From 35f5b16646d872c8b31c30fd2a6f9cd266f5dfcd Mon Sep 17 00:00:00 2001 From: Cursor Agent Date: Tue, 20 Oct 2026 02:50:36 +0000 Subject: [PATCH] Record nonnegative raw-moment invoices for two-neighbour ADD moves. On both pinned staged544 providers, every legal first ADD that crosses at least two scalar neighbours has a nonnegative raw rank moment at every feasible frame dimension. One changed-frame witness also keeps every single-ADD continuation certified nonnegative. No new kappa. Co-authored-by: unpaidmoon --- .../staged544-two-neighbour-invoice/README.md | 83 +++ .../SOURCES.json | 18 + .../staged544-two-neighbour-invoice/TASK.json | 66 +++ .../VERIFY.json | 18 + .../inputs/BORROW-WORD-43base.json.gz | Bin 0 -> 72769 bytes .../inputs/BORROW-WORD-43extra.json.gz | Bin 0 -> 72766 bytes .../vendor/audit_core.py | 480 ++++++++++++++++++ .../vendor/retiming.py | 269 ++++++++++ .../staged544-two-neighbour-invoice/verify.py | 262 ++++++++++ 9 files changed, 1196 insertions(+) create mode 100644 research/staged544-two-neighbour-invoice/README.md create mode 100644 research/staged544-two-neighbour-invoice/SOURCES.json create mode 100644 research/staged544-two-neighbour-invoice/TASK.json create mode 100644 research/staged544-two-neighbour-invoice/VERIFY.json create mode 100644 research/staged544-two-neighbour-invoice/inputs/BORROW-WORD-43base.json.gz create mode 100644 research/staged544-two-neighbour-invoice/inputs/BORROW-WORD-43extra.json.gz create mode 100644 research/staged544-two-neighbour-invoice/vendor/audit_core.py create mode 100644 research/staged544-two-neighbour-invoice/vendor/retiming.py create mode 100644 research/staged544-two-neighbour-invoice/verify.py diff --git a/research/staged544-two-neighbour-invoice/README.md b/research/staged544-two-neighbour-invoice/README.md new file mode 100644 index 0000000000..6319cf796b --- /dev/null +++ b/research/staged544-two-neighbour-invoice/README.md @@ -0,0 +1,83 @@ +# Two-neighbour ADD moves do not improve the raw moment + +**No new κ.** Selected κ stays 0.001672660197076918. + +This is a scoped obstruction for one frame-path change left open by +[PR #3942](https://github.com/CrocSwap/integer-mult-bounds/pull/3942). +It is not a review of that paper's interaction or new-gap reduction, and it +is not the radius-one theorem. The first displacement there is one neighbour. +Here the first ADD crosses at least two scalar neighbours. + +## Result + +Fix either literal PR #3734 provider word carried by PR #3942. Consider an +existing ADD, a cut in its commuting corridor that passes at least two gates, +and any common frame dimension legal for the removed-gate interval at that +cut. The raw rank-moment delta of that first move is nonnegative for every +real `0 < a < 1`. The certificate is the predecessor curvature test: rank +mass zero and nonnegative partial sums of `C_k = sum_r d_r min(r, k)`. +The first-move price depends only on dimension, by the interval formula in +PR #3942, PROOF.md §4, so this dimension census covers every subspace of +the same dimension. + +Each provider has 5,501 ADD gates, 4,979 of them with a long cut, and +1,761,760 dimension cases: 239,103 nonzero and 1,522,657 neutral. The two +providers agree on these counts. None improves. + +One changed-frame witness on the base word is gate `A[595] = add 459 510` +with coefficient `-1` and empty frame. Moving it to cut `1214` crosses 618 +gates, including both an ADD and a SCALE, and the only legal rank-1 frame +is `span{85}`. The frame bill changes by `+3` rank-1 children and `-1` +rank-3 child. Its caps are `[2, 1, 0, ...]`, so the move is strictly losing. +After the coefficient update and rederived cleanup, the edited word passes +the vendored frame auditor. Every one of the 1,767,681 single-ADD +retimings of that edited word keeps the combined histogram certified +nonnegative. This witness does not unlock a saving inside that single-move +class. + +## What this does not show + +A second move that itself changes a frame interval of quotient rank greater +than 1, or a second cut that is priced only after another long move, is +outside the continuation census. Native phase, hosting, stock, precision, +tape, all-size transfer and both supplier caps are not repriced. Unknown +costs are not zero. The scalar crossing rule is the sufficient PR #3886 +condition, not every algebraic commutation. No 632-input free-operator +replay was repeated. This is not a multiplication theorem. + +## Reproduce + +Python 3.12, standard library only, from the repository root: + +```sh +python3 -B research/staged544-two-neighbour-invoice/verify.py +python3 -B scripts/research_package.py --package research/staged544-two-neighbour-invoice +``` + +The expected first line starts +`PASS_STAGED544_TWO_NEIGHBOUR_INVOICE` and ends with `improving=0 no_new_kappa`. +The registered timeout is 180 seconds. A local run is well under that. + +`vendor/retiming.py` is byte-identical to PR #3942 at +`1416f8cd6bfb2f2eb9aa5cc22f0388a85fdbac91`. `vendor/audit_core.py` and both +`inputs/BORROW-WORD-43*.json.gz` files are the copies carried in that +package. SHA256 values are checked before use. + +## Open next questions + +1. Does every long first move, not only `A[595]`, keep every single-ADD + continuation nonnegative? One witness cannot extend the radius-one + theorem. The first step is the same continuation census on a move whose + frame interval has quotient rank greater than 1. +2. Can a second ADD that itself crosses two neighbours improve the combined + raw moment? Freeze one edited word and one such second cut before any + larger search. + +## Credit + +PR #3734 / dataisfire for the provider words. PR #3886 and PR #3942 / +Chris R, Clear1nsight, for the retiming rules, curvature test and the open +two-neighbour question. Sagar Thakrar for the frame auditor. The radius-one +interaction reduction remains their argument; this package does not review +it. New census and witness by unpaidmoon, with substantial Cursor Grok +assistance. Apache-2.0. diff --git a/research/staged544-two-neighbour-invoice/SOURCES.json b/research/staged544-two-neighbour-invoice/SOURCES.json new file mode 100644 index 0000000000..a604c6a640 --- /dev/null +++ b/research/staged544-two-neighbour-invoice/SOURCES.json @@ -0,0 +1,18 @@ +{ + "schema_version": 1, + "base_commit": "bb4bccbf42844d2801487450727c2f63e10d1d0f", + "files": [ + { + "path": "certificates/selected-result.json", + "usage": "provenance", + "git_blob": "b1fea0c94436b236cc2b7d41a7be032811b94c81", + "sha256": "bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129" + }, + { + "path": "docs/research/agent-task-catalog.json", + "usage": "provenance", + "git_blob": "67f085acd86acd7d4e03922d9cf4b26bca66fed5", + "sha256": "47b42433f5a85809a3aadd29c2c339da2c6ed728e4f7762df6b88bccb7874cf0" + } + ] +} diff --git a/research/staged544-two-neighbour-invoice/TASK.json b/research/staged544-two-neighbour-invoice/TASK.json new file mode 100644 index 0000000000..e3a285227d --- /dev/null +++ b/research/staged544-two-neighbour-invoice/TASK.json @@ -0,0 +1,66 @@ +{ + "schema_version": 1, + "task_id": "scalar-to-moment", + "priority_revision": 6, + "base_commit": "bb4bccbf42844d2801487450727c2f63e10d1d0f", + "original_card": { + "id": "scalar-to-moment", + "question": "Can one known scalar simplification be converted into an actual paid-profile improvement?", + "starting_points": [ + "research/r439-bsection-stars-seed01/README.md", + "certificates/selected-result.json" + ], + "methods": [ + "Derive the changed legal frame itinerary and exact child histogram.", + "Prove a scoped obstruction showing why that scalar gain cannot change the paid contract." + ], + "acceptance_gate": "An unchanged histogram is not a kappa gain; record any separate runtime or proof benefit explicitly.", + "first_step": { + "command": [ + "python3", + "-B", + "research/r439-bsection-stars-seed01/verify.py" + ], + "expected": "PASS_R439_BSECTION_STARS", + "inspect": "Observe that the positive control improves scalar counts while retaining the paid histogram.", + "scope": "Positive control / source-bound orientation only; this is not a new construction or full cold replay." + }, + "first_experiment": "Choose one simplification and derive the complete changed frame itinerary, or prove why it cannot change the histogram.", + "bottleneck_link": "A legal change to the histogram, not addition count alone, is the bridge to an exponent gain.", + "allowed_variations": [ + "One existing scalar simplification and one proposed frame-path change." + ], + "scope_change_triggers": [ + "Submitting only another scalar count as completion of a paid-profile task." + ], + "overlap_terms": [ + "scalar simplification", + "paid profile", + "R439" + ] + }, + "scope_status": "refined", + "actual_scope": "On both pinned PR3734 staged544 providers, price every legal first ADD move that crosses at least two scalar neighbours, at every feasible common-frame dimension, and price every single-ADD continuation after one explicit changed-frame witness.", + "scope_change_reason": "The card allows one frame-path change. This is that change for the PR3942 radius-one contract: the first ADD crosses two or more neighbours and may change frame. It is not an R439 scalar-count reduction, and it does not review the radius-one interaction reduction.", + "bottleneck_link": "A negative raw-moment delta on this frame path would be a paid-histogram change. The certified nonnegative deltas show this path does not supply one. No kappa is claimed.", + "budget_minutes": 60, + "stop_rule": "Stop after the dimension-complete long-first census on both providers and the single-move continuation census of one changed-frame witness. Do not search a second long move or review PROOF.md sections 2-3.", + "outcome": "negative-result", + "evidence": "Exact nonnegative S_j certificates for every long first-move dimension and for every single-move continuation of witness A/595/cut 1214/frame [85].", + "author": "unpaidmoon", + "ai_assistance": "Cursor Grok assisted the census script, packaging, and write-up. The predecessor trace and frame auditor are vendored unchanged.", + "open_questions": [ + { + "question": "After every long first move, not only witness A/595, does every single-ADD continuation stay nonnegative?", + "why_it_matters": "One witness does not extend the radius-one theorem to the whole two-neighbour class.", + "first_step": "Repeat the continuation census on a long move whose feasible frame interval has quotient rank greater than 1.", + "blocked_by": "The pair of censuses is a different budget from this witness." + }, + { + "question": "Can a second ADD that itself crosses two or more neighbours improve the combined raw moment?", + "why_it_matters": "The continuation census uses the single-move corridor, which prices every distance inside that corridor, but a second changed-frame long move can change geometry again.", + "first_step": "Freeze one edited word and one second cut that crosses two neighbours, then add the two histograms.", + "blocked_by": "No source-bound obstruction for that second long move is claimed here." + } + ] +} diff --git a/research/staged544-two-neighbour-invoice/VERIFY.json b/research/staged544-two-neighbour-invoice/VERIFY.json new file mode 100644 index 0000000000..604af2c776 --- /dev/null +++ b/research/staged544-two-neighbour-invoice/VERIFY.json @@ -0,0 +1,18 @@ +{ + "schema_version": 1, + "status": "ready", + "python": "3.12", + "requirements": [], + "inputs": [], + "commands": [ + { + "argv": [ + "{python}", + "-B", + "{package}/verify.py" + ], + "timeout_seconds": 180, + "checks": "SHA256 of the vendored trace, auditor and both provider words; dimension-complete long-first census on both providers; one changed-frame witness frame bill; every single-ADD continuation certificate; a negative curvature control." + } + ] +} diff --git a/research/staged544-two-neighbour-invoice/inputs/BORROW-WORD-43base.json.gz b/research/staged544-two-neighbour-invoice/inputs/BORROW-WORD-43base.json.gz new file mode 100644 index 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Nothing is imported from the audited authors' code +(PR3133/PR3605 producers, cleanup generator, evaluator or frame solver); the word +format and its semantic contract were read from those pinned sources and are +credited there. The frame-bill and free-word structure (point-set spans, warp +frame and lifted-frame checks, target levels keyed by register, dual symbol +naming) re-implements, without importing, Arham Tahir's +research/coupled-carrier-independent-audit/verify.py (Apache-2.0) and shares its +reading of the contract, so this module is not independent of that audit. + +Sagar Thakrar (thakrarsagar), with substantial AI assistance from Claude +(Anthropic, Claude Opus 5.5). Apache-2.0. +""" +from collections import Counter +from fractions import Fraction as Q + +V, N, H = 112, 704, 9 # sources 0..111, targets 112..223, helpers 224..703 +DUAL = 10 ** 6 # offset naming the independent dual symbols D_k = K_k^(-T) + + +class AuditFailure(Exception): + """Explicit failure; never disabled by python -O.""" + + +def need(ok, *why): + if not ok: + raise AuditFailure(' '.join(map(str, why))) + + +def is_target(r): + return V <= r < 2 * V + + +def touched(g): + return g[1:3] if g[0] == 'add' else g[1:2] + + +# ---------------------------------------------------------------------------- +# Binary frames: a subspace of F_2^9 is stored as a 512-bit point-set mask +# (bit x set iff x lies in the subspace). Containment is mask inclusion. +# ---------------------------------------------------------------------------- +_SPAN = {} + + +def span(vectors): + key = tuple(vectors) + mask = _SPAN.get(key) + if mask is None: + points = {0} + for u in key: + need(type(u) is int and 0 <= u < 512, 'frame vector out of range', u) + if u not in points: + points |= {p ^ u for p in points} + mask = sum(1 << p for p in points) + _SPAN[key] = mask + return mask + + +def points(mask): + return [x for x in range(512) if mask >> x & 1] + + +def dim(mask): + size = bin(mask).count('1') + need(size and size & (size - 1) == 0, 'not a subspace point set') + return size.bit_length() - 1 + + +FULL = (1 << 512) - 1 +ZERO = 1 + + +def hyperplane(port): + return sum(1 << x for x in range(512) if bin(x & port).count('1') % 2 == 0) + + +def warp_images(columns): + """Images of all 512 vectors under the F_2-linear map with columns G e_i.""" + need(len(columns) == H and all(type(c) is int and 0 <= c < 512 for c in columns), 'warp columns') + images = [0] * 512 + for x in range(1, 512): + low = x & -x + images[x] = images[x ^ low] ^ columns[low.bit_length() - 1] + need(len(set(images)) == 512, 'singular warp') + return images + + +def image_mask(images, mask): + return sum(1 << images[x] for x in points(mask)) + + +def lagrangian_action_ok(images, U, E): + """K_G(x,z)=(Gx, Gx+G^{-T}(x+z)) is symplectic and maps L_U to L_E, L_0 and L_FULL to themselves. + + L_U={(x,x+p): x in U, p in U^perp}. This is the binary frame action only; it + is not a Clifford phase or Gaussian-product certificate. For invertible G with + G(U)=E it is implied by the frame-map check ( = ), so it is a + consistency check of the implementation, not extra evidence. + """ + inverse = [0] * 512 + for x, y in enumerate(images): + inverse[y] = x + # G^{-T} z: bit j of the result is . + git = lambda z: sum((bin(inverse[1 << j] & z).count('1') & 1) << j for j in range(H)) + lift = lambda x, z: (images[x], images[x] ^ git(x ^ z)) + pair = lambda a, b: (bin(a[0] & b[1]).count('1') + bin(a[1] & b[0]).count('1')) & 1 + basis = [(1 << i, 0) for i in range(H)] + [(0, 1 << i) for i in range(H)] + lifted = [lift(*b) for b in basis] + if any(pair(lifted[i], lifted[j]) != pair(basis[i], basis[j]) for i in range(18) for j in range(i + 1, 18)): + return False + + def frame(mask): + us = points(mask) + perp = [p for p in range(512) if all(bin(p & u).count('1') % 2 == 0 for u in us)] + return {(u, u ^ p) for u in us for p in perp} + return all({lift(*pt) for pt in frame(a)} == frame(b) for a, b in ((ZERO, ZERO), (FULL, FULL), (U, E))) + + +# ---------------------------------------------------------------------------- +# Chronological binary-frame bill (BORROW-WORD contract) +# ---------------------------------------------------------------------------- +def frame_bill(w, lagrangian=False): + rep = w['report'] + need((rep['v'], 2 * rep['v'] + rep['R'], rep['h']) == (V, N, H), 'word geometry') + removed = set(w['removed']) + need(len(removed) == len(w['removed']) and all(2 * V <= r < N for r in removed), 'removed helpers') + live = [r for r in range(N) if r not in removed] + liveset = set(live) + B, warps = w['B'], w['warps'] + for k, (pos, lender, cols, U, E) in enumerate(warps, 1): + need(0 <= pos <= len(B), 'warp position', k) + need(lender in liveset and not is_target(lender), 'warp lender', k) + images = warp_images(cols) + su, se = span(U), span(E) + need(dim(su) == len(U) == len(E) == dim(se), 'warp frame bases', k) + need(image_mask(images, su) == se, 'warp does not map its frame', k) + if lagrangian: + need(lagrangian_action_ok(images, su, se), 'lifted frame action', k) + for name in ('A', 'B', 'restore'): + for g in w[name]: + if g[0] != 'warp': + need(all(r in liveset for r in touched(g)), 'removed/out-of-range register', name, g) + if g[0] == 'add' and not is_target(g[1]): + need(not is_target(g[2]), 'non-target reads a target', name, g) + need(all(g[-1] is None and is_target(g[1]) and g[0] == 'add' for g in w['cut']), 'cut gates') + need(all(g[-1] == [] and is_target(g[1]) for g in w['precondition'] + w['compensation']), 'zero-frame wrapper writes') + need(all(not is_target(g[1]) for g in w['restore']), 'restore writes a target') + + ports = w['ports'] + start, end = {}, {} + for r in live: + if r < V: + start[r], end[r] = span((ports[r],)), FULL + elif r < 2 * V: + start[r], end[r] = ZERO, hyperplane(ports[r - V]) + else: + start[r], end[r] = ZERO, FULL + for q, U in w['start_extra'].items(): + need(int(q) in liveset and int(q) >= 2 * V, 'entrance names a live helper', q) + start[int(q)] = span(U) + for q, U in w['helper_final'].items(): + need(int(q) in liveset and int(q) >= 2 * V, 'terminal names a live helper', q) + end[int(q)] = span(U) + + current, bill, chain = dict(start), Counter(), {} + + def climb(r, mask, where): + need(current[r] & ~mask == 0, 'frame containment fails', where, r) + d = dim(mask) - dim(current[r]) + if d: + bill[d] += 1 + chain.setdefault(r, []).append((where, d, mask)) + current[r] = mask + + npre = w['prelude_events'] + for i, g in enumerate(w['A']): + if g[0] == 'warp': + need(i < npre and len(g) == 5, 'warp outside the prelude', i) + _, r, op, fr, to = g + need(op != 0 and abs(op) <= len(warps) and warps[abs(op) - 1][1] == r, 'prelude warp lender', i) + images = warp_images(warps[abs(op) - 1][2]) + if op < 0: + inverse = [0] * 512 + for x, y in enumerate(images): + inverse[y] = x + images = inverse + need(image_mask(images, span(fr)) == span(to), 'prelude warp frame action', i) + need(current[r] == span(fr), 'prelude warp entry frame', i, r) + current[r] = span(to) + chain.setdefault(r, []).append((('A', i), 'warp', span(to))) + else: + if i < npre: + need(is_target(g[1]), 'prelude scalar writes a non-target', i) + for r in touched(g): + climb(r, span(g[-1]), ('A', i)) + levels = {V + int(t): span(U) for t, U in w['target_levels'].items()} + need(all(current[t] == levels.get(t, ZERO) for t in range(V, 2 * V)), 'target cut levels') + for q, U in zip(w['centers'], w['center_frames']): + U = span(U) + need(current[q] == U, 'centre entry frame', q) + served = {levels.get(g[1], ZERO) for g in w['cut'] if g[2] == q} + for T in sorted(served, key=lambda m: -dim(m)): + need(T & ~U == 0, 'centre descent not nested', q) + d = dim(U) - dim(T) + if d: + bill[d] += 1 + chain.setdefault(q, []).append((('centre',), d, T)) + U = T + at = {} + for k, rec in enumerate(warps, 1): + at.setdefault(rec[0], []).append(k) + for p in range(len(B) + 1): + for k in at.get(p, ()): + _, lender, _, U, E = warps[k - 1] + need(current[lender] == span(U), 'native warp entry frame', k, lender) + current[lender] = span(E) + chain.setdefault(lender, []).append((('warp', k), 'warp', span(E))) + if p < len(B): + for r in touched(B[p]): + climb(r, span(B[p][-1]), ('B', p)) + for i, g in enumerate(w['restore']): + for r in touched(g): + climb(r, span(g[-1]), ('restore', i)) + for r in live: + climb(r, end[r], ('end',)) + restored = set(map(int, w['helper_final'])) + need(all(end[r] == FULL for r in live if r not in restored and not is_target(r)), 'a FULL-cleanup register ends low') + widths = Counter(dim(end[r]) - dim(start[r]) for r in live if r >= 2 * V) + return dict(sorted(bill.items())), dict(sorted(widths.items())), chain, start, end + + +def hygiene(w): + """Inherited structural contract: dyadic scalars, power-of-two scales, wrapper and correction access.""" + entering = set(map(int, w['start_extra'])) + restored = set(map(int, w['helper_final'])) + live = set(range(N)) - set(w['removed']) + for name in ('precondition', 'compensation', 'A', 'cut', 'B', 'restore', 'cleanup'): + for g in w[name]: + if g[0] == 'warp': + continue + q = Q(g[3], g[4]) if g[0] == 'add' else Q(g[2], g[3]) + need(q != 0 and q.denominator & (q.denominator - 1) == 0, 'non-dyadic scalar', name, g) + if g[0] == 'scale': + need(abs(q.numerator) & (abs(q.numerator) - 1) == 0, 'non power-of-two scale', name, g) + for g in w['precondition'] + w['compensation']: + need(not any(r in entering | restored for r in touched(g)), 'wrapper touches an entering or restored helper', g) + for c in w['initial_corrections']: + word = c['operator_word'] + need(is_target(c['target']) and c['source'] in live and c['source'] >= 2 * V + and c['source'] not in entering, 'correction access', c) + need(word and all(w['warps'][abs(o) - 1][1] == c['source'] for o in word), 'correction operator lender', c) + q = Q(c['coefficient']) + need(q != 0 and q.denominator & (q.denominator - 1) == 0, 'correction coefficient', c) + return True + + +# ---------------------------------------------------------------------------- +# Literal inverse cleanup, derived from the contract +# ---------------------------------------------------------------------------- +def ordinary_forward(w): + """Chronological non-wrapper actions whose inverse forms cleanup.""" + out = [g for g in w['A'][w['prelude_events']:]] + at = {} + for k, rec in enumerate(w['warps'], 1): + at.setdefault(rec[0], []).append(['warp', rec[1], k]) + for p in range(len(w['B']) + 1): + out += at.get(p, []) + if p < len(w['B']): + out.append(w['B'][p]) + return out + list(w['restore']) + + +def derive_cleanup(w): + restored = set(map(int, w['helper_final'])) + buf = lambda r: r + N if r in restored else r + full = [256, 128, 64, 32, 16, 8, 4, 2, 1] + out = [] + for g in reversed(ordinary_forward(w)): + if g[0] == 'warp': + out.append(['warp', buf(g[1]), -g[2], full]) + elif is_target(g[1]): + continue + elif g[0] == 'add': + out.append(['add', buf(g[1]), buf(g[2]), -g[3], g[4], full]) + else: + need(g[0] == 'scale', 'unknown primitive', g) + out.append(['scale', buf(g[1]), g[3], g[2], full]) + return out + + +def same_cleanup(a, b): + norm = lambda c: [(g[:-1], span(g[-1])) for g in c] + return len(a) == len(b) and norm(a) == norm(b) + + +# ---------------------------------------------------------------------------- +# Exact free-operator semantics. A value is a dict {(input, word): Fraction}; +# word is a reduced tuple of signed operator ids (leftmost = applied last). +# ---------------------------------------------------------------------------- +def program(w, cleanup=None): + """Literal executed sequence: corrections, wrapper, A, cut, B+warps, restore | cleanup.""" + items = [('corr', c['target'], c['source'], tuple(c['operator_word']), Q(c['coefficient'])) + for c in w['initial_corrections']] + items += w['precondition'] + w['compensation'] + w['A'] + w['cut'] + at = {} + for k, rec in enumerate(w['warps'], 1): + at.setdefault(rec[0], []).append(['warp', rec[1], k]) + for p in range(len(w['B']) + 1): + items += at.get(p, []) + if p < len(w['B']): + items.append(w['B'][p]) + items += w['restore'] + return items, list(w['cleanup'] if cleanup is None else cleanup) + + +def dual_op(op): + return (1 if op > 0 else -1) * (abs(op) + DUAL) + + +def _left(op, word): + return word[1:] if word and word[0] == -op else (op,) + word + + +def _right(word, op): + return word[:-1] if word and word[-1] == -op else word + (op,) + + +def _axpy(dst, src, q): + for key, x in src.items(): + y = dst.get(key, 0) + q * x + if y: + dst[key] = y + else: + dst.pop(key, None) + + +def forward_rows(w, cleanup=None, dual=False, symbolic_buffers=True, snapshot=None): + """Schrodinger pass: every register's value as a combination of initial inputs. + + Live inputs are independent symbols. Private buffers are independent symbols + when symbolic_buffers is set (dirty), otherwise zero. The optional snapshot + callback sees the rows at the cleanup boundary. + """ + removed = set(w['removed']) + live = [r for r in range(N) if r not in removed] + restored = sorted(map(int, w['helper_final'])) + rows = {r: {(r, ()): Q(1)} for r in live} + for c in restored: + rows[c + N] = {(c + N, ()): Q(1)} if symbolic_buffers else {} + prefix, tail = program(w, cleanup) + + def apply(g): + kind = g[0] + if kind == 'add': + t, s, q = g[1], g[2], Q(g[3], g[4]) + need(t != s and q, 'add gate', g) + if dual: + t, s, q = s, t, -q + _axpy(rows[t], rows[s], q) + elif kind == 'scale': + q = Q(g[2], g[3]) + need(q != 0, 'zero scale', g) + if dual: + q = 1 / q + rows[g[1]] = {k: q * x for k, x in rows[g[1]].items()} + elif kind == 'warp': + op = dual_op(g[2]) if dual else g[2] + rows[g[1]] = {(var, _left(op, word)): x for (var, word), x in rows[g[1]].items()} + elif kind == 'corr': + _, t, s, word, c = g + if dual: + src, ops, dst, c = rows[t], [-dual_op(o) for o in word], s, -c + else: + src, ops, dst = rows[s], list(reversed(word)), t + moved = {} + for (var, wd), x in src.items(): + for o in ops: + wd = _left(o, wd) + moved[var, wd] = x + _axpy(rows[dst], moved, c) + else: + raise AuditFailure('unknown primitive ' + repr(g)) + + for g in prefix: + apply(g) + if snapshot is not None: + snapshot(rows) + for g in tail: + apply(g) + return rows + + +def reverse_columns(w, cleanup=None, upto_cleanup=False): + """Heisenberg pull-back: process the forward program backwards. + + cols[s] = {(output, word): coefficient}: the final output register 'output' + contains coefficient*word*x_s. Words grow on the right. Every live input and + every private buffer is an independent symbol. + """ + removed = set(w['removed']) + live = [r for r in range(N) if r not in removed] + restored = sorted(map(int, w['helper_final'])) + regs = live + [c + N for c in restored] + cols = {r: {(r, ()): Q(1)} for r in regs} + prefix, tail = program(w, cleanup) + seq = prefix if upto_cleanup else prefix + tail + for g in reversed(seq): + kind = g[0] + if kind == 'add': + t, s, q = g[1], g[2], Q(g[3], g[4]) + need(t != s and q, 'add gate', g) + _axpy(cols[s], cols[t], q) + elif kind == 'scale': + q = Q(g[2], g[3]) + need(q != 0, 'zero scale', g) + cols[g[1]] = {k: q * x for k, x in cols[g[1]].items()} + elif kind == 'warp': + op = g[2] + cols[g[1]] = {(out, _right(word, op)): x for (out, word), x in cols[g[1]].items()} + elif kind == 'corr': + _, t, s, word, c = g + moved = {} + for (out, wd), x in cols[t].items(): + for o in word: + wd = _right(wd, o) + moved[out, wd] = x + _axpy(cols[s], moved, c) + else: + raise AuditFailure('unknown primitive ' + repr(g)) + return cols + + +def transpose(cols): + rows = {} + for s, col in cols.items(): + for (r, word), x in col.items(): + rows.setdefault(r, {})[s, word] = x + return rows + + +def endpoint_defects(w, rows, dual=False): + """Compare final rows with the contract on the zero-buffer (live-input) domain. + + Returns (bad live registers, dirty buffers, buffer->live leaks, buffer self-map identity). + """ + removed = set(w['removed']) + live = [r for r in range(N) if r not in removed] + restored = sorted(map(int, w['helper_final'])) + bad = [] + for r in live: + expect = {(r, ()): Q(1)} + if dual and r < V: + expect[r + V, ()] = Q(-1) + if not dual and is_target(r): + expect[r - V, ()] = Q(1) + got = {k: x for k, x in rows.get(r, {}).items() if k[0] < N} + if got != expect: + bad.append(r) + dirty = [c for c in restored if any(k[0] < N for k in rows.get(c + N, {}))] + leaks = sorted({r for r in live for k in rows.get(r, {}) if k[0] >= N}) + buffer_identity = all({k: x for k, x in rows.get(c + N, {}).items() if k[0] >= N} == {(c + N, ()): Q(1)} + for c in restored) + return bad, dirty, leaks, buffer_identity + + +def boundary_defects(w, rows): + """Contract at the cleanup boundary (forward): targets sheared, restored helpers clean and isolated.""" + restored = set(map(int, w['helper_final'])) + out = [] + for t in range(V, 2 * V): + if {k: x for k, x in rows[t].items() if k[0] < N} != {(t, ()): Q(1), (t - V, ()): Q(1)}: + out.append(('target', t)) + for c in restored: + if rows[c] != {(c, ()): Q(1)}: + out.append(('restored', c)) + for r, row in rows.items(): + if r < N and r not in restored and any(k[0] in restored for k in row): + out.append(('restored input read', r)) + return out diff --git a/research/staged544-two-neighbour-invoice/vendor/retiming.py b/research/staged544-two-neighbour-invoice/vendor/retiming.py new file mode 100644 index 0000000000..c33d7bbcdf --- /dev/null +++ b/research/staged544-two-neighbour-invoice/vendor/retiming.py @@ -0,0 +1,269 @@ +# SPDX-License-Identifier: Apache-2.0 +"""Exact, fixed-neighbour single-ADD retiming relaxation. + +Chris R / Clear1nsight, with substantial OpenAI assistance. The BORROW-WORD +frame contract and scalar-retiming mechanism are credited in README.md. +This module does not import the retained auditor or a numerical optimiser. +""" +from bisect import bisect_left +from collections import Counter +from copy import deepcopy +from fractions import Fraction +from functools import lru_cache + + +def need(ok, message): + if not ok: + raise ValueError(message) + + +@lru_cache(maxsize=None) +def span(vectors): + points = {0} + for v in vectors: + need(type(v) is int and 0 <= v < 512, 'invalid frame vector') + points |= {x ^ v for x in tuple(points)} + return sum(1 << x for x in points) + + +@lru_cache(maxsize=None) +def basis(mask): + answer = [] + have = 1 + for v in range(1, 512): + if (mask >> v) & 1 and not (have >> v) & 1: + answer.append(v) + have = span(tuple(answer)) + need(have == mask, 'not a binary subspace') + return tuple(answer) + + +@lru_cache(maxsize=None) +def join(a, b): + return span(basis(a) + basis(b)) + + +@lru_cache(maxsize=None) +def rank(mask): + n = mask.bit_count() + need(n > 0 and n & (n - 1) == 0, 'invalid subspace cardinality') + return n.bit_length() - 1 + + +def contained(a, b): + return not a & ~b + + +def touched(gate): + return gate[1:3] if gate[0] == 'add' else gate[1:2] + + +def tracing(word): + """Own chronological trace; centre descent is NOT persistent state. + + A check node is a fixed boundary, not a charged instruction. The census + relaxes it to a virtual climb. Every legal witness has zero such charge. + """ + full = (1 << 512) - 1 + live = set(range(704)) - set(word['removed']) + start, end = {}, {} + for r in live: + if r < 112: + start[r], end[r] = span((word['ports'][r],)), full + elif r < 224: + p = word['ports'][r - 112] + start[r] = 1 + end[r] = sum(1 << x for x in range(512) if (x & p).bit_count() % 2 == 0) + else: + start[r], end[r] = 1, full + for r, fr in word['start_extra'].items(): + start[int(r)] = span(tuple(fr)) + for r, fr in word['helper_final'].items(): + end[int(r)] = span(tuple(fr)) + current = dict(start) + nodes = {r: [] for r in live} + where = {} + bill = Counter() + + def event(r, frame, address, kind='climb'): + before = current[r] + if kind != 'map': + need(contained(before, frame), 'source frame containment') + d = rank(frame) - rank(before) + if kind == 'check': + need(d == 0, 'source fixed boundary') + elif d: + bill[d] += 1 + if kind == 'climb': + where[(address, r)] = len(nodes[r]) + nodes[r].append((address, kind, before, frame)) + current[r] = frame + + for i, gate in enumerate(word['A']): + if gate[0] == 'warp': + event(gate[1], span(tuple(gate[3])), ('check-A', i), 'check') + event(gate[1], span(tuple(gate[4])), ('map-A', i), 'map') + else: + for r in touched(gate): + event(r, span(tuple(gate[-1])), ('A', i)) + levels = {112 + int(r): span(tuple(fr)) for r, fr in word['target_levels'].items()} + for r in range(112, 224): + event(r, levels.get(r, 1), ('target-cut', r), 'check') + for r, fr in zip(word['centers'], word['center_frames']): + u = span(tuple(fr)) + event(r, u, ('centre-cut', r), 'check') + served = {levels.get(g[1], 1) for g in word['cut'] if g[2] == r} + for v in sorted(served, key=lambda x: -rank(x)): + need(contained(v, u), 'centre nesting') + if rank(u) > rank(v): + bill[rank(u) - rank(v)] += 1 + u = v + # The main forward register remains at its declared centre entry. + warps = {} + for j, rec in enumerate(word['warps']): + warps.setdefault(rec[0], []).append((j, rec)) + for i in range(len(word['B']) + 1): + for j, rec in warps.get(i, []): + event(rec[1], span(tuple(rec[3])), ('check-B', j), 'check') + event(rec[1], span(tuple(rec[4])), ('map-B', j), 'map') + if i < len(word['B']): + gate = word['B'][i] + for r in touched(gate): + event(r, span(tuple(gate[-1])), ('B', i)) + for i, gate in enumerate(word['restore']): + for r in touched(gate): + event(r, span(tuple(gate[-1])), ('restore', i)) + for r in live: + event(r, end[r], ('end',)) + return nodes, where, dict(sorted(bill.items())) + + +def crosses(g, h): + """Sufficient exact scalar normal form, not all algebraic commutations.""" + if h[0] == 'add': + return g[1] != h[2] and h[1] != g[2] + return h[0] == 'scale' and h[2] != 0 + + +def segments(word, section): + if section == 'A': + cuts = [word['prelude_events'], len(word['A'])] + elif section == 'B': + cuts = sorted({0, len(word['B'])} | {rec[0] for rec in word['warps']}) + else: + cuts = [0, len(word[section])] + return list(zip(cuts, cuts[1:])) + + +def caps(delta): + return [sum(n * min(r, k) for r, n in enumerate(delta)) for k in range(1, 10)] + + +def all_power_nonnegative(delta): + """Sufficient exact certificate using decreasing positive curvatures.""" + values = caps(delta) + prefix = 0 + for value in values[:-1]: + prefix += value + if prefix < 0: + return False + return values[-1] == 0 + + +def census(word): + nodes, where, bill = tracing(word) + deltas = Counter() + counts = {} + for section in ('A', 'B', 'restore'): + gates = word[section] + count = 0 + for lo, hi in segments(word, section): + occurrences = {} + for i in range(lo, hi): + need(gates[i][0] in ('add', 'scale'), 'unexpected scalar segment') + for r in touched(gates[i]): + occurrences.setdefault(r, []).append(i) + for i in range(lo, hi): + g = gates[i] + if g[0] != 'add': + continue + lower = i + while lower > lo and crosses(g, gates[lower - 1]): + lower -= 1 + upper = i + 1 + while upper < hi and crosses(g, gates[upper]): + upper += 1 + removal = [0] * 10 + reduced, entries, exits = {}, {}, {} + for r in touched(g): + seq = nodes[r] + pos = where[((section, i), r)] + _, _, p, u = seq[pos] + need(pos + 1 < len(seq) and seq[pos + 1][1] != 'map', 'missing successor') + q = seq[pos + 1][3] + removal[rank(u) - rank(p)] -= 1 + removal[rank(q) - rank(u)] -= 1 + removal[rank(q) - rank(p)] += 1 + indices = occurrences[r] + reduced[r] = [x for x in indices if x != i] + entries[r] = seq[where[((section, indices[0]), r)]][2] + last = where[((section, indices[-1]), r)] + need(seq[last + 1][1] != 'map', 'missing exit check') + exits[r] = seq[last + 1][3] + for cut in range(lower, upper + 1): + if cut == i + 1: # Same placement as cut i, counted once. + continue + boundaries = [] + for r in touched(g): + indices = reduced[r] + j = bisect_left(indices, cut) + p = span(tuple(gates[indices[j - 1]][-1])) if j else entries[r] + q = span(tuple(gates[indices[j]][-1])) if j < len(indices) else exits[r] + boundaries.append((p, q)) + lower_frame = join(boundaries[0][0], boundaries[1][0]) + upper_frame = boundaries[0][1] & boundaries[1][1] + if not contained(lower_frame, upper_frame): + continue + dims = [(rank(p), rank(q)) for p, q in boundaries] + for d in range(rank(lower_frame), rank(upper_frame) + 1): + delta = removal.copy() + for p, q in dims: + delta[q - p] -= 1 + delta[d - p] += 1 + delta[q - d] += 1 + delta[0] = 0 + need(sum(r * n for r, n in enumerate(delta)) == 0, 'rank mass drift') + deltas[tuple(delta)] += 1 + count += 1 + counts[section] = count + return {'per_section': counts, 'candidates': sum(counts.values()), + 'source_profile': bill, + 'deltas': [{'delta': {r: n for r, n in enumerate(d) if n}, 'count': n, + 'caps': caps(d), 'certificate': all_power_nonnegative(d)} + for d, n in sorted(deltas.items())]} + + +def apply_move(word, section, index, cut, frame): + """Apply one exact scalar retiming. Caller must rederive cleanup and audit.""" + need(section in ('A', 'B', 'restore'), 'unknown section') + gates = word[section] + need(type(index) is int and 0 <= index < len(gates), 'bad source index') + need(type(cut) is int and 0 <= cut <= len(gates), 'bad insertion cut') + need(any(lo <= index < hi and lo <= cut <= hi for lo, hi in segments(word, section)), + 'crosses prelude or native warp boundary') + g = deepcopy(gates[index]) + need(g[0] == 'add', 'only ADD moves are covered') + crossed = gates[index + 1:cut] if cut > index else gates[cut:index] + need(all(crosses(g, h) for h in crossed), 'noncommuting scalar barrier') + coefficient = Fraction(g[3], g[4]) + for h in crossed: + if h[0] == 'scale' and h[1] in touched(g): + power = (1 if h[1] == g[1] else -1) * (1 if cut > index else -1) + coefficient *= Fraction(h[2], h[3]) ** power + g[3:5] = [coefficient.numerator, coefficient.denominator] + g[-1] = list(basis(span(tuple(frame)))) + result = deepcopy(word) + result[section].pop(index) + result[section].insert(cut - (cut > index), g) + # Segment length and all warp cuts are unchanged. No warp is crossed. + return result diff --git a/research/staged544-two-neighbour-invoice/verify.py b/research/staged544-two-neighbour-invoice/verify.py new file mode 100644 index 0000000000..814daa043b --- /dev/null +++ b/research/staged544-two-neighbour-invoice/verify.py @@ -0,0 +1,262 @@ +#!/usr/bin/env python3 +# SPDX-License-Identifier: Apache-2.0 +"""Long first-ADD retiming invoices on the two pinned staged544 providers. + +The first-move price depends only on dimension. Every legal cut that crosses +at least two scalar neighbours is certified nonnegative for every feasible +common-frame dimension. One changed-frame witness is then continued through +every single-ADD retiming of the edited word. +""" +import gzip +import hashlib +import json +from importlib.machinery import SourceFileLoader +from pathlib import Path + +P = Path(__file__).resolve().parent +HASHES = { + "vendor/retiming.py": "591d7278541ac4de9e9b6fc1e17aba23b205ac4b6c81824a28fc08294658ef0d", + "vendor/audit_core.py": "888679ca8502cdcb100420fe5382a052529a494bf76cb332928b86e62612b951", + "inputs/BORROW-WORD-43base.json.gz": "5ca4be99851f8878cbfe0fd6c454df926b11218f17feefa1664721cf03156699", + "inputs/BORROW-WORD-43extra.json.gz": "965268a9be73d3f62e7ef680d18f108cf064bfe1f44b82157baa61443232904e", +} +WITNESS = { + "provider": "base", + "section": "A", + "index": 595, + "cut": 1214, + "frame": [85], + "gate_head": ["add", 459, 510, -1, 1], + "original_frame": [], + "crossed": 618, + "first_delta": [0, 3, 0, -1, 0, 0, 0, 0, 0, 0], + "first_caps": [2, 1, 0, 0, 0, 0, 0, 0, 0], + "second_candidates": 1767681, + "edited_profile": {1: 2443, 2: 725, 3: 223, 4: 102, 5: 20, 8: 8}, + "original_profile": {1: 2440, 2: 725, 3: 224, 4: 102, 5: 20, 8: 8}, +} +# Dimension-complete long-first censuses. Locked after the source-bound run. +EXPECTED = { + "base": {"adds": 5501, "long_gates": 4979, "cases": 1761760, "nonzero": 239103, "neutral": 1522657, "improving": 0}, + "extra": {"adds": 5501, "long_gates": 4979, "cases": 1761760, "nonzero": 239103, "neutral": 1522657, "improving": 0}, +} + + +def need(ok, message): + if not ok: + raise SystemExit(message) + + +def load(name, path): + return SourceFileLoader(name, str(path)).load_module() + + +def authenticate(): + for rel, digest in HASHES.items(): + raw = (P / rel).read_bytes() + need(hashlib.sha256(raw).hexdigest() == digest, "sha256 mismatch: " + rel) + + +def load_word(tag): + return json.loads(gzip.decompress((P / "inputs" / f"BORROW-WORD-43{tag}.json.gz").read_bytes())) + + +def segment_bounds(R, word, section, index): + for lo, hi in R.segments(word, section): + if lo <= index < hi: + return lo, hi + raise SystemExit("index outside every segment") + + +def long_cuts(R, gates, lo, hi, index): + gate = gates[index] + lower, upper = index, index + 1 + while lower > lo and R.crosses(gate, gates[lower - 1]): + lower -= 1 + while upper < hi and R.crosses(gate, gates[upper]): + upper += 1 + cuts = [] + for cut in range(lower, upper + 1): + if cut == index + 1: + continue + crossed = gates[index + 1:cut] if cut > index else gates[cut:index] + if len(crossed) >= 2: + cuts.append(cut) + return cuts + + +def removal_histogram(R, word, nodes, where, section, index): + gate = word[section][index] + delta = [0] * 10 + for register in R.touched(gate): + seq = nodes[register] + pos = where[((section, index), register)] + _, _, before, frame = seq[pos] + need(seq[pos + 1][1] != "map", "missing successor") + after = seq[pos + 1][3] + delta[R.rank(frame) - R.rank(before)] -= 1 + delta[R.rank(after) - R.rank(frame)] -= 1 + delta[R.rank(after) - R.rank(before)] += 1 + return delta + + +def cut_bounds(R, gates, occurrences, entries, exits, index, cut): + bounds = [] + for register in R.touched(gates[index]): + indices = [x for x in occurrences[register] if x != index] + j = 0 + while j < len(indices) and indices[j] < cut: + j += 1 + before = R.span(tuple(gates[indices[j - 1]][-1])) if j else entries[register] + after = R.span(tuple(gates[indices[j]][-1])) if j < len(indices) else exits[register] + bounds.append((before, after)) + low = R.join(bounds[0][0], bounds[1][0]) + high = bounds[0][1] & bounds[1][1] + return low, high, bounds + + +def insertion_delta(removal, dims, dimension): + delta = removal.copy() + for before, after in dims: + delta[after - before] -= 1 + delta[dimension - before] += 1 + delta[after - dimension] += 1 + delta[0] = 0 + return delta + + +def long_first_census(R, word): + nodes, where, traced = R.tracing(word) + counts = {"adds": 0, "long_gates": 0, "cases": 0, "nonzero": 0, "neutral": 0, "improving": 0} + for section in ("A", "B", "restore"): + gates = word[section] + for lo, hi in R.segments(word, section): + occurrences = {} + for index in range(lo, hi): + for register in R.touched(gates[index]): + occurrences.setdefault(register, []).append(index) + entries, exits = {}, {} + for register, indices in occurrences.items(): + entries[register] = nodes[register][where[((section, indices[0]), register)]][2] + last = where[((section, indices[-1]), register)] + need(nodes[register][last + 1][1] != "map", "missing exit") + exits[register] = nodes[register][last + 1][3] + for index in range(lo, hi): + if gates[index][0] != "add": + continue + counts["adds"] += 1 + cuts = long_cuts(R, gates, lo, hi, index) + if not cuts: + continue + counts["long_gates"] += 1 + removal = removal_histogram(R, word, nodes, where, section, index) + for cut in cuts: + low, high, bounds = cut_bounds(R, gates, occurrences, entries, exits, index, cut) + if not R.contained(low, high): + continue + dims = [(R.rank(before), R.rank(after)) for before, after in bounds] + for dimension in range(R.rank(low), R.rank(high) + 1): + delta = insertion_delta(removal, dims, dimension) + need(sum(rank * count for rank, count in enumerate(delta)) == 0, "rank mass drift") + counts["cases"] += 1 + if any(delta): + counts["nonzero"] += 1 + else: + counts["neutral"] += 1 + if not R.all_power_nonnegative(delta): + counts["improving"] += 1 + need(traced == {int(rank): count for rank, count in word["report"]["local_profile"].items()} + or traced == word["report"]["local_profile"], "trace/profile disagreement") + # local_profile keys may already be ints + profile = {int(rank): count for rank, count in word["report"]["local_profile"].items()} + need(traced == profile, "trace bill differs from declared profile") + return counts, nodes, where + + +def witness_invoice(R, C, word): + section = WITNESS["section"] + index = WITNESS["index"] + cut = WITNESS["cut"] + gates = word[section] + gate = gates[index] + need(gate[:5] == WITNESS["gate_head"], "witness gate changed") + need(gate[-1] == WITNESS["original_frame"], "witness original frame changed") + crossed = gates[index + 1:cut] + need(len(crossed) == WITNESS["crossed"], "witness crossing length changed") + need(any(item[0] == "add" for item in crossed) and any(item[0] == "scale" for item in crossed), + "witness must cross both an ADD and a SCALE") + nodes, where, _ = R.tracing(word) + lo, hi = segment_bounds(R, word, section, index) + occurrences = {} + for cursor in range(lo, hi): + for register in R.touched(gates[cursor]): + occurrences.setdefault(register, []).append(cursor) + entries, exits = {}, {} + for register, indices in occurrences.items(): + entries[register] = nodes[register][where[((section, indices[0]), register)]][2] + last = where[((section, indices[-1]), register)] + exits[register] = nodes[register][last + 1][3] + low, high, bounds = cut_bounds(R, gates, occurrences, entries, exits, index, cut) + need(R.contained(low, high), "witness interval empty") + need(R.basis(high) == tuple(WITNESS["frame"]), "witness frame is not the unique upper line") + need(not R.contained(R.span((1,)), high), "control vector 1 must lie outside the witness line") + dims = [(R.rank(before), R.rank(after)) for before, after in bounds] + removal = removal_histogram(R, word, nodes, where, section, index) + delta = insertion_delta(removal, dims, 1) + need(delta == WITNESS["first_delta"], "witness first delta changed: " + str(delta)) + need(R.caps(delta) == WITNESS["first_caps"], "witness caps changed") + need(R.all_power_nonnegative(delta), "witness first move lost its certificate") + edited = R.apply_move(word, section, index, cut, WITNESS["frame"]) + C.hygiene(edited) + edited["cleanup"] = C.derive_cleanup(edited) + C.hygiene(edited) + original_bill, _widths, *_rest = C.frame_bill(word) + edited_bill, _widths, *_rest = C.frame_bill(edited) + need(original_bill == WITNESS["original_profile"], "original frame bill changed") + need(edited_bill == WITNESS["edited_profile"], "edited frame bill changed") + traced = R.tracing(edited)[2] + need(traced == edited_bill, "edited trace disagrees with frame bill") + second = R.census(edited) + need(second["candidates"] == WITNESS["second_candidates"], "second-move count changed") + first = WITNESS["first_delta"] + for row in second["deltas"]: + combined = first.copy() + for rank, count in row["delta"].items(): + combined[int(rank)] += count + need(sum(rank * count for rank, count in enumerate(combined)) == 0, "combined rank mass") + need(R.all_power_nonnegative(combined), "combined continuation improves: " + str(combined)) + return second["candidates"] + + +def failure_controls(R): + losing = [0, -1, 0, 0, 0, 0, 0, 0, 0, 0] + need(not R.all_power_nonnegative(losing), "negative control was certified") + neutral = [0] * 10 + need(R.all_power_nonnegative(neutral), "zero delta must be neutral") + need(R.rank(R.span(())) == 0, "empty frame rank") + + +def main(): + authenticate() + R = load("staged544_retiming", P / "vendor" / "retiming.py") + C = load("staged544_audit_core", P / "vendor" / "audit_core.py") + failure_controls(R) + summary = {} + for tag in ("base", "extra"): + word = load_word(tag) + counts, _nodes, _where = long_first_census(R, word) + need(counts["improving"] == 0, tag + " has an improving long first move") + need(counts["cases"] == counts["nonzero"] + counts["neutral"], tag + " case split") + expected = EXPECTED[tag] + if expected is not None: + need(counts == expected, tag + " counts changed: " + str(counts)) + summary[tag] = counts + if tag == WITNESS["provider"]: + witness_invoice(R, C, word) + print("PASS_STAGED544_TWO_NEIGHBOUR_INVOICE " + + " ".join(f"{tag}_cases={summary[tag]['cases']}" for tag in summary) + + f" witness_second={WITNESS['second_candidates']} improving=0 no_new_kappa") + + +if __name__ == "__main__": + main()