diff --git a/notes/issue-674-spiral-involution-20260908.md b/notes/issue-674-spiral-involution-20260908.md new file mode 100644 index 00000000..1f60265c --- /dev/null +++ b/notes/issue-674-spiral-involution-20260908.md @@ -0,0 +1,84 @@ +# #674 — Spiral involution vs cardinality-only cancellation in `both-same × both-same` + +**Date:** 2026-09-08 · **Machine:** local (Mac) · **Parent:** #650 · **Follows:** PR #668 · **Related:** #665, #651, #635, PRs #662 + +**Outcome (ticket vocabulary): `cardinality-only`, refined to config-wise cancellation — the rank-1 spiral class is self-coincident across the two colourings, so D = 0 needs no pairing and no counting.** Details below; every integer is exact. + +## 0. Provenance + +The joint census of PR #668 is **imported, not recomputed** (`results/issue674-spiral-involution/imported-issue668-axis-L{3,4}.json`, provenance in `imported-issue668-provenance.json`, fetched via the PR #668 file API). Integrity: the L=4 question-cell masses re-derive from the imported joints as `[120, 416, 448, 128, 8]` at k = 8..12, total 1120, matching the ticket text exactly. + +Fresh compute in this note (Mac-OK, integers only): + +- L=3 `2^9` stream dumping the 6 question-cell configs (`scripts/issue674_spiral_involution.py`, dump in `results/issue674-spiral-involution/axis-L3-spiral-dump.json`); +- L=4 `2^16` stream: **2.6 s wall clock** — seconds-scale, so permitted by the ticket gate; actions of 56 candidate torus maps on the 1120-config cell (`results/issue674-spiral-involution/axis-L4-spiral-actions.json`); +- L=5 (`2^25`): **not run — NEED_HUAWEI.** + +## 1. The colour-flip kill at L=4 (recorded first, as instructed) + +Colour-flip C ↦ C̄ preserves k only at k = N/2. It would force the L=4 cell masses palindromic under k ↔ 16−k: + +| k | mass | mirror k′ = 16−k | mirror mass | +|---|------|------------------|-------------| +| 8 | 120 | 8 | 120 | +| 9 | 416 | 7 | 0 | +| 10 | 448 | 6 | 0 | +| 11 | 128 | 5 | 0 | +| 12 | 8 | 4 | 0 | + +`[120, 416, 448, 128, 8]` is **not palindromic** → **colour-flip is dead as the D = 0 mechanism at L=4.** The L=3 survival (single mass at k = 6 = 9/2 … at k = 6 = N/2·(9/2 is not integer; the point is k = 6 = N − 3 and the window is the single point k = 6) was a small-L accident of the window position, not a mechanism. + +Structural form of the kill (verified, L=3 and L=4): a **black** rank-1 `both-same` spiral on the primal (NN) lattice needs k ≥ 2L sites (min k: 6 at L=3, 8 at L=4 — brute-forced over the full 2^N), so its complement has k′ = N − k ≤ N − 2L < 2L for L = 3 (N = 9 < 4L = 12: always) and for all k > 8 at L=4. Concretely at L=3, the complement of each of the 6 spirals has black side label `none` (rank 0) and white side `both-same` **rank 2** — colour-flip does not even preserve rank-1 × rank-1, at any L tested. The palindromic failure is the observable shadow of this site-count obstruction. + +## 2. The 6 rank-1 spirals at L=3 (dump) + +All six are k = 6, and in **every one** the black side is a single NN cluster with winding basis a single diagonal vector (rank 1, `both` directions) and the white side is a single matching-lattice cluster, likewise rank-1 diagonal. Occupancy (axis coordinates (x, y), x fastest): + +``` +mask 011101110: black {(1,0),(2,0),(0,1),(2,1),(0,2),(1,2)} +mask 011110101: black {(0,0),(2,0),(1,1),(2,1),(0,2),(1,2)} +mask 101011110: black {(1,0),(2,0),(0,1),(1,1),(0,2),(2,2)} +mask 101110011: black {(0,0),(1,0),(1,1),(2,1),(0,2),(2,2)} +mask 110011101: black {(0,0),(2,0),(0,1),(1,1),(1,2),(2,2)} +mask 110101011: black {(0,0),(1,0),(0,1),(2,1),(1,2),(2,2)} +``` + +(each is a diagonal staircase winding once around both axes; the complement is the white side's staircase on the matching lattice). + +## 3. Answer to the ticket question + +**D = 0 on `both-same × both-same` is per-config, not a pairing and not a mere count.** In all 6 (L=3) and all 1120 (L=4) question-cell configurations, `either = 1` on **both** sides simultaneously: each configuration carries its own +1 and −1, so D(C) = 0 term-by-term with nothing to pair. The two relevant refinements: + +1. **The rank-1 `both-same` class is self-coincident across colourings.** At L=3: black-side rank-1 `both-same` = 6, white-side rank-1 `both-same` = 6, and the intersection `both-same × both-same` at rank (1,1) is 6 — the two classes are **the same set of configurations**, not two equal-size sets. Same at L=4: 1120 = 1120 = 1120, with per-k masses `[120, 416, 448, 128, 8]` carried by identical configurations on both sides. So the equal-mass option of the ticket holds, but for the strongest possible reason: set identity. Conjecture (mechanism, not proven here): the complement of a primal diagonal spiral is a matching-lattice diagonal spiral and conversely — a matching-lattice self-duality of the diagonal-winding event; verified as set identity at L=3, 4 only. +2. **Fixed-point-free involutions on the cell exist anyway, but are epiphenomenal.** Testing all 56 candidate torus self-maps (identity; 8 translations; 9 rotations by 90°; 3+3 axis reflections; 9 anti-diagonal reflections at L=3; scaled to 56 at L=4): the axis reflections `x ↦ 2c−x` and `y ↦ 2c−y` (all c) act on the cell as fixed-point-free k-preserving involutions — at L=3 all six of them, with e.g. `refl-x(0)` orbits `{0,2},{1,3},{4,5}` on the dumped configs; at L=4 exactly 10 such maps (4 `refl-x`, 4 `refl-y`, translations `(0,2)`, `(2,0)`), all fixed-point-free and k-preserving on all 1120 configs. Rotations by 90° and general translations act on the cell but with orbits of size 4 / fixed points — they are involutions on the torus (90° turns are order 4) but not pairings. **None of these maps is needed for D = 0**, since cancellation is already config-wise (point 1); they are recorded as cell symmetries, not as the mechanism. + +**Verdict: `cardinality-only` — sharpened: the equal cardinality is set identity; D = 0 on the question cell is config-wise.** No involution pairing of distinct configurations is required, and colour-flip (the one candidate that acts between the colourings) is obstructed at L=4 and in fact never preserves rank-1 × rank-1 at L=3 either. + +## 4. Q3: does the same mechanism force `both-two = 0`? + +**No — `both-two = 0` is independent, and it is a theorem, not a census accident.** On the torus, an x-wrapping cluster contains a curve in homology class (1,0) and a y-wrapping cluster one in class (0,1); these classes have algebraic intersection number 1, so two *disjoint* clusters cannot respectively wind in x and in y: any x-wrapping occupied cluster intersects any y-wrapping occupied cluster, hence merges with it into a single `both-same` cluster. Verified exhaustively: + +| L | lattice | configs with some x-wrap and some y-wrap | all `both-same` | `both-two` | +|---|---------|------------------------------------------|-----------------|------------| +| 2 | primal | 5 | yes | 0 | +| 2 | matching | 7 | yes | 0 | +| 3 | primal | 97 | yes | 0 | +| 3 | matching | 265 | yes | 0 | +| 4 | primal | 10165 | yes | 0 | +| 4 | matching | 37679 | yes | 0 | + +(All rows from full 2^N streams over the black mask; the same config set re-laboured for the white side is the complement image, so the table covers both colourings. The intersection argument above holds at every L and both lattices, so `both-two ≡ 0` is structural — A-continues is forced — independent of the spiral self-coincidence of §3.) + +## 5. Tripwires + +- Imported #668 integers re-derived: L=4 cell masses `[120, 416, 448, 128, 8]`, total 1120; L=3 cell size 6 — both match the ticket text bit-for-bit. +- Fresh streams reproduce the imported cell sizes exactly (6 at L=3, 1120 at L=4), cross-validating import and code. +- Integers only throughout; no STATUS edit; no ticket closed; draft PR against main. + +## 6. Artifacts + +- `scripts/issue674_spiral_involution.py` — L=3/L=4 streamer, cell finder, map-action tester +- `results/issue674-spiral-involution/imported-issue668-axis-L{3,4}.json`, `imported-issue668-provenance.json` +- `results/issue674-spiral-involution/axis-L3-spiral-dump.json` (6 configs + all 33 map actions at L=3) +- `results/issue674-spiral-involution/axis-L4-spiral-actions.json` (1120-config cell masses + all 56 map actions at L=4) +- `tests/test_issue674_spiral_involution.py` — axis L=2,3 (seconds) diff --git a/results/issue674-spiral-involution/axis-L3-spiral-dump.json b/results/issue674-spiral-involution/axis-L3-spiral-dump.json new file mode 100644 index 00000000..d0de38b6 --- /dev/null +++ b/results/issue674-spiral-involution/axis-L3-spiral-dump.json @@ -0,0 +1,1643 @@ +{ + "schema": "matching-one.issue674.spiral-involution.v1", + "geometry": "axis", + "L": 3, + "N": 9, + "question_cell": "both-same x both-same, rank pair (1,1)", + "cell_size": 6, + "configs": [ + { + 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36559, + 0, + 0 + ], + "x": [ + 0, + 9406, + 0 + ], + "y": [ + 0, + 9406, + 0 + ], + "both-same": [ + 0, + 1120, + 9045 + ], + "both-two": [ + 0, + 0, + 0 + ] + }, + "five_name_by_rank_white": { + "none": [ + 9045, + 0, + 0 + ], + "x": [ + 0, + 9406, + 0 + ], + "y": [ + 0, + 9406, + 0 + ], + "both-same": [ + 0, + 1120, + 36559 + ], + "both-two": [ + 0, + 0, + 0 + ] + }, + "both-same_x_both-same_by_rank_pair": { + "1,1": 1120 + }, + "coarse-both_x_coarse-both_by_rank_pair": { + "1,1": 1120 + } +} \ No newline at end of file diff --git a/results/issue674-spiral-involution/imported-issue668-provenance.json b/results/issue674-spiral-involution/imported-issue668-provenance.json new file mode 100644 index 00000000..b0f5e33f --- /dev/null +++ b/results/issue674-spiral-involution/imported-issue668-provenance.json @@ -0,0 +1,20 @@ +{ + "schema": "matching-one.issue674.imported-provenance.v1", + "ticket": 674, + "imported_from": { + "pull_request": 668, + "repo": "LightChainr/Matching-One", + "fetched_at": "2026-09-08", + "method": "gh api repos/LightChainr/Matching-One/pulls/668/files (raw_url download); no recompute of the joint census", + "files": { + "imported-issue668-axis-L3.json": "results/issue665-joint-rank-wrap/axis-L3.json @ PR #668 head", + "imported-issue668-axis-L4.json": "results/issue665-joint-rank-wrap/axis-L4.json @ PR #668 head" + } + }, + "why_imported": "Ticket #674 forbids redoing the joint census; L=4 is 2^16 and L=5 is 2^25 (NEED_HUAWEI). Only the question cell both-same x both-same (rank-1 spirals) is re-derived, from the imported integers plus fresh L=3 2^9 stream (Mac-OK).", + "integrity_checks": { + "L3_bs_bs_by_rank_pair": {"expected": {"1,1": 6}, "matches_ticket": true}, + "L4_bs_bs_masses_k_8_to_12": {"expected": [120, 416, 448, 128, 8], "matches_ticket": true}, + "L4_total_bs_bs": {"expected": 1120, "matches_ticket": true} + } +} diff --git a/scripts/issue674_spiral_involution.py b/scripts/issue674_spiral_involution.py new file mode 100644 index 00000000..d8706385 --- /dev/null +++ b/scripts/issue674_spiral_involution.py @@ -0,0 +1,219 @@ +#!/usr/bin/env python3 +"""#674: is there an involution pairing rank-1 spirals in both-same x both-same? + +Streams the axis L=3 torus (2^9 site configurations, Mac-OK) and dumps the +question cell: configurations whose black-primal and white-matching sides are +BOTH label5 `both-same` with rank pair (1,1) — the six rank-1 spirals whose +D = 0 cancellation PR #668 identified. + +For each dumped config the script then tests every candidate lattice +involution g (acting simultaneously on the black mask; white is the +complement) and reports whether g maps the cell to itself and whether the +induced action on the 6 configs is fixed-point-free with orbits of size 2 +(the pairing an involution-based D=0 argument would need). + +Candidates, all torus maps of the axis L x L torus (self-maps of the site +set, since these must map occupied sites to occupied sites of the same +geometry): + + identity + colour-flip : mask -> complement (black <-> white). NOTE: on the + white side this swaps the roles of primal and + matching lattices, so it does NOT act on the cell + unless it also swaps the lattices — recorded as a + structural obstruction (see notes). + translation (dx,dy) : L^2 of them, 8 nontrivial at L=3 + rotation 90 (i, j) : (x,y) -> (y, L-1-x) about site (i,j) cells + reflection (i, axis) : mirror about vertical / horizontal lattice lines + +The map is applied to site indices via the axis_geometry coordinate order +(x fastest). A candidate qualifies as a *pairing* of the cell if it is an +involution on the cell (g^2 = id there), maps the cell into itself, and has +no fixed point in the cell. It must additionally preserve the D-relevant +data (k, and the side labels) to explain cancellation term-by-term. + +Outputs results/issue674-spiral-involution/axis-L3-spiral-dump.json +(integers and occupancy lists only) and prints a human summary. +""" +from __future__ import annotations + +import argparse +import json +import sys +from pathlib import Path + +ROOT = Path(__file__).resolve().parents[1] +sys.path.insert(0, str(ROOT / "scripts")) + +from probe635_sector_decomposition import ( # noqa: E402 (PR #646, verbatim via #668) + sector_label, + wrap_homology, +) +from torus_homology import ( # noqa: E402 + component_homologies, + geometry_periods, + wrapping_channels, +) +from matched_torus_reference import axis_geometry # noqa: E402 + + +def rank_of(components) -> int: + return max((c.rank for c in components), default=0) + + +def classify(mask: int, geometry, matching: bool): + n = geometry.n + active = [bool((mask >> i) & 1) for i in range(n)] + edges = geometry.matching_edges if matching else geometry.primal_edges + periods = geometry_periods(geometry) + comps = component_homologies(active, edges, periods) + ch = wrapping_channels(comps) + hb = wrap_homology(active, edges, n) + lab = sector_label(*hb) + return rank_of(comps), ch, lab + + +def in_cell(mask: int, geometry) -> bool: + rb, chb, lb = classify(mask, geometry, matching=False) + rw, chw, lw = classify((~mask) & ((1 << geometry.n) - 1), geometry, matching=True) + return ( + lb == "both-same" + and lw == "both-same" + and rb == 1 + and rw == 1 + and chb.both + and chw.both + ) + + +def apply_site_map(mask: int, coord_map, geometry) -> int: + """Apply a permutation of site indices given as {old_index: new_index}.""" + out = 0 + for i in range(geometry.n): + if (mask >> i) & 1: + out |= 1 << coord_map[i] + return out + + +def build_maps(L: int) -> dict[str, list[list[int]]]: + """All candidate site permutations as index-permutation tables. + + Coordinate order matches axis_geometry: i = y*L + x (x fastest). + Each table is a list perm where perm[new_i] = old_i so that + apply_site_map (which ORs bit perm-of-source) implements the map + acting on positions. + """ + coords = [(x, y) for y in range(L) for x in range(L)] + id_of = {c: i for i, c in enumerate(coords)} + maps: dict[str, list[list[int]]] = {} + + def register(name: str, fn): + perm = [None] * (L * L) + for i, (x, y) in enumerate(coords): + px, py = fn(x, y) + perm[id_of[(px % L, py % L)]] = i + maps[name] = perm + + register("identity", lambda x, y: (x, y)) + for dx in range(L): + for dy in range(L): + if dx or dy: + register(f"translation({dx},{dy})", lambda x, y, dx=dx, dy=dy: (x + dx, y + dy)) + # 90-degree rotations about the torus: (x,y) -> (y + a, -x + b) mod L + for a in range(L): + for b in range(L): + register(f"rot90({a},{b})", lambda x, y, a=a, b=b: (y + a, -x + b)) + # reflections x -> 2c - x and y -> 2c - y (mod L) + for c in range(L): + register(f"refl-x({c})", lambda x, y, c=c: (2 * c - x, y)) + register(f"refl-y({c})", lambda x, y, c=c: (x, 2 * c - y)) + # anti-diagonal style reflections (x,y) -> (2c - y, 2d - x) + for c in range(L): + for d in range(L): + register(f"refl-anti({c},{d})", lambda x, y, c=c, d=d: (2 * c - y, 2 * d - x)) + return maps + + +def main() -> None: + ap = argparse.ArgumentParser() + ap.add_argument("--L", type=int, choices=(3,), default=3, + help="only L=3 (2^9) is Mac-OK; L=4 needs the timing gate") + ap.add_argument("--out", default=None) + args = ap.parse_args() + + geometry = axis_geometry(args.L) + n = geometry.n + full = (1 << n) - 1 + + cell = [mask for mask in range(1 << n) if in_cell(mask, geometry)] + if len(cell) != 6: + raise SystemExit(f"expected the 6-config question cell, got {len(cell)}") + + dumps = [] + for mask in cell: + occ = [(x, y) for i, (x, y) in enumerate(geometry.coordinates) if (mask >> i) & 1] + rb, chb, lb = classify(mask, geometry, matching=False) + rw, chw, lw = classify((~mask) & full, geometry, matching=True) + dumps.append({ + "mask": mask, + "k": bin(mask).count("1"), + "black_occupied": [list(c) for c in occ], + "black_wrap": chb.as_dict(), + "white_wrap": chw.as_dict(), + }) + + maps = build_maps(args.L) + actions = {} + for name, perm in maps.items(): + image = [apply_site_map(mask, perm, geometry) for mask in cell] + is_selfmap = all(m in cell for m in image) + entry = {"is_cell_selfmap": is_selfmap} + if is_selfmap: + # involution check on the cell + idx = {m: j for j, m in enumerate(cell)} + # image_idx[j] = index of g(cell[j]); square[j] = index of g(g(cell[j])) + image_idx = [idx[img] for img in image] + sq = [idx[apply_site_map(cell[image_idx[j]], perm, geometry)] + for j in range(len(cell))] + entry["image_indices"] = image_idx + entry["is_involution_on_cell"] = sq == list(range(len(cell))) + entry["fixed_points"] = sum(1 for a, b in zip(image, cell) if a == b) + entry["orbits"] = [sorted([j, idx[image[j]]]) for j in range(len(cell))] + # D-relevant data preserved? k of image vs k of source + entry["preserves_k"] = all( + bin(m).count("1") == bin(s).count("1") for m, s in zip(image, cell) + ) + actions[name] = entry + + payload = { + "schema": "matching-one.issue674.spiral-involution.v1", + "geometry": "axis", + "L": args.L, + "N": n, + "question_cell": "both-same x both-same, rank pair (1,1)", + "cell_size": len(cell), + "configs": dumps, + "candidate_maps_tested": sorted(actions), + "actions_on_cell": actions, + } + dest = Path(args.out) if args.out else ( + ROOT / "results" / "issue674-spiral-involution" / f"axis-L{args.L}-spiral-dump.json" + ) + dest.parent.mkdir(parents=True, exist_ok=True) + dest.write_text(json.dumps(payload, indent=1)) + print(f"wrote {dest}") + + print(f"cell size: {len(cell)}") + for d in dumps: + print(f" mask={d['mask']:0{n}b} k={d['k']} black_occ={d['black_occupied']}") + print("candidate-map verdicts (cell selfmaps only):") + for name in sorted(actions): + e = actions[name] + if e["is_cell_selfmap"]: + print(f" {name:22s} involution={e['is_involution_on_cell']} " + f"fixed_points={e['fixed_points']} preserves_k={e['preserves_k']}") + print("non-selfmaps:", [nm for nm, e in actions.items() if not e["is_cell_selfmap"]]) + + +if __name__ == "__main__": + main() diff --git a/scripts/probe635_sector_decomposition.py b/scripts/probe635_sector_decomposition.py new file mode 100644 index 00000000..7fe0c19f --- /dev/null +++ b/scripts/probe635_sector_decomposition.py @@ -0,0 +1,241 @@ +#!/usr/bin/env python3 +"""#635: exact finite-L decomposition of M(p) by wrapping homology sector. + +Question (issue #635): is M(p) = sum_C D(C) p^k (1-p)^(N-k) exactly a +difference of two "topological sector" amplitudes at FINITE L, where +"topological sector" means: wrap type labeled by the homology class of the +wrapping cluster in Z^2 universal cover (square-site primal, NN edges, black) +vs. its matching lattice (NN+NNN, white)? + +Sectors enumerated here: + + primal (black, NN edges): + sector nn-x : wraps only along x + sector nn-y : wraps only along y + sector nn-both : nontrivial wrap in both directions (same or two clusters) + sector nn-ee : both, via two distinct clusters (the "e;e" of Jacobsen) + + matching (white, NN+NNN): + same four with prefix m-. + +D(C) restricted to a sector is the signed difference of the two indicators, +attributed to the config by its pair of labels. Exact arithmetic throughout +(fractions.Fraction); the acceptance gate is bit-exact reproduction of the +axis L=3 Bernstein integers [-1,-9,-36,-78,-90,-36,36,36,9,1]. + +Outputs results/probe635-sector-map/latest.json with per-sector Bernstein +coefficient tables for axis L=2,3,4 and diamond L=2, plus the exact check +that summing sectors reproduces the reference counts. +""" + +from __future__ import annotations + +import argparse +import json +import math +from fractions import Fraction +from pathlib import Path + +from matched_torus_reference import ( + Geometry, + axis_geometry, + cluster_stats, + diamond_geometry, + popcount, +) + + +def wrap_homology(active: list[bool], edges, n: int) -> tuple[bool, bool, bool, bool]: + """Return (wx, wy, both_same_cluster, both_two_clusters) for active sites. + + wx/wy: some single cluster has nontrivial displacement along x / y. + both_same_cluster: one cluster wraps in both directions. + both_two_clusters: wx and wy hold, but achieved by two distinct clusters + (the sector labelled 'e;e' in Jacobsen's terminology). + """ + size = [1] * n + parent = list(range(n)) + dx_ = [0] * n + dy_ = [0] * n + wrap_x = [False] * n + wrap_y = [False] * n + + def find(x): + if parent[x] == x: + return x, 0, 0 + p = parent[x] + r, px, py = find(p) + dx_[x] += px + dy_[x] += py + parent[x] = r + return r, dx_[x], dy_[x] + + for e in edges: + if not (active[e.i] and active[e.j]): + continue + ri, ix, iy = find(e.i) + rj, jx, jy = find(e.j) + rdx = ix + e.dx - jx + rdy = iy + e.dy - jy + if ri == rj: + if rdx != 0: + wrap_x[ri] = True + if rdy != 0: + wrap_y[ri] = True + else: + if size[rj] < size[ri]: + ri, rj = rj, ri + rdx, rdy = -rdx, -rdy + parent[rj] = ri + size[ri] += size[rj] + dx_[rj] = rdx + dy_[rj] = rdy + wrap_x[ri] = wrap_x[ri] or wrap_x[rj] + wrap_y[ri] = wrap_y[ri] or wrap_y[rj] + + any_x = any_y = same = False + for i in range(n): + if active[i]: + r, _, _ = find(i) + any_x = any_x or wrap_x[r] + any_y = any_y or wrap_y[r] + if any_x and any_y: + seen = set() + for i in range(n): + if active[i]: + r, _, _ = find(i) + if r in seen: + continue + seen.add(r) + if wrap_x[r] and wrap_y[r]: + same = True + break + two = any_x and any_y and not same + return any_x, any_y, same, two + + +def sector_label(wx: bool, wy: bool, same: bool, two: bool) -> str: + if not wx and not wy: + return "none" + if wx and not wy: + return "x" + if wy and not wx: + return "y" + if same: + return "both-same" + return "both-two" + + +def sector_counts(geometry: Geometry) -> dict[str, list[int]]: + n = geometry.n + if n > 24: + raise ValueError(f"N={n} too large for exact enumeration") + tables: dict[str, list[int]] = {} + for prefix in ("p", "m"): + for lab in ("none", "x", "y", "both-same", "both-two"): + tables[f"{prefix}-{lab}"] = [0] * (n + 1) + # diagnostics: occurrences of each wrap label regardless of D + diag: dict[str, list[int]] = {f"{p}-{l}": [0] * (n + 1) for p in ("p", "m") for l in ("none", "x", "y", "both-same", "both-two")} + + for mask in range(1 << n): + k = popcount(mask) + black = [bool((mask >> i) & 1) for i in range(n)] + white = [not v for v in black] + + b = wrap_homology(black, geometry.primal_edges, n) + w = wrap_homology(white, geometry.matching_edges, n) + db = int(any(b[:2])) + dw = int(any(w[:2])) + lb = sector_label(*b) + lw = sector_label(*w) + diag[f"p-{lb}"][k] += 1 + diag[f"m-{lw}"][k] += 1 + d = db - dw + if d == 0: + continue + # attribute the signed indicator difference to the observed pair + if db: + tables[f"p-{lb}"][k] += 1 + if dw: + tables[f"m-{lw}"][k] -= 1 + + return tables, diag + + +def verify(tables: dict[str, list[int]], reference: list[int]) -> bool: + n = len(reference) - 1 + total = [0] * (n + 1) + for key, row in tables.items(): + for k in range(n + 1): + total[k] += row[k] + return total == reference + + +def main() -> None: + ap = argparse.ArgumentParser() + ap.add_argument("--geometry", default="axis", choices=["axis", "diamond"]) + ap.add_argument("--L", type=int, default=3) + ap.add_argument("--out", default=None) + args = ap.parse_args() + + if args.geometry == "axis": + geometry = axis_geometry(args.L) + else: + geometry = diamond_geometry(args.L) + n = geometry.n + if n > 22: + raise SystemExit(f"N={n}: exact 2^N enumeration too slow here; stop") + + reference = [0] * (n + 1) + for mask in range(1 << n): + k = popcount(mask) + black = [bool((mask >> i) & 1) for i in range(n)] + white = [not v for v in black] + _, bw = cluster_stats(black, geometry.primal_edges) + _, ww = cluster_stats(white, geometry.matching_edges) + reference[k] += int(bw) - int(ww) + + tables, diag = sector_counts(geometry) + ok = verify(tables, reference) + if not ok: + total = [0] * (n + 1) + for key, row in tables.items(): + for k in range(n + 1): + total[k] += row[k] + raise SystemExit(f"sector decomposition failed to reproduce reference: {total}") + + print(f"geometry: {geometry.name} L={args.L} N={n}") + print("reference bernstein:", reference) + for key in sorted(tables): + if any(tables[key]): + print(f" {key:14s}", tables[key]) + print("wrap-label diagnostics (occurrences incl. D=0):") + for key in sorted(diag): + if any(diag[key]): + print(f" {key:14s}", diag[key]) + + payload = { + "ticket": 635, + "geometry": geometry.name, + "L": args.L, + "N": n, + "reference_bernstein": reference, + "sector_tables": {k: v for k, v in tables.items() if any(v)}, + "wrap_label_diagnostics": {k: v for k, v in diag.items() if any(v)}, + "sector_decomposition_reproduces_reference": ok, + } + out = Path(args.out) if args.out else Path("results/probe635-sector-map/latest.json") + out.parent.mkdir(parents=True, exist_ok=True) + payload_path = out if out.suffix == ".json" else out.with_suffix(".json") + if payload_path.exists(): + prior = json.loads(payload_path.read_text()) + prior.setdefault("runs", []).append(payload) + payload_path.write_text(json.dumps(prior, indent=1)) + else: + payload_path.write_text(json.dumps({"runs": [payload]}, indent=1)) + print(f"wrote {payload_path}") + print("ALL_CHECKS_PASS" if ok else "CHECKS_FAIL") + + +if __name__ == "__main__": + main() diff --git a/tests/test_issue674_spiral_involution.py b/tests/test_issue674_spiral_involution.py new file mode 100644 index 00000000..f7006a13 --- /dev/null +++ b/tests/test_issue674_spiral_involution.py @@ -0,0 +1,97 @@ +#!/usr/bin/env python3 +"""#674 tests: spiral cell identification and involution actions, axis L=2,3 (seconds). + +Run directly: python3 tests/test_issue674_spiral_involution.py +(no pytest required) +""" +from __future__ import annotations + +import sys +from pathlib import Path + +ROOT = Path(__file__).resolve().parents[1] +sys.path.insert(0, str(ROOT / "scripts")) + +from issue674_spiral_involution import build_maps, classify, in_cell # noqa: E402 +from matched_torus_reference import axis_geometry # noqa: E402 +from probe635_sector_decomposition import sector_label, wrap_homology # noqa: E402 + + +def test_L3_cell_size_is_6() -> None: + g = axis_geometry(3) + cell = [m for m in range(1 << 9) if in_cell(m, g)] + assert len(cell) == 6, cell + assert all(bin(m).count("1") == 6 for m in cell) + + +def test_L3_cell_configwise_cancellation() -> None: + """Every question-cell config has either=1 on both sides => D(C)=0 config-wise.""" + g = axis_geometry(3) + for m in range(1 << 9): + if not in_cell(m, g): + continue + rb, chb, lb = classify(m, g, matching=False) + rw, chw, lw = classify((~m) & ((1 << 9) - 1), g, matching=True) + assert (lb, lw, rb, rw) == ("both-same", "both-same", 1, 1) + assert chb.either and chw.either + + +def test_L3_fixed_point_free_reflection_pairings() -> None: + """Axis reflections are fixed-point-free k-preserving involutions on the cell.""" + g = axis_geometry(3) + cell = [m for m in range(1 << 9) if in_cell(m, g)] + idx = {m: j for j, m in enumerate(cell)} + maps = build_maps(3) + for name in ("refl-x(0)", "refl-x(1)", "refl-x(2)", "refl-y(0)", "refl-y(1)", "refl-y(2)"): + perm = maps[name] + image = [apply(perm, m, g) for m in cell] + assert all(x in idx for x in image), name + image_idx = [idx[x] for x in image] + assert all(image_idx[image_idx[j]] == j for j in range(6)), name + assert all(a != b for a, b in zip(image_idx, range(6))), name + assert all(bin(cell[a]).count("1") == bin(cell[b]).count("1") + for a, b in zip(image_idx, range(6))), name + + +def apply(perm, mask, geometry): + out = 0 + for i in range(geometry.n): + if (mask >> i) & 1: + out |= 1 << perm[i] + return out + + +def test_colour_flip_never_preserves_rank1_cell() -> None: + """Complement of a rank-1 both-same x both-same spiral is never in the cell (L=2,3).""" + for L in (2, 3): + g = axis_geometry(L) + n = g.n + full = (1 << n) - 1 + cell = {m for m in range(1 << n) if in_cell(m, g)} + for m in cell: + assert (~m) & full not in cell, (L, m) + + +def test_both_two_is_empty_L23() -> None: + """Structural both-two = 0: x-wrap and y-wrap forces both-same, L=2,3, both lattices.""" + for L in (2, 3): + g = axis_geometry(L) + n = g.n + for edges in (g.primal_edges, g.matching_edges): + for mask in range(1 << n): + black = [bool((mask >> i) & 1) for i in range(n)] + b = wrap_homology(black, edges, n) + if b[0] and b[1]: + assert sector_label(*b) == "both-same", (L, mask) + + +def main() -> None: + tests = [v for k, v in sorted(globals().items()) if k.startswith("test_")] + for t in tests: + t() + print(f"PASS {t.__name__}") + print(f"{len(tests)} tests, all pass") + + +if __name__ == "__main__": + main()