From 1889253fdbfd37e0f984ac412cf0ada4f36fa676 Mon Sep 17 00:00:00 2001 From: Nick Petalas Date: Wed, 28 Oct 2026 00:54:25 +0000 Subject: [PATCH] feat(research): census PR5718-shape helper splits on the PR5907 word Calibrated on the PR5713 source word, where the exact census recovers PR5718's own split (cut 14330, chart 602, helper 708). On PR5907 no class passes: 4,206 leak to roles not final at V and 4 fail the pairing, so any further split of this kind needs a mid-word correction. --- .../p104-pr5718-shape-split-census/README.md | 87 +++++++++ .../RESULT.json | 1 + .../SOURCES.json | 30 +++ .../p104-pr5718-shape-split-census/TASK.json | 123 ++++++++++++ .../VERIFY.json | 21 +++ .../shapesplit.py | 176 ++++++++++++++++++ .../p104-pr5718-shape-split-census/verify.py | 114 ++++++++++++ 7 files changed, 552 insertions(+) create mode 100644 research/p104-pr5718-shape-split-census/README.md create mode 100644 research/p104-pr5718-shape-split-census/RESULT.json create mode 100644 research/p104-pr5718-shape-split-census/SOURCES.json create mode 100644 research/p104-pr5718-shape-split-census/TASK.json create mode 100644 research/p104-pr5718-shape-split-census/VERIFY.json create mode 100644 research/p104-pr5718-shape-split-census/shapesplit.py create mode 100644 research/p104-pr5718-shape-split-census/verify.py diff --git a/research/p104-pr5718-shape-split-census/README.md b/research/p104-pr5718-shape-split-census/README.md new file mode 100644 index 0000000000..dce1272e73 --- /dev/null +++ b/research/p104-pr5718-shape-split-census/README.md @@ -0,0 +1,87 @@ +# No PR5718-shape helper split remains on the PR5907 P104 word + +**Scoped finite certificate; no new κ.** Base: canonical main `19fdb086ea96af9a9f87936a2b888e10af4ed810`. +The selected record is unchanged. + +Matarener's open [PR #5994](https://github.com/CrocSwap/integer-mult-bounds/pull/5994) +(`research/p104-helper-split-exhaustion`) shows that no PR5599-type helper split remains on the latest conditional +P104 word, DreamingOfClouds's [PR #5907](https://github.com/CrocSwap/integer-mult-bounds/pull/5907). It names +splits of the kind in flyingviper's merged [PR #5718](https://github.com/CrocSwap/integer-mult-bounds/pull/5718) +as the remaining route: different input and output bases, with an output correction. This package tests that +route on the PR5907 word. + +## Result + +The split shape of PR5718 (see its `PROOF.md`) is: a helper `p` of a boundary group with charts `(U, V)` is retired +at a strictly intermediate chart `F` after event `i`; a new independent helper with arbitrary input `z` takes over +`p`'s continuation (unit injection `b = e_p`); the input functional `c = aP` may use any role whose initial chart is +zero-dimensional, main inputs included; and the output defect is normalised on roles whose final chart is `V`. +The census in [shapesplit.py](shapesplit.py) decides exactly over Q, for every helper group, every strictly +intermediate chart, every cut after an event that touches that chart, and every group helper at the chart, whether + +- some combination `a` of the prefix rows at `F` has `a_p ≠ 0` and `aP` in the allowed input support, and +- the z-direction `d = S e_p` vanishes on every role whose final chart is not `V` (no **leak**), and +- `a·b = c·d' ≠ 0` for some `d'` that agrees with `d` except on freely corrected `V`-final roles (the **pairing**). + +| Word | Input rule | Evaluations | Leak | Pairing fails | Witnesses | +|---|---|---:|---:|---:|---:| +| PR5713 source (calibration) | group + U-initial | 8,579 | 3,817 | 2 | **7** | +| PR5713 source (calibration) | + empty-frame roles | 8,579 | 3,817 | 2 | **7** | +| PR5907 | group + U-initial | 8,913 | 4,202 | 4 | **0** | +| PR5907 | + empty-frame roles | 8,913 | 4,206 | 4 | **0** | + +**Calibration.** On the PR5713 source word, the census recovers PR5718's own split: cut after event 14330, +chart 602, helper 708, ranks (2, 7). All 7 witnesses lie on chart 602 and helper 708 (earlier cuts of the same +meeting). + +**PR5907.** No class passes. In 4,206 classes the new helper's z-direction leaks to a role whose final chart is +not `V`. In the other 4 (chart 549, helper 173, cuts 15974–15988) only the pairing `a_p = d_p c_p` fails. So on +PR5907, any further PR5718-type split must cancel that leak with a correction in the middle of the word. The +receipt lists how many leaked roles each class has. 425 classes leak to exactly one role; these are the nearest +candidates. + +PR5718's split itself is a boundary-relaxation witness of the PR5994 census on its source word. So PR5994's +boundary-support exclusion already rules out PR5718-shape splits on PR5907 when the output defect stays on +`V`-final roles. This package gives that link an exact calibration and a separate decision procedure for unit +injection, and it records where the leak goes. + +## Scope and limits + +- Scalar necessary condition only, for the z-part of the split. The non-z part of the output normalisation, native + maps, owned lifetimes, caller, compiler and outer checks are not involved. A witness would still need all of them. +- Unit injection on one group helper, as in PR5718. Injections along a combination of several fields are not + covered. +- Mid-word corrections, such as `r += q·new` at a later meeting of the new helper with a leaked role, are not + modelled. They are the open route, not an exclusion. A direct exact implementation of that relaxation was + written but not run to completion, and it is not part of this package. + +## Reproduce + +Python 3.12, standard library, from the repository root (about 5–30 s): + +```sh +python3.12 -B research/p104-pr5718-shape-split-census/verify.py +python3.12 -B scripts/research_package.py --package research/p104-pr5718-shape-split-census +``` + +Expected marker: `PASS_P104_PR5718_SHAPE_SPLIT_CENSUS`. The verifier authenticates both inputs: the PR5907 word +`research/p104-helper468-rung-removal/WORD.json.gz` and the PR5713 word read from +`research/p104-two-boundary-helper-split/inputs/pr5713-source.tar`. It also runs six synthetic controls of the pairing +decision and compares `RESULT.json` byte for byte. + +## Open next questions + +- **Leak-1 classes on PR5907.** Can a mid-word correction remove the z-leak of one of the 425 classes that leak to + exactly one role outside `V`? Each one that closes adds one zero-paid split per LOCAL. First step: for one such + class, list the later meetings of the pivot's chart with the leaked role. Then test whether a correction vector + `S_τ e_r` reaches the leaked output coordinate, and check the non-z part of the correction. Blocked by a fast exact + span update for the meeting corrections. +- **Chart 549, helper 173.** The four PR5907 classes without leak fail only the pairing. Does an input role outside + the empty-frame rule make `a_p = d_p c_p` solvable? First step: print `A` and `d_p` at cut 15974. + +## Credit + +PR5994 (Matarener) supplies the census criterion, the pure-subspace construction and the question. PR5718 +(flyingviper) supplies the split shape. PR5713 (Ali Romman) supplies the calibration word. PR5907 (DreamingOfClouds) +supplies the target word. PR5599 (Ali Romman) supplies the split criterion. The P104 lineage is retained in those +packages. Nothing of theirs is modified. This package was produced by Nick Petalas. 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diff --git a/research/p104-pr5718-shape-split-census/SOURCES.json b/research/p104-pr5718-shape-split-census/SOURCES.json new file mode 100644 index 0000000000..5fd89ee199 --- /dev/null +++ b/research/p104-pr5718-shape-split-census/SOURCES.json @@ -0,0 +1,30 @@ +{ + "schema_version": 1, + "base_commit": "19fdb086ea96af9a9f87936a2b888e10af4ed810", + "files": [ + { + "path": "certificates/selected-result.json", + "usage": "provenance", + "git_blob": "581f8d87008354eb5b869f7ed9de1317ad837ce8", + "sha256": "2a0220e866417774606e0f991e41b9c1d26b1f43b97857238cf478dbc7d330b5" + }, + { + "path": "docs/research/agent-task-catalog.json", + "usage": "provenance", + "git_blob": "3404fbdd5e7529a0674eef26114b5071e4586cec", + "sha256": "ead6cdc9d0af6d58e8a49744d8ec8c7c15e13d2ba93c276c434bcf9b51b93a81" + }, + { + "path": "research/p104-helper468-rung-removal/WORD.json.gz", + "usage": "input", + "git_blob": "7ffe7b500b02b9d0de49a85ec53e36004f1a411f", + "sha256": "b69a9cb3a26d4f40aa7ad14f814b188fe16a782999f6f56292538e447d67b284" + }, + { + "path": "research/p104-two-boundary-helper-split/inputs/pr5713-source.tar", + "usage": "input", + "git_blob": "ec8f4bccaca147bc80cec078147fb95bc515036e", + "sha256": "c4d8d0bcd6231eb4539a76d66b0dbd465313cbc50d279ca974a55fecb935d544" + } + ] +} diff --git a/research/p104-pr5718-shape-split-census/TASK.json b/research/p104-pr5718-shape-split-census/TASK.json new file mode 100644 index 0000000000..04e7f52c9b --- /dev/null +++ b/research/p104-pr5718-shape-split-census/TASK.json @@ -0,0 +1,123 @@ +{ + "schema_version": 1, + "task_id": "p104-side-correction", + "priority_revision": 8, + "base_commit": "19fdb086ea96af9a9f87936a2b888e10af4ed810", + "original_card": { + "id": "p104-side-correction", + "question": "Can joint helper bases and a legal causal split improve the complete P104 productive/paid invoice?", + "starting_points": [ + "docs/research/current-priorities.md", + "docs/research/research-family-status.md", + "certificates/selected-result.json", + "docs/research/pr-intake-evidence/pr5599-completion/PROOF-REVIEW.md", + "research/p104-helper-subspace-splits/README.md", + "research/dyadic-helper-channel-capacity/README.md" + ], + "methods": [ + "Construct and independently check one source-bound instance of the stated first experiment.", + "Seek an exact counterexample or target-specific complete-budget obstruction to that same proposed change." + ], + "acceptance_gate": "An exact arbitrary-input identity, source/target frame availability and restoration at the chosen cut, plus the complete channel+correction+idle/hosting bill or an explicit favorable bound. The native channel alone is not a supplier. A scoped local result may be retained without a complete supplier. Expanding it into further construction rounds requires the family-level budget and obligation gate in research-family-status.md; an optimistic passing relaxation alone is not acceptance.", + "first_step": { + "command": [ + "python3", + "-B", + "scripts/research_selected_baseline.py" + ], + "expected": "PASS_RESEARCH_BASELINE_BINDINGS_ONLY", + "inspect": "Read revision 8, the selected review and live exact-source handoffs. Then follow this card's bounded first_experiment.", + "scope": "Source-bound orientation only, not a supplier replay or theorem proof." + }, + "first_experiment": "Start with the selected #5599 emitted word and review pending #5718 distinct input/output bases plus #5717/#5719 coverage before claiming work. Pick one uncovered source word, helper group and cut region. Prove the arbitrary-input relation and legal entry/exit corrections, then compare full target and paid profiles. Reject if completion, owned lifetimes or consumer costs repay the gain. A static pairing rank alone is not a physical split.", + "bottleneck_link": "Judge the actual current supplier contract and complete signed target/paid bill; frozen-profile ceilings require an applicability proof.", + "allowed_variations": [ + "One exact source head, helper/cut region or quantified proposition and changed hypothesis; check live handoffs first. Different seeds are not different scopes." + ], + "scope_change_triggers": [ + "Changing source head, helper/cut domain, operation alphabet or caller boundary without recording the new scope.", + "Treating an archived proposal or local numerical pass as complete supplier admission." + ], + "overlap_terms": [ + "P104", + "helper basis", + "helper split", + "5718", + "dyadic capacity" + ], + "existing_checks": [ + { + "scope": "PR #4133: literal-slot defect", + "evidence": "research/p104-literal-slot-defect/README.md", + "remaining": "Independently validate the stated scope or change its producer/consumer premise and pay the complete boundary.", + "status": "author-checked", + "source_commit": "88666f1dee93fbd85b31fd5d6f91a219e111b5f4", + "selected_record_sha256": "bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129" + }, + { + "scope": "PR #4136: uniform commutation gap", + "evidence": "research/p104-uniform-commutation-gap/README.md", + "remaining": "Independently validate the stated scope or change its producer/consumer premise and pay the complete boundary.", + "status": "author-checked", + "source_commit": "281ce601a8be9db470de630759179c23e1dfaa88", + "selected_record_sha256": "bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129" + }, + { + "scope": "PR #4140: uniform encoding gap", + "evidence": "research/p104-uniform-encoding-gap/README.md", + "remaining": "Independently validate the stated scope or change its producer/consumer premise and pay the complete boundary.", + "status": "author-checked", + "source_commit": "de25c6525aa866962309df5d107b32d55e6e5628", + "selected_record_sha256": "bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129" + }, + { + "scope": "PR #4153: source-chart shortcut exhausts its optimistic allowance", + "evidence": "research/p104-source-chart-shortcut/README.md", + "remaining": "Independently validate the stated scope or change its producer/consumer premise and pay the complete boundary.", + "status": "author-checked", + "source_commit": "9123241fea53df77e51ffe30d9aca1625d4bf3a8", + "selected_record_sha256": "bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129" + }, + { + "scope": "PR #4154: fiber-tag seam mismatch", + "evidence": "research/p104-fiber-tag-seam/README.md", + "remaining": "Independently validate the stated scope or change its producer/consumer premise and pay the complete boundary.", + "status": "author-checked", + "source_commit": "4ffcdaee5d6255a9cea1fe53a5424435068089d0", + "selected_record_sha256": "bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129" + }, + { + "scope": "Selected PR5599: complete helper-subspace construction and independent caller replay; five framework assumptions remain.", + "evidence": "docs/research/pr-intake-evidence/pr5599-completion/PROOF-REVIEW.md", + "remaining": "The next experiment must identify uncovered source-specific work. Successor archive intake does not transfer this admission.", + "status": "reviewed", + "source_commit": "09dd0965711ca7eeb169057a420abab1c9052137", + "selected_record_sha256": "2a0220e866417774606e0f991e41b9c1d26b1f43b97857238cf478dbc7d330b5" + } + ] + }, + "scope_status": "changed", + "actual_scope": "Exact scalar census, on the PR5907 P104 word, of helper splits with the shape of PR5718: a helper retired at a strictly intermediate chart with a unit injection of a new independent helper, an input functional on group, U-initial or empty-frame-initial roles, and output normalisation only on roles whose final chart is V. Calibrated on the PR5713 source word, where it recovers PR5718's own split.", + "scope_change_reason": "The card asks for a complete legal split with its invoice. PR5994 excluded PR5599-type splits on PR5907 and named PR5718-type splits as the remaining route; this package tests that route's scalar necessary condition and locates where a mid-word correction would be needed, without building a supplier.", + "bottleneck_link": "Complex currently binds the selected assembly; a zero-paid helper split adds H_r+H_s-H_(r+s) per LOCAL to the productive side. This census says which split shapes remain possible on the latest conditional P104 word.", + "budget_minutes": 60, + "stop_rule": "Stop at one exact census with calibration; do not build or price a split.", + "outcome": "completed", + "evidence": "verify.py: pinned inputs; calibration recovers PR5718's split (cut 14330, chart 602, helper 708) among 7 witnesses on PR5713, all at chart 602 and helper 708; PR5907 has 0 witnesses under both input rules (4,206 leak and 4 pairing classes under the empty-frame rule); 6 synthetic decision controls; RESULT.json compared byte-for-byte.", + "author": "Nick Petalas", + "ai_assistance": "Independent human and formal proof-kernel review are unclaimed.", + "open_questions": [ + { + "question": "Can a mid-word correction remove the z-leak of one of the 425 PR5907 classes whose leak reaches exactly one role outside V?", + "why_it_matters": "These are the only PR5718-type candidates on PR5907; each one that closes adds one zero-paid split per LOCAL.", + "first_step": "For a leak-1 class, list the later meetings of the pivot's chart with the leaked role and test whether S_tau e_r reaches the leaked output coordinate; then check the non-z part of the correction.", + "blocked_by": "A fast exact span maintenance for the meeting corrections; a direct Fraction implementation took more than ten minutes per word." + }, + { + "question": "Do the four PR5907 pairing failures at chart 549 (helper 173) survive a changed input functional outside the empty-frame rule?", + "why_it_matters": "They are the only PR5907 classes with no output leak; only the pairing a_p = d_p c_p fails.", + "first_step": "Print A and d_p for cut 15974 and test which extra input role would make a_p = d_p c_p solvable.", + "blocked_by": "None." + } + ] +} diff --git a/research/p104-pr5718-shape-split-census/VERIFY.json b/research/p104-pr5718-shape-split-census/VERIFY.json new file mode 100644 index 0000000000..c70491ec4a --- /dev/null +++ b/research/p104-pr5718-shape-split-census/VERIFY.json @@ -0,0 +1,21 @@ +{ + "schema_version": 1, + "status": "ready", + "python": "3.12", + "requirements": [], + "inputs": [ + "research/p104-helper468-rung-removal/WORD.json.gz", + "research/p104-two-boundary-helper-split/inputs/pr5713-source.tar" + ], + "commands": [ + { + "argv": [ + "{python}", + "-B", + "{package}/verify.py" + ], + "timeout_seconds": 300, + "checks": "Authenticate the PR5907 word and the PR5713 source archive; exact census of PR5718-shape helper splits under group+U-initial and empty-frame input rules on both words; calibration recovers PR5718's split at cut 14330, chart 602, helper 708 on PR5713; zero witnesses on PR5907; six synthetic pairing-decision controls; RESULT.json compared byte-for-byte." + } + ] +} diff --git a/research/p104-pr5718-shape-split-census/shapesplit.py b/research/p104-pr5718-shape-split-census/shapesplit.py new file mode 100644 index 0000000000..6eedc849e7 --- /dev/null +++ b/research/p104-pr5718-shape-split-census/shapesplit.py @@ -0,0 +1,176 @@ +"""Exact census of PR5718-shape helper splits on a P104 word. Apache-2.0. Python 3.12, standard library only. + +Prepared by Nick Petalas. Extends the criterion and pure-subspace decision of Matarener's PR5994 census +(`research/p104-helper-split-exhaustion`, PR5599 PROOF.md section 1) to the shape of flyingviper's PR5718 split. + +Model (one helper p of a boundary group g = (U, V), cut after event i, strictly intermediate chart F holding p): + * input side: a combination a of the prefix rows of the fields at F with a_p != 0 and c = aP supported on the + group, on roles whose initial chart is U, or (in_kind='empty', PR5718's rule) on every role whose initial chart + is zero-dimensional; + * a new independent helper z replaces p after the cut (unit injection b = e_p, as in PR5718); its z-direction + reaches the outputs as d = S e_p (S = suffix columns of the original word); + * output normalisation only at V: every role whose final chart is V (other than p) may be corrected freely, so d + must vanish on O = {roles whose final chart is not V}; the pair needs a.b = c.d' != 0. +Classes whose d leaks into O are reported as `leak`: such a split needs a mid-word correction of that leak. +""" +from collections import defaultdict +from fractions import Fraction as Q +import gzip, json + + +def need(ok, why): + if not ok: + raise ValueError(why) + + +def read(path): + raw = open(path, 'rb').read() + return json.loads(gzip.decompress(raw) if str(path).endswith('.gz') else raw) + + +def spans(w): + out = [] + for basis in w['frames']: + s = {0} + for v in basis: + need(type(v) is int and 0 < v < 512 and v not in s, 'independent binary basis') + s |= {x ^ v for x in s} + out.append(frozenset(s)) + return out + + +def add(dst, src, q): + for k, v in src.items(): + x = dst.get(k, 0) + q * v + if x: + dst[k] = x + else: + dst.pop(k, None) + + +def groups_of(w): + n = w['public']; main = set(w['live']) | {r + 112 for r in w['live']} + g = defaultdict(set) + for r in range(n): + if r not in main: + g[(w['initial'][r], w['final'][r])].add(r) + return g + + +def pure_subspace(vecs, roles, support): + """Basis of {x : sum x_r vecs[r] supported in `support`} as (coefficients, image) pairs; kernel vectors included.""" + pivots, out = [], [] + for r in roles: + outside = {k: v for k, v in vecs[r].items() if k not in support} + coef = {r: Q(1)} + for key, prow, pcoef in pivots: + if key in outside: + s = -outside[key]; add(outside, prow, s); add(coef, pcoef, s) + if outside: + key = min(outside); s = 1 / outside[key] + pivots.append((key, {k: v * s for k, v in outside.items()}, {k: v * s for k, v in coef.items()})) + else: + img = {} + for x, q in coef.items(): + add(img, vecs[x], q) + out.append((coef, img)) + return out + + +def functional_witness(A, p, free, rho): + """Exact decision over the span of A. With L1 = a_p, L2 = c_p, L3 = c on the free coordinates and rho = d_p, a + split exists iff some a has L1 != 0 and (L3 != 0 or L1 = rho * L2): free coordinates of d' adjust c.d' at will, + otherwise c.d' = rho * c_p must equal a.b = a_p.""" + L1 = [coef.get(p, Q(0)) for coef, img in A] + L2 = [img.get(p, Q(0)) for coef, img in A] + L3 = [{k: v for k, v in img.items() if k in free} for coef, img in A] + if not any(L1): + return False + if any(L3): + return True + M = [L1[k] - rho * L2[k] for k in range(len(A))] # is L1 nonzero on ker M ? + if not any(M): + return True + j = next(k for k in range(len(A)) if M[k]) + return any(L1[k] * M[j] - L1[j] * M[k] for k in range(len(A))) + + +def census(w, in_kind='empty'): + """Returns (counts, classes). in_kind: 'boundary' (group + roles initial at U) or 'empty' (also every role + initial at a zero-dimensional chart).""" + n = w['public']; m = w.get('owned_fields', max(e[1] for e in w['program']) + 1 - n); N = n + m + prog = w['program']; S = spans(w); dims = [len(f) for f in w['frames']] + groups = groups_of(w) + valid = {g: {f for f in range(len(S)) if S[g[0]] < S[f] < S[g[1]]} for g in groups} + insup = {} + for g, rs in groups.items(): + s = set(rs) | {r for r in range(n) if w['initial'][r] == g[0]} + if in_kind == 'empty': + s |= {r for r in range(n) if dims[w['initial'][r]] == 0} + insup[g] = s + rows = [{r: Q(1)} if r < n else {} for r in range(N)] + cur = list(w['initial']) + [None] * m + at = defaultdict(set) + for r in range(n): + at[cur[r]].add(r) + snaps = defaultdict(list); counts = defaultdict(int) + for i, e in enumerate(prog): + op, r = e[0], e[1] + if op == 'MOVE': + at[e[2]].discard(r); at[e[3]].add(r); cur[r] = e[3]; touched = (e[2], e[3]) + elif op == 'INIT': + rows[r] = {}; cur[r] = e[2]; at[e[2]].add(r); touched = (e[2],) + elif op == 'CLEAR': + rows[r] = {}; at[e[2]].discard(r); cur[r] = None; touched = (e[2],) + elif op == 'SCALE': + rows[r] = {k: v * Q(e[-2]) for k, v in rows[r].items()}; touched = (cur[r],) + elif op == 'COPY': + rows[r] = {k: v * Q(e[-2]) for k, v in rows[e[2]].items()}; touched = (cur[r],) + else: + add(rows[r], rows[e[2]], Q(e[-2])); touched = (cur[r],) + for F in set(touched): + if F is None or not at[F]: + continue + roles = sorted(at[F]) + for g in groups: + if F not in valid[g] or not (groups[g] & at[F]): + continue + counts['evaluations'] += 1 + A = pure_subspace(rows, roles, insup[g]) + hp = [p for p in sorted(groups[g] & at[F]) if any(coef.get(p) for coef, img in A)] + if not any(img for coef, img in A) or not hp: + counts['no_helper_prefix'] += 1 + continue + snaps[i].append((F, g, hp, A)) + pivots = {p for v in snaps.values() for (F, g, hp, A) in v for p in hp} + fin = {p: w['final'][p] for p in pivots} + outside = {p: {r for r in range(n) if w['final'][r] != fin[p]} for p in pivots} + keep = {p: outside[p] | {p} for p in pivots} + cols = [{r: Q(1)} if r < n else {} for r in range(N)] + classes = [] + for i in range(len(prog) - 1, -1, -1): + for (F, g, hp, A) in snaps.get(i, []): + for p in hp: + d = {k: x for k, x in cols[p].items() if k in keep[p]} + leak = sum(1 for k in d if k in outside[p]) + if leak: + counts['kind_leak'] += 1 + kind = 'leak' + else: + free = {r for r in range(n) if r not in keep[p]} + kind = 'witness' if functional_witness(A, p, free, d.get(p, Q(0))) else 'pairing' + counts['kind_' + kind] += 1 + classes.append({'cut_after': i, 'frame': F, 'group': list(g), 'pivot': p, + 'ranks': [dims[F] - dims[g[0]], dims[g[1]] - dims[F]], 'kind': kind, 'leak': leak}) + e = prog[i]; op, r = e[0], e[1] + if op in ('INIT', 'CLEAR'): + cols[r] = {} + elif op == 'COPY': + add(cols[e[2]], cols[r], Q(e[-2])); cols[r] = {} + elif op == 'SCALE': + cols[r] = {k: v * Q(e[-2]) for k, v in cols[r].items()} + elif op == 'ADD': + add(cols[e[2]], cols[r], Q(e[-2])) + counts['witnesses'] = sum(1 for c in classes if c['kind'] == 'witness') + counts['pivots'] = len(pivots) + return dict(counts), sorted(classes, key=lambda c: (c['cut_after'], c['frame'], c['pivot'])) diff --git a/research/p104-pr5718-shape-split-census/verify.py b/research/p104-pr5718-shape-split-census/verify.py new file mode 100644 index 0000000000..956bf01291 --- /dev/null +++ b/research/p104-pr5718-shape-split-census/verify.py @@ -0,0 +1,114 @@ +#!/usr/bin/env python3 +"""Verify the PR5718-shape split census on the PR5713 source word and the PR5907 word. Apache-2.0. + +Prepared by Nick Petalas. Python 3.12, standard library only. +Checks: (0) pinned input bytes; (1) calibration: on the PR5713 source word the census finds PR5718's own split +(cut after event 14330, chart 602, helper 708, ranks (2, 7)) and every witness lies on that chart and helper; +(2) on the PR5907 word the census finds no witness under either input rule; (3) synthetic controls of the exact +pairing decision; (4) RESULT.json equals the recomputed receipt. Run with --write to regenerate RESULT.json. +""" +from collections import Counter, defaultdict +from fractions import Fraction as Q +from hashlib import sha256 +from pathlib import Path +import gzip, importlib.util, io, json, sys, tarfile, time + +HERE = Path(__file__).resolve().parent +ROOT = HERE.parents[1] +WORD5907 = 'research/p104-helper468-rung-removal/WORD.json.gz' +TAR5713 = 'research/p104-two-boundary-helper-split/inputs/pr5713-source.tar' +MEMBER5713 = 'research/p104-temporal-updates/WORD.json.gz' + + +def need(ok, why): + if not ok: + raise SystemExit('FAIL: ' + why) + + +def load_module(): + spec = importlib.util.spec_from_file_location('p104_shape_split', HERE/'shapesplit.py') + mod = importlib.util.module_from_spec(spec); spec.loader.exec_module(mod) + return mod + + +def pinned_inputs(): + pins = {row['path']: row['sha256'] for row in json.loads((HERE/'SOURCES.json').read_text())['files'] + if row['usage'] == 'input'} + need(set(pins) == {WORD5907, TAR5713}, 'declared live inputs') + for path, digest in pins.items(): + need(sha256((ROOT/path).read_bytes()).hexdigest() == digest, 'pinned bytes of ' + path) + with tarfile.open(ROOT/TAR5713) as tar: + raw = tar.extractfile(MEMBER5713).read() + return json.loads(gzip.decompress((ROOT/WORD5907).read_bytes())), json.loads(gzip.decompress(raw)), \ + sha256(raw).hexdigest() + + +def summary(counts, classes): + leak = [c for c in classes if c['kind'] == 'leak'] + per_pivot = defaultdict(list) + for c in leak: + per_pivot[c['pivot']].append(c) + return { + 'evaluations': counts['evaluations'], 'pivots': counts['pivots'], + 'no_helper_prefix': counts.get('no_helper_prefix', 0), + 'classes': dict(sorted(Counter(c['kind'] for c in classes).items())), + 'witnesses': [{k: c[k] for k in ('cut_after', 'frame', 'group', 'pivot', 'ranks')} + for c in classes if c['kind'] == 'witness'], + 'pairing_failures': [{k: c[k] for k in ('cut_after', 'frame', 'group', 'pivot', 'ranks')} + for c in classes if c['kind'] == 'pairing'], + 'min_leak': min((c['leak'] for c in leak), default=None), + 'leak_size_counts': dict(sorted(Counter(str(min(c['leak'], 6)) if c['leak'] < 6 else '6+' for c in leak).items())), + 'leak_by_pivot': {str(p): {'classes': len(v), 'first_cut': v[0]['cut_after'], 'last_cut': v[-1]['cut_after'], + 'min_leak': min(c['leak'] for c in v), 'group': v[0]['group']} + for p, v in sorted(per_pivot.items())}, + } + + +def controls(M): + """Exact pairing decision on synthetic subspaces (each A entry is (coefficients over fields, image c)).""" + p = 'p' + A = [({p: Q(1)}, {'x': Q(1)})] + need(M.functional_witness(A, p, {'x'}, Q(0)), 'free image coordinate gives a witness') + need(not M.functional_witness(A, p, set(), Q(0)), 'no free coordinate and c_p = 0 gives none') + A = [({p: Q(1)}, {p: Q(2)})] + need(M.functional_witness(A, p, set(), Q(1, 2)), 'a_p = d_p * c_p gives a witness') + need(not M.functional_witness(A, p, set(), Q(1)), 'a_p != d_p * c_p on a line gives none') + A = [({p: Q(1)}, {p: Q(2)}), ({'q': Q(1)}, {p: Q(1)})] + need(M.functional_witness(A, p, set(), Q(1)), 'a second direction repairs the pairing') + A = [({'q': Q(1)}, {'x': Q(1)})] + need(not M.functional_witness(A, p, {'x'}, Q(0)), 'a_p = 0 everywhere gives none') + return 6 + + +def main(): + t0 = time.time() + M = load_module() + w5907, w5713, sha5713 = pinned_inputs() + receipt = {'schema': 'p104-pr5718-shape-split-census/1', + 'inputs': {'PR5907_word': WORD5907, 'PR5713_word': TAR5713 + ':' + MEMBER5713, + 'PR5713_word_sha256': sha5713}, + 'runs': {}} + for name, w in (('PR5713', w5713), ('PR5907', w5907)): + for in_kind in ('boundary', 'empty'): + counts, classes = M.census(w, in_kind) + receipt['runs'][name + '/' + in_kind] = summary(counts, classes) + for in_kind in ('boundary', 'empty'): + cal = receipt['runs']['PR5713/' + in_kind]['witnesses'] + need({'cut_after': 14330, 'frame': 602, 'group': [3, 127], 'pivot': 708, 'ranks': [2, 7]} in cal, + 'calibration recovers PR5718 split at cut 14330, chart 602, helper 708') + need(all(c['frame'] == 602 and c['pivot'] == 708 for c in cal), 'calibration witnesses on chart 602 only') + need(receipt['runs']['PR5907/' + in_kind]['witnesses'] == [], 'no PR5718-shape split on PR5907') + receipt['synthetic_controls'] = controls(M) + path = HERE/'RESULT.json' + text = json.dumps(receipt, sort_keys=True, separators=(',', ':')) + '\n' + if '--write' in sys.argv: + path.write_text(text) + need(path.read_text() == text, 'RESULT.json equals the recomputed receipt') + r = receipt['runs']['PR5907/empty'] + print('PR5713 calibration witnesses:', len(receipt['runs']['PR5713/empty']['witnesses']), + '| PR5907 classes:', r['classes'], '| min leak', r['min_leak'], '| %.1fs' % (time.time() - t0)) + print('PASS_P104_PR5718_SHAPE_SPLIT_CENSUS') + + +if __name__ == '__main__': + main()