnlyNeighbors": [
-        "27d8000000000000",
+        "27e8000000000000",
         "27f8000000000000",
         "5bf8000000000000",
         "5c28000000000000"
       ],
       "supersetNeighbors": [
-        "27d8000000000000",
+        "27c8000000000000",
         "27e8000000000000",
         "27f8000000000000",
         "5be8000000000000",
@@ -1059,23 +1059,23 @@
       "cell": "5e08000000000000",
       "resolution": 4,
       "edgeOnlyNeighbors": [
-        "5e28000000000000",
+        "5e18000000000000",
         "5e58000000000000",
-        "5fa8000000000000"
+        "60b8000000000000",
+        "60c8000000000000"
       ],
       "supersetNeighbors": [
+        "5df8000000000000",
         "5e18000000000000",
         "5e28000000000000",
         "5e38000000000000",
         "5e48000000000000",
         "5e58000000000000",
         "5e68000000000000",
-        "5ef8000000000000",
-        "5f08000000000000",
-        "5f78000000000000",
-        "5f98000000000000",
-        "5fa8000000000000",
-        "5fb8000000000000"
+        "60a8000000000000",
+        "60b8000000000000",
+        "60c8000000000000",
+        "6258000000000000"
       ]
     },
     {
@@ -1096,7 +1096,7 @@
         "59a8000000000000",
         "59b8000000000000",
         "59c8000000000000",
-        "5f88000000000000",
+        "5fb8000000000000",
         "5fd8000000000000",
         "5fe8000000000000",
         "6008000000000000",
@@ -1119,7 +1119,7 @@
         "67f8000000000000",
         "6818000000000000",
         "6828000000000000",
-        "6878000000000000",
+        "6848000000000000",
         "6e38000000000000",
         "6e48000000000000",
         "6e58000000000000",
@@ -1133,7 +1133,7 @@
       "resolution": 4,
       "edgeOnlyNeighbors": [
         "6468000000000000",
-        "69b8000000000000",
+        "69a8000000000000",
         "6a18000000000000"
       ],
       "supersetNeighbors": [
@@ -1141,8 +1141,8 @@
         "6738000000000000",
         "6988000000000000",
         "6998000000000000",
-        "69b8000000000000",
-        "69e8000000000000",
+        "69a8000000000000",
+        "69f8000000000000",
         "6a18000000000000",
         "6a28000000000000",
         "6a78000000000000"
@@ -1153,14 +1153,14 @@
       "resolution": 4,
       "edgeOnlyNeighbors": [
         "5008000000000000",
-        "5028000000000000",
+        "5018000000000000",
         "6bd8000000000000",
         "6c08000000000000"
       ],
       "supersetNeighbors": [
         "5008000000000000",
         "5018000000000000",
-        "5028000000000000",
+        "5038000000000000",
         "6bc8000000000000",
         "6bd8000000000000",
         "6be8000000000000",
@@ -1192,23 +1192,23 @@
       "cell": "8608000000000000",
       "resolution": 4,
       "edgeOnlyNeighbors": [
-        "8628000000000000",
+        "8618000000000000",
         "8658000000000000",
-        "87a8000000000000"
+        "88b8000000000000",
+        "88c8000000000000"
       ],
       "supersetNeighbors": [
+        "85f8000000000000",
         "8618000000000000",
         "8628000000000000",
         "8638000000000000",
         "8648000000000000",
         "8658000000000000",
         "8668000000000000",
-        "86f8000000000000",
-        "8708000000000000",
-        "8778000000000000",
-        "8798000000000000",
-        "87a8000000000000",
-        "87b8000000000000"
+        "88a8000000000000",
+        "88b8000000000000",
+        "88c8000000000000",
+        "8a58000000000000"
       ]
     },
     {
@@ -1229,7 +1229,7 @@
         "81a8000000000000",
         "81b8000000000000",
         "81c8000000000000",
-        "8788000000000000",
+        "87b8000000000000",
         "87d8000000000000",
         "87e8000000000000",
         "8808000000000000",
@@ -1260,23 +1260,23 @@
       "cell": "9a08000000000000",
       "resolution": 4,
       "edgeOnlyNeighbors": [
-        "9a28000000000000",
+        "9a18000000000000",
         "9a58000000000000",
-        "9ba8000000000000"
+        "9cb8000000000000",
+        "9cc8000000000000"
       ],
       "supersetNeighbors": [
+        "99f8000000000000",
         "9a18000000000000",
         "9a28000000000000",
         "9a38000000000000",
         "9a48000000000000",
         "9a58000000000000",
         "9a68000000000000",
-        "9af8000000000000",
-        "9b08000000000000",
-        "9b78000000000000",
-        "9b98000000000000",
-        "9ba8000000000000",
-        "9bb8000000000000"
+        "9ca8000000000000",
+        "9cb8000000000000",
+        "9cc8000000000000",
+        "9e58000000000000"
       ]
     },
     {
@@ -1297,7 +1297,7 @@
         "95a8000000000000",
         "95b8000000000000",
         "95c8000000000000",
-        "9b88000000000000",
+        "9bb8000000000000",
         "9bd8000000000000",
         "9be8000000000000",
         "9c08000000000000",
@@ -1329,10 +1329,10 @@
       "edgeOnlyNeighbors": [
         "a9f8000000000000",
         "aa18000000000000",
-        "aaa8000000000000"
+        "aab8000000000000"
       ],
       "supersetNeighbors": [
-        "a958000000000000",
+        "a978000000000000",
         "a988000000000000",
         "a9d8000000000000",
         "a9e8000000000000",
@@ -1342,8 +1342,8 @@
         "aa78000000000000",
         "aa88000000000000",
         "aa98000000000000",
-        "aaa8000000000000",
-        "aaf8000000000000"
+        "aab8000000000000",
+        "aac8000000000000"
       ]
     },
     {
@@ -1351,32 +1351,32 @@
       "resolution": 4,
       "edgeOnlyNeighbors": [
         "7008000000000000",
-        "7028000000000000",
+        "7018000000000000",
         "abd8000000000000",
         "ac08000000000000"
       ],
       "supersetNeighbors": [
         "7008000000000000",
         "7018000000000000",
-        "7028000000000000",
+        "7038000000000000",
         "abc8000000000000",
         "abd8000000000000",
         "abe8000000000000",
         "ac08000000000000",
-        "ac28000000000000"
+        "ac18000000000000"
       ]
     },
     {
       "cell": "b408000000000000",
       "resolution": 4,
       "edgeOnlyNeighbors": [
-        "b3d8000000000000",
+        "b3e8000000000000",
         "b3f8000000000000",
         "b428000000000000",
         "baa8000000000000"
       ],
       "supersetNeighbors": [
-        "b3d8000000000000",
+        "b3c8000000000000",
         "b3e8000000000000",
         "b3f8000000000000",
         "b418000000000000",
@@ -1390,23 +1390,23 @@
       "cell": "b608000000000000",
       "resolution": 4,
       "edgeOnlyNeighbors": [
-        "b628000000000000",
+        "b618000000000000",
         "b658000000000000",
-        "b7a8000000000000"
+        "c4b8000000000000",
+        "c4c8000000000000"
       ],
       "supersetNeighbors": [
+        "b5f8000000000000",
         "b618000000000000",
         "b628000000000000",
         "b638000000000000",
         "b648000000000000",
         "b658000000000000",
         "b668000000000000",
-        "b6f8000000000000",
-        "b708000000000000",
-        "b778000000000000",
-        "b798000000000000",
-        "b7a8000000000000",
-        "b7b8000000000000"
+        "c4a8000000000000",
+        "c4b8000000000000",
+        "c4c8000000000000",
+        "c658000000000000"
       ]
     },
     {
@@ -1421,13 +1421,13 @@
         "c408000000000000"
       ],
       "supersetNeighbors": [
-        "b788000000000000",
+        "b7b8000000000000",
         "b7d8000000000000",
         "b7e8000000000000",
         "b808000000000000",
         "b808000000000000",
         "b818000000000000",
-        "b878000000000000",
+        "b848000000000000",
         "be58000000000000",
         "c3f8000000000000",
         "c408000000000000",
@@ -1459,10 +1459,10 @@
       "edgeOnlyNeighbors": [
         "d1f8000000000000",
         "d218000000000000",
-        "d2a8000000000000"
+        "d2b8000000000000"
       ],
       "supersetNeighbors": [
-        "d158000000000000",
+        "d178000000000000",
         "d188000000000000",
         "d1d8000000000000",
         "d1e8000000000000",
@@ -1472,8 +1472,8 @@
         "d278000000000000",
         "d288000000000000",
         "d298000000000000",
-        "d2a8000000000000",
-        "d2f8000000000000"
+        "d2b8000000000000",
+        "d2c8000000000000"
       ]
     },
     {
@@ -1493,7 +1493,7 @@
         "d3d8000000000000",
         "d3e8000000000000",
         "d408000000000000",
-        "d428000000000000"
+        "d418000000000000"
       ]
     },
     {
@@ -1501,7 +1501,7 @@
       "resolution": 4,
       "edgeOnlyNeighbors": [
         "1bf8000000000000",
-        "dc28000000000000",
+        "dc18000000000000",
         "e2a8000000000000"
       ],
       "supersetNeighbors": [
@@ -1519,23 +1519,23 @@
       "cell": "de08000000000000",
       "resolution": 4,
       "edgeOnlyNeighbors": [
-        "1b08000000000000",
-        "dcf8000000000000",
-        "dd08000000000000",
-        "de18000000000000"
+        "dd28000000000000",
+        "de18000000000000",
+        "de48000000000000"
       ],
       "supersetNeighbors": [
-        "1958000000000000",
-        "1b08000000000000",
-        "dcd8000000000000",
-        "dce8000000000000",
-        "dcf8000000000000",
         "dd08000000000000",
         "dd18000000000000",
         "dd28000000000000",
+        "dde8000000000000",
+        "ddf8000000000000",
         "de18000000000000",
-        "de28000000000000",
-        "de48000000000000"
+        "de38000000000000",
+        "de48000000000000",
+        "de58000000000000",
+        "de68000000000000",
+        "de78000000000000",
+        "df18000000000000"
       ]
     },
     {
@@ -1576,7 +1576,7 @@
       ],
       "supersetNeighbors": [
         "11aa800000000000",
-        "3f8800000000000",
+        "3fb800000000000",
         "3fe800000000000",
         "3ff800000000000",
         "3ff800000000000",
@@ -1592,30 +1592,30 @@
       "cell": "600800000000000",
       "resolution": 6,
       "edgeOnlyNeighbors": [
-        "1fe800000000000",
-        "1ff800000000000",
-        "4ff800000000000",
-        "601800000000000"
+        "4e5800000000000",
+        "601800000000000",
+        "615800000000000"
       ],
       "supersetNeighbors": [
-        "1f8800000000000",
-        "1fe800000000000",
-        "1ff800000000000",
-        "215800000000000",
-        "4aa800000000000",
-        "4fc800000000000",
-        "4fd800000000000",
-        "4ff800000000000",
+        "4e3800000000000",
+        "4e4800000000000",
+        "4e5800000000000",
+        "5ea800000000000",
+        "5ff800000000000",
         "601800000000000",
         "602800000000000",
-        "604800000000000"
+        "603800000000000",
+        "614800000000000",
+        "615800000000000",
+        "617800000000000",
+        "6da800000000000"
       ]
     },
     {
       "cell": "7ff800000000000",
       "resolution": 6,
       "edgeOnlyNeighbors": [
-        "7fd800000000000",
+        "7fe800000000000",
         "8000800000000000",
         "800800000000000"
       ],
@@ -1635,7 +1635,7 @@
       "resolution": 6,
       "edgeOnlyNeighbors": [
         "1fff800000000000",
-        "2002800000000000",
+        "2001800000000000",
         "2955800000000000"
       ],
       "supersetNeighbors": [
@@ -1653,23 +1653,23 @@
       "cell": "2200800000000000",
       "resolution": 6,
       "edgeOnlyNeighbors": [
-        "20ff800000000000",
-        "2100800000000000",
+        "2125800000000000",
         "2201800000000000",
-        "2900800000000000"
+        "2215800000000000"
       ],
       "supersetNeighbors": [
-        "20fd800000000000",
-        "20fe800000000000",
-        "20ff800000000000",
-        "2100800000000000",
-        "2101800000000000",
-        "2102800000000000",
+        "2123800000000000",
+        "2124800000000000",
+        "2125800000000000",
+        "21ea800000000000",
+        "21ff800000000000",
         "2201800000000000",
         "2202800000000000",
-        "2204800000000000",
-        "2900800000000000",
-        "2a00800000000000"
+        "2203800000000000",
+        "2214800000000000",
+        "2215800000000000",
+        "2217800000000000",
+        "231a800000000000"
       ]
     },
     {
@@ -1722,21 +1722,21 @@
       "edgeOnlyNeighbors": [
         "31ff800000000000",
         "3201800000000000",
-        "32aa800000000000"
+        "32bf800000000000"
       ],
       "supersetNeighbors": [
-        "3155800000000000",
+        "317f800000000000",
         "3180800000000000",
         "31fd800000000000",
         "31fe800000000000",
         "31ff800000000000",
         "3201800000000000",
         "3202800000000000",
-        "3207800000000000",
-        "32a8800000000000",
-        "32a9800000000000",
-        "32aa800000000000",
-        "32ff800000000000"
+        "3204800000000000",
+        "32bd800000000000",
+        "32be800000000000",
+        "32bf800000000000",
+        "32c0800000000000"
       ]
     },
     {
@@ -1753,7 +1753,7 @@
         "33fd800000000000",
         "33fe800000000000",
         "3400800000000000",
-        "3402800000000000",
+        "3401800000000000",
         "bc00800000000000",
         "bc01800000000000",
         "bc03800000000000"
@@ -1764,7 +1764,7 @@
       "resolution": 6,
       "edgeOnlyNeighbors": [
         "3555800000000000",
-        "3c02800000000000",
+        "3c01800000000000",
         "4eaa800000000000"
       ],
       "supersetNeighbors": [
@@ -1782,23 +1782,23 @@
       "cell": "3e00800000000000",
       "resolution": 6,
       "edgeOnlyNeighbors": [
-        "3500800000000000",
-        "3cff800000000000",
-        "3d00800000000000",
-        "3e01800000000000"
+        "3d25800000000000",
+        "3e01800000000000",
+        "3e15800000000000"
       ],
       "supersetNeighbors": [
-        "3500800000000000",
-        "3600800000000000",
-        "3cfd800000000000",
-        "3cfe800000000000",
-        "3cff800000000000",
-        "3d00800000000000",
-        "3d01800000000000",
-        "3d02800000000000",
+        "3d23800000000000",
+        "3d24800000000000",
+        "3d25800000000000",
+        "3dea800000000000",
+        "3dff800000000000",
         "3e01800000000000",
         "3e02800000000000",
-        "3e04800000000000"
+        "3e03800000000000",
+        "3e14800000000000",
+        "3e15800000000000",
+        "3e17800000000000",
+        "3f1a800000000000"
       ]
     },
     {
@@ -1819,7 +1819,7 @@
         "4000800000000000",
         "4000800000000000",
         "4001800000000000",
-        "4007800000000000",
+        "4004800000000000",
         "4655800000000000",
         "4bff800000000000",
         "4c00800000000000",
@@ -1830,13 +1830,13 @@
       "cell": "5c00800000000000",
       "resolution": 6,
       "edgeOnlyNeighbors": [
-        "27fd800000000000",
+        "27fe800000000000",
         "27ff800000000000",
         "5bff800000000000",
         "5c02800000000000"
       ],
       "supersetNeighbors": [
-        "27fd800000000000",
+        "27fc800000000000",
         "27fe800000000000",
         "27ff800000000000",
         "5bfe800000000000",
@@ -1850,23 +1850,23 @@
       "cell": "5e00800000000000",
       "resolution": 6,
       "edgeOnlyNeighbors": [
-        "5e02800000000000",
+        "5e01800000000000",
         "5e55800000000000",
-        "5faa800000000000"
+        "60bf800000000000",
+        "60c0800000000000"
       ],
       "supersetNeighbors": [
+        "5dff800000000000",
         "5e01800000000000",
         "5e02800000000000",
         "5e03800000000000",
         "5e54800000000000",
         "5e55800000000000",
         "5e56800000000000",
-        "5eff800000000000",
-        "5f00800000000000",
-        "5f7f800000000000",
-        "5fa9800000000000",
-        "5faa800000000000",
-        "5fab800000000000"
+        "60be800000000000",
+        "60bf800000000000",
+        "60c0800000000000",
+        "6255800000000000"
       ]
     },
     {
@@ -1887,7 +1887,7 @@
         "59aa800000000000",
         "59ab800000000000",
         "59ac800000000000",
-        "5ff8800000000000",
+        "5ffb800000000000",
         "5ffd800000000000",
         "5ffe800000000000",
         "6000800000000000",
@@ -1910,7 +1910,7 @@
         "67ff800000000000",
         "6801800000000000",
         "6802800000000000",
-        "6807800000000000",
+        "6804800000000000",
         "6e53800000000000",
         "6e54800000000000",
         "6e55800000000000",
@@ -1924,19 +1924,19 @@
       "resolution": 6,
       "edgeOnlyNeighbors": [
         "646a800000000000",
-        "69bf800000000000",
+        "69aa800000000000",
         "6a01800000000000"
       ],
       "supersetNeighbors": [
         "646a800000000000",
         "673f800000000000",
-        "69bc800000000000",
-        "69bd800000000000",
-        "69bf800000000000",
-        "69ea800000000000",
+        "69a8800000000000",
+        "69a9800000000000",
+        "69aa800000000000",
+        "69ff800000000000",
         "6a01800000000000",
         "6a02800000000000",
-        "6a07800000000000"
+        "6a04800000000000"
       ]
     },
     {
@@ -1944,14 +1944,14 @@
       "resolution": 6,
       "edgeOnlyNeighbors": [
         "5000800000000000",
-        "5002800000000000",
+        "5001800000000000",
         "6bfd800000000000",
         "6c00800000000000"
       ],
       "supersetNeighbors": [
         "5000800000000000",
         "5001800000000000",
-        "5002800000000000",
+        "5003800000000000",
         "6bfc800000000000",
         "6bfd800000000000",
         "6bfe800000000000",
@@ -1983,23 +1983,23 @@
       "cell": "8600800000000000",
       "resolution": 6,
       "edgeOnlyNeighbors": [
-        "8602800000000000",
+        "8601800000000000",
         "8655800000000000",
-        "87aa800000000000"
+        "88bf800000000000",
+        "88c0800000000000"
       ],
       "supersetNeighbors": [
+        "85ff800000000000",
         "8601800000000000",
         "8602800000000000",
         "8603800000000000",
         "8654800000000000",
         "8655800000000000",
         "8656800000000000",
-        "86ff800000000000",
-        "8700800000000000",
-        "877f800000000000",
-        "87a9800000000000",
-        "87aa800000000000",
-        "87ab800000000000"
+        "88be800000000000",
+        "88bf800000000000",
+        "88c0800000000000",
+        "8a55800000000000"
       ]
     },
     {
@@ -2020,7 +2020,7 @@
         "81aa800000000000",
         "81ab800000000000",
         "81ac800000000000",
-        "87f8800000000000",
+        "87fb800000000000",
         "87fd800000000000",
         "87fe800000000000",
         "8800800000000000",
@@ -2051,23 +2051,23 @@
       "cell": "9a00800000000000",
       "resolution": 6,
       "edgeOnlyNeighbors": [
-        "9a02800000000000",
+        "9a01800000000000",
         "9a55800000000000",
-        "9baa800000000000"
+        "9cbf800000000000",
+        "9cc0800000000000"
       ],
       "supersetNeighbors": [
+        "99ff800000000000",
         "9a01800000000000",
         "9a02800000000000",
         "9a03800000000000",
         "9a54800000000000",
         "9a55800000000000",
         "9a56800000000000",
-        "9aff800000000000",
-        "9b00800000000000",
-        "9b7f800000000000",
-        "9ba9800000000000",
-        "9baa800000000000",
-        "9bab800000000000"
+        "9cbe800000000000",
+        "9cbf800000000000",
+        "9cc0800000000000",
+        "9e55800000000000"
       ]
     },
     {
@@ -2088,7 +2088,7 @@
         "95aa800000000000",
         "95ab800000000000",
         "95ac800000000000",
-        "9bf8800000000000",
+        "9bfb800000000000",
         "9bfd800000000000",
         "9bfe800000000000",
         "9c00800000000000",
@@ -2120,21 +2120,21 @@
       "edgeOnlyNeighbors": [
         "a9ff800000000000",
         "aa01800000000000",
-        "aaaa800000000000"
+        "aabf800000000000"
       ],
       "supersetNeighbors": [
-        "a955800000000000",
+        "a97f800000000000",
         "a980800000000000",
         "a9fd800000000000",
         "a9fe800000000000",
         "a9ff800000000000",
         "aa01800000000000",
         "aa02800000000000",
-        "aa07800000000000",
-        "aaa8800000000000",
-        "aaa9800000000000",
-        "aaaa800000000000",
-        "aaff800000000000"
+        "aa04800000000000",
+        "aabd800000000000",
+        "aabe800000000000",
+        "aabf800000000000",
+        "aac0800000000000"
       ]
     },
     {
@@ -2142,32 +2142,32 @@
       "resolution": 6,
       "edgeOnlyNeighbors": [
         "7000800000000000",
-        "7002800000000000",
+        "7001800000000000",
         "abfd800000000000",
         "ac00800000000000"
       ],
       "supersetNeighbors": [
         "7000800000000000",
         "7001800000000000",
-        "7002800000000000",
+        "7003800000000000",
         "abfc800000000000",
         "abfd800000000000",
         "abfe800000000000",
         "ac00800000000000",
-        "ac02800000000000"
+        "ac01800000000000"
       ]
     },
     {
       "cell": "b400800000000000",
       "resolution": 6,
       "edgeOnlyNeighbors": [
-        "b3fd800000000000",
+        "b3fe800000000000",
         "b3ff800000000000",
         "b402800000000000",
         "baaa800000000000"
       ],
       "supersetNeighbors": [
-        "b3fd800000000000",
+        "b3fc800000000000",
         "b3fe800000000000",
         "b3ff800000000000",
         "b401800000000000",
@@ -2181,23 +2181,23 @@
       "cell": "b600800000000000",
       "resolution": 6,
       "edgeOnlyNeighbors": [
-        "b602800000000000",
+        "b601800000000000",
         "b655800000000000",
-        "b7aa800000000000"
+        "c4bf800000000000",
+        "c4c0800000000000"
       ],
       "supersetNeighbors": [
+        "b5ff800000000000",
         "b601800000000000",
         "b602800000000000",
         "b603800000000000",
         "b654800000000000",
         "b655800000000000",
         "b656800000000000",
-        "b6ff800000000000",
-        "b700800000000000",
-        "b77f800000000000",
-        "b7a9800000000000",
-        "b7aa800000000000",
-        "b7ab800000000000"
+        "c4be800000000000",
+        "c4bf800000000000",
+        "c4c0800000000000",
+        "c655800000000000"
       ]
     },
     {
@@ -2212,13 +2212,13 @@
         "c400800000000000"
       ],
       "supersetNeighbors": [
-        "b7f8800000000000",
+        "b7fb800000000000",
         "b7fd800000000000",
         "b7fe800000000000",
         "b800800000000000",
         "b800800000000000",
         "b801800000000000",
-        "b807800000000000",
+        "b804800000000000",
         "be55800000000000",
         "c3ff800000000000",
         "c400800000000000",
@@ -2250,21 +2250,21 @@
       "edgeOnlyNeighbors": [
         "d1ff800000000000",
         "d201800000000000",
-        "d2aa800000000000"
+        "d2bf800000000000"
       ],
       "supersetNeighbors": [
-        "d155800000000000",
+        "d17f800000000000",
         "d180800000000000",
         "d1fd800000000000",
         "d1fe800000000000",
         "d1ff800000000000",
         "d201800000000000",
         "d202800000000000",
-        "d207800000000000",
-        "d2a8800000000000",
-        "d2a9800000000000",
-        "d2aa800000000000",
-        "d2ff800000000000"
+        "d204800000000000",
+        "d2bd800000000000",
+        "d2be800000000000",
+        "d2bf800000000000",
+        "d2c0800000000000"
       ]
     },
     {
@@ -2284,7 +2284,7 @@
         "d3fd800000000000",
         "d3fe800000000000",
         "d400800000000000",
-        "d402800000000000"
+        "d401800000000000"
       ]
     },
     {
@@ -2292,7 +2292,7 @@
       "resolution": 6,
       "edgeOnlyNeighbors": [
         "1bff800000000000",
-        "dc02800000000000",
+        "dc01800000000000",
         "e2aa800000000000"
       ],
       "supersetNeighbors": [
@@ -2310,23 +2310,23 @@
       "cell": "de00800000000000",
       "resolution": 6,
       "edgeOnlyNeighbors": [
-        "1b00800000000000",
-        "dcff800000000000",
-        "dd00800000000000",
-        "de01800000000000"
+        "dd25800000000000",
+        "de01800000000000",
+        "de15800000000000"
       ],
       "supersetNeighbors": [
-        "1955800000000000",
-        "1b00800000000000",
-        "dcfd800000000000",
-        "dcfe800000000000",
-        "dcff800000000000",
-        "dd00800000000000",
-        "dd01800000000000",
-        "dd02800000000000",
+        "dd23800000000000",
+        "dd24800000000000",
+        "dd25800000000000",
+        "ddea800000000000",
+        "ddff800000000000",
         "de01800000000000",
         "de02800000000000",
-        "de04800000000000"
+        "de03800000000000",
+        "de14800000000000",
+        "de15800000000000",
+        "de17800000000000",
+        "df1a800000000000"
       ]
     },
     {
diff --git a/tests/fixtures/traversal/line.json b/tests/fixtures/traversal/line.json
index 00b9122..ac109b8 100644
--- a/tests/fixtures/traversal/line.json
+++ b/tests/fixtures/traversal/line.json
@@ -13,7 +13,7 @@
       "resolution": 3,
       "cells": [
         "5160000000000000",
-        "6360000000000000",
+        "63a0000000000000",
         "63e0000000000000"
       ]
     },
@@ -31,7 +31,7 @@
       "cells": [
         "5160000000000000",
         "6320000000000000",
-        "6360000000000000",
+        "63a0000000000000",
         "63e0000000000000",
         "6a60000000000000",
         "6ae0000000000000"
@@ -66,10 +66,10 @@
       ],
       "resolution": 3,
       "cells": [
-        "4de0000000000000",
+        "4da0000000000000",
         "4f20000000000000",
-        "4fa0000000000000",
-        "55e0000000000000",
+        "4f60000000000000",
+        "55a0000000000000",
         "56e0000000000000"
       ]
     }
diff --git a/tests/fixtures/traversal/quintant-neighbors.json b/tests/fixtures/traversal/quintant-neighbors.json
index 9404227..c8660ad 100644
--- a/tests/fixtures/traversal/quintant-neighbors.json
+++ b/tests/fixtures/traversal/quintant-neighbors.json
@@ -22,11 +22,11 @@
       "neighbors": [
         1633,
         1634,
-        1636,
+        1635,
         1637,
         1639,
         1640,
-        1643
+        1641
       ]
     }
   },
@@ -74,13 +74,13 @@
     },
     "output": {
       "neighbors": [
-        6545,
-        6551,
+        6532,
+        6542,
+        6546,
+        6547,
+        6548,
         6552,
-        6554,
-        6555,
-        6557,
-        6559
+        6554
       ]
     }
   },
@@ -92,9 +92,9 @@
     },
     "output": {
       "neighbors": [
-        7164,
-        7167,
-        7850,
+        6824,
+        6826,
+        8191,
         8193,
         8194
       ]
@@ -109,12 +109,12 @@
     "output": {
       "neighbors": [
         9825,
-        9826,
+        9827,
         9828,
         9829,
         9831,
         9832,
-        9835
+        9838
       ]
     }
   },
@@ -162,13 +162,13 @@
     },
     "output": {
       "neighbors": [
-        14737,
-        14743,
         14744,
         14746,
         14747,
-        14749,
-        14751
+        14748,
+        14750,
+        14768,
+        14771
       ]
     }
   },
@@ -198,8 +198,8 @@
         1635,
         1637,
         1639,
-        1641,
-        1643
+        1640,
+        1641
       ]
     }
   },
@@ -211,13 +211,13 @@
     },
     "output": {
       "neighbors": [
+        3275,
         3277,
-        3278,
-        3288,
-        3290,
-        3291,
-        3300,
-        3310
+        3319,
+        3320,
+        3321,
+        3340,
+        3369
       ]
     }
   },
@@ -229,13 +229,13 @@
     },
     "output": {
       "neighbors": [
+        4822,
+        4851,
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diff --git a/tests/fixtures/utils/spiral.json b/tests/fixtures/utils/spiral.json
deleted file mode 100644
index 31770e0..0000000
--- a/tests/fixtures/utils/spiral.json
+++ /dev/null
@@ -1,922 +0,0 @@
-{
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diff --git a/tests/integration/wireframe-3.json b/tests/integration/wireframe-3.json
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-              -145.61520822696104,
-              46.60932193274887
+              -152.0087582438406,
+              51.12807443480634
             ],
             [
-              -144.74293125805139,
-              46.756198837044806
+              -152.9540672119913,
+              50.91472948513698
             ],
             [
-              -143.86702278062,
-              46.89667247174303
+              -153.89205207105528,
+              50.69377429821495
             ],
             [
-              -142.98758168987519,
-              47.03075109682092
+              -154.82256605115367,
+              50.465219688039035
             ],
             [
-              -142.10471019533935,
-              47.15844040167466
+              -155.7454673689292,
+              50.229073601655884
             ],
             [
-              -141.21851395810796,
-              47.27974378301808
+              -156.66061855951767,
+              49.98534085570773
             ],
             [
-              -141.0506089790597,
-              47.98921558777709
+              -156.60045858158878,
+              49.29460316147575
             ],
             [
-              -140.87813044011978,
-              48.6968441966417
+              -156.54088762277502,
+              48.6039329348543
             ],
             [
-              -140.70050365740485,
-              49.402774078529035
+              -156.48190919660408,
+              47.9132427497043
             ],
             [
-              -140.5171561508107,
-              50.10713576802993
+              -156.4235343032019,
+              47.22243799460534
             ],
             [
-              -140.32751179067782,
-              50.810046923517156
+              -156.3657824309405,
+              46.531415695053745
             ],
             [
-              -140.13098527901042,
-              51.51161323229016
+              -156.30868284768877,
+              45.840063112265945
             ],
             [
-              -139.92697684018043,
-              52.21192917541767
+              -156.2522762571985,
+              45.148256067705866
             ],
             [
-              -139.71486701004198,
-              52.911078663009754
+              -156.19661692139545,
+              44.45585692899723
             ],
             [
-              -140.37881947546748,
-              53.42362989311592
+              -155.4742514798952,
+              44.041723240624385
             ],
             [
-              -141.0598296397934,
-              53.93135891202086
+              -154.7642821190119,
+              43.61923501944753
             ],
             [
-              -141.7582040682572,
-              54.43416919789364
+              -154.06707780197257,
+              43.18831419682945
             ],
             [
-              -142.4742705834014,
-              54.93196003118566
+              -153.38304575010704,
+              42.748880612430085
             ],
             [
-              -143.20837781059504,
-              55.42462607672502
+              -152.71263548465095,
+              42.300852917166665
             ],
             [
-              -143.9608946579056,
-              55.91205696943879
+              -152.05634317840753,
+              41.84414965820928
             ],
             [
-              -144.73220971607952,
-              56.39413690370067
+              -151.41471633508786,
+              41.378690571860965
             ],
             [
-              -145.52273056293836,
-              56.870744226531954
+              -150.7883588121141,
+              40.90439811308672
             ]
           ]
         ]
@@ -169577,168 +169577,168 @@
         "coordinates": [
           [
             [
-              -150.7883588121141,
-              40.90439811308672
+              -145.52273056293836,
+              56.870744226531954
             ],
             [
-              -150.49003910703863,
-              41.563053366076964
+              -146.03155804156165,
+              56.23106135195437
             ],
             [
-              -150.18575101123452,
-              42.219972056995324
+              -146.52197066091344,
+              55.59010253185378
             ],
             [
-              -149.87503610359084,
-              42.87526886648155
+              -146.9949904303187,
+              54.94796442830572
             ],
             [
-              -149.5574445136166,
-              43.52903798879164
+              -147.45157050749447,
+              54.304733607705074
             ],
             [
-              -149.23252900381146,
-              44.18135589124764
+              -147.8926006700807,
+              53.66048732174956
             ],
             [
-              -148.89984001832516,
-              44.83228351241983
+              -148.31891233900478,
+              53.01529419366314
             ],
             [
-              -148.55892143645326,
-              45.48186801122973
+              -148.7312831931066,
+              52.369214817076134
             ],
             [
-              -148.20930683638824,
-              46.13014415306687
+              -149.13044141230137,
+              51.722302273605706
             ],
             [
-              -148.31440673147188,
-              46.83472904063177
+              -149.0060224681937,
+              51.027615834712044
             ],
             [
-              -148.42267245217306,
-              47.53733544268485
+              -148.88410693022365,
+              50.33200986648408
             ],
             [
-              -148.5339127424558,
-              48.2381775027391
+              -148.76473582175356,
+              49.63534030556225
             ],
             [
               -148.6479740324002,
               48.93745201687548
             ],
             [
-              -148.76473582175356,
-              49.63534030556225
+              -148.5339127424558,
+              48.2381775027391
             ],
             [
-              -148.88410693022365,
-              50.33200986648408
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             ],
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-              -149.0060224681937,
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-              -149.13044141230137,
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             ],
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             [
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             ],
             [
-              -151.41471633508786,
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             ],
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-              -150.7883588121141,
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             ]
           ]
         ]
diff --git a/tests/lattice/curve.test.ts b/tests/lattice/curve.test.ts
index 5e8d489..33b9657 100644
--- a/tests/lattice/curve.test.ts
+++ b/tests/lattice/curve.test.ts
@@ -1,7 +1,7 @@
 import {describe, it, expect} from 'vitest';
 import type {IJ} from 'a5/core/coordinate-systems';
 import type {Orientation, Triple} from 'a5/lattice';
-import {sToCell, sToTriple, tripleToS, tripleParity, tripleInBounds, IJToS} from 'a5/lattice';
+import {roundToTriple, sToCell, sToTriple, tripleToS, tripleParity, tripleInBounds, tripleFlavor} from 'a5/lattice';
 import fixtures from '../fixtures/lattice/curve.json';
 
 type SToCellFixture = {
@@ -15,7 +15,7 @@ type SToCellFixture = {
   flavor: number;
 };
 
-type IJToSFixture = {
+type PointToSFixture = {
   i: number;
   j: number;
   resolution: number;
@@ -71,10 +71,10 @@ describe('tripleToS', () => {
   });
 });
 
-describe('IJToS', () => {
+describe('pointToS (roundToTriple + tripleToS)', () => {
   it('locates the containing cell of a fractional IJ point', () => {
-    for (const f of fixtures.IJToS as IJToSFixture[]) {
-      const s = IJToS([f.i, f.j] as IJ, f.resolution, f.orientation);
+    for (const f of fixtures.pointToS as PointToSFixture[]) {
+      const s = tripleToS(roundToTriple([f.i, f.j] as IJ, f.resolution), f.resolution, f.orientation);
       expect(Number(s), `s for (${f.i},${f.j}) res=${f.resolution} ori=${f.orientation}`).toBe(f.s);
     }
   });
@@ -88,3 +88,16 @@ describe('tripleInBounds', () => {
     }
   });
 });
+
+describe('tripleFlavor', () => {
+  it('matches the descent flavor for every cell (closed form)', () => {
+    // The pentagon flavor depends only on (parity, y mod 2); pin the closed
+    // form against the descent over all cells at res 6, two orientations.
+    for (const orientation of ['uv', 'wu'] as const) {
+      for (let s = 0n; s < 1n << 12n; s++) {
+        const cell = sToCell(s, 6, orientation);
+        expect(tripleFlavor(cell.triple)).toBe(cell.flavor);
+      }
+    }
+  });
+});
diff --git a/tests/lattice/lsystem.test.ts b/tests/lattice/lsystem.test.ts
index 4927330..c422fd7 100644
--- a/tests/lattice/lsystem.test.ts
+++ b/tests/lattice/lsystem.test.ts
@@ -2,7 +2,7 @@ import {describe, it, expect} from 'vitest';
 import type {IJ} from 'a5/core/coordinate-systems';
 import type {Orientation, Triple} from 'a5/lattice';
 import {sToCell, sToTriple, tripleToSLattice} from 'a5/lattice/lsystem';
-import {IJToS} from 'a5/lattice/curve';
+import {roundToTriple} from 'a5/lattice/curve';
 import fixtures from '../fixtures/lattice/lsystem.json';
 
 type SToCellFixture = {
@@ -16,7 +16,7 @@ type SToCellFixture = {
   flavor: number;
 };
 
-type IJToSFixture = {
+type PointToSFixture = {
   i: number;
   j: number;
   resolution: number;
@@ -59,10 +59,10 @@ describe('lsystem tripleToSLattice', () => {
   });
 });
 
-describe('lsystem IJToS', () => {
+describe('lsystem pointToS (roundToTriple + tripleToSLattice)', () => {
   it('locates the containing cell of a fractional IJ point', () => {
-    for (const f of fixtures.IJToS as IJToSFixture[]) {
-      const s = IJToS([f.i, f.j] as IJ, f.resolution, f.orientation);
+    for (const f of fixtures.pointToS as PointToSFixture[]) {
+      const s = tripleToSLattice(roundToTriple([f.i, f.j] as IJ, f.resolution), f.resolution, f.orientation);
       expect(Number(s), `s for (${f.i},${f.j}) res=${f.resolution} ori=${f.orientation}`).toBe(f.s);
     }
   });
diff --git a/tests/utils/spiral.test.ts b/tests/utils/spiral.test.ts
deleted file mode 100644
index 478e670..0000000
--- a/tests/utils/spiral.test.ts
+++ /dev/null
@@ -1,32 +0,0 @@
-import {describe, it, expect} from 'vitest';
-import {Spiral, SPIRAL_SAMPLE_COUNT} from 'a5/utils/spiral';
-import type {Cartesian, Spherical} from 'a5/core/coordinate-systems';
-import fixtures from '../fixtures/utils/spiral.json';
-import './matchers';
-
-type Fixture = {
-  name: string;
-  center: [number, number];
-  scaleRad: number;
-  sampleCount: number;
-  samples: number[][];
-};
-
-describe('Spiral', () => {
-  it('SPIRAL_SAMPLE_COUNT matches fixture', () => {
-    expect(SPIRAL_SAMPLE_COUNT).toBe((fixtures as any).sampleCount);
-  });
-
-  for (const f of (fixtures as any).spiral as Fixture[]) {
-    it(`${f.name}`, () => {
-      const center = f.center as unknown as Spherical;
-      const spiral = new Spiral(center, f.scaleRad);
-      const out = new Float64Array(3);
-      expect(f.sampleCount).toBe(SPIRAL_SAMPLE_COUNT);
-      for (let i = 0; i < SPIRAL_SAMPLE_COUNT; i++) {
-        spiral.sample(out as unknown as Cartesian, i);
-        expect([...out]).toBeCloseToArray(f.samples[i], 6);
-      }
-    });
-  }
-});