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Correct word-census parity budgets; 22 <= f(7) <= 24 in the PR943 model - #2973
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…ngth degree-filter justification Checks the retained PR #2542 joint_covers set enumerator, at its actual coordinate-bit-0 split sizes, against a separate unpruned subset oracle: all 32,906 zero-containing sets of F2^n for n = 1..4 and all 200 exact split/filter domains agree (covers 1, 4, 64, 23,552; minimum-degree-two subcounts 0, 1, 20, 5,074), confirming on the actual function the set-level scope that PR #2973 states. The minimum-length universal word 010122 (prefix set {0,1,2,3,4}, vertex 4 of degree one) refutes the docstring's claim that minimal words walk a Hamiltonian cycle, so the optional degree-two filter is justified only under |P| = L >= 4; the (3,2) call returns 18 covers unfiltered and none filtered. A pinned call-site map finds six Python word calls plus PR #2691's native rule on the invalid balanced budget and four set calls with the filter off; PR #2773's set rows reproduce without the word engine, conditional on its recorded Sidon floors. No new bound, f(7) claim or kappa change. Adds research/f7-set-word-pruning-boundary/ only. Submitted by @commdata2338 with substantial AI assistance (OpenAI Codex research and implementation; packaged with Claude Code). Co-Authored-By: Claude Opus 5.5 (1M context) <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_01X86sCSXdoDd61SDFfC1PKG
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…its simple-word boundary Proves that Engine::capacity, the parity-capacity filter in conorholds' simple length-22 exclusion, is a necessary condition for simple restored universal words under its four-low, three-high projection, including pairs between different blocks at one repeated low vertex, and that each of the sixteen low-linear parity changes preserves its verdict. A separately written position-pair oracle agrees with the compiled predicate on all 791,827 declared gap inputs (53,379 accepted, not claimed to be words); all 176 projections of a universal simple 24-step word pass, 120 with repeated low vertices; parity-reset and omitted-pair mutants are detected. The universal word 010201030102010345464546 has 23 distinct prefixes and is rejected because nine positions at low zero carry eight high states, so the filter needs the simplicity premise that the predecessor's length-22 branch has; this is not a source bug or a length-22 counterexample. It also reconstructs PR #2973's 01021323 calibration and pins the old bit-0 call sites of PR #2542, #2634 and #2691. Complete censuses, the other propagation rules, the published classification premises and the non-simple branch are not checked. No new kappa. Adds research/connector-capacity-parity-audit/ only. Submitted by @commdata2338 with substantial AI assistance (OpenAI Codex research and implementation; packaged with Claude Code). Co-Authored-By: Claude Opus 5.5 (1M context) <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_01X86sCSXdoDd61SDFfC1PKG
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The CrocSwap#2973 correction reports that the retained PR2542/PR2634/PR2691 word engines group prefix states by coordinate bit 0 while applying a collision budget derived for Hamming-weight parity. That report singles out bit 0. This package tests the changed hypothesis that the substitution is not a bit-0 artifact but a property of the L/2 substitution for any functional other than the parity one. It recomputes the 01021323 fixture from scratch, then classifies all 2^n - 1 nonzero linear functionals on nine small singleton prefix-walk domains with n <= 7 and L <= 14. At (4,10) and (5,12) the substitution falsely prunes a universal word for every functional of Hamming weight <= n-2 and for none of weight >= n-1. At (4,8) the same holds except for one weight-2 functional. Bit 0 is the first member of that class, not a special case. The package also proves and machine-checks the alternation lemma l(q_{i+1}) XOR l(q_i) = v_{w_i}, which identifies the all-ones functional as the only one whose class value alternates with time and therefore the only one for which the L/2 substitution has a justification. Scope: finite certificate on a stated small domain plus one scoped lemma. The seven-label decision regime (7,18) and (7,20) is not reached; the only seven-label domain here is vacuous. No new f(7) bound, no kappa, no selected-frontier change, and no claim that any old exclusion is right or wrong. Co-Authored-By: Nick Petalas <petalas@users.noreply.github.com>
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The CrocSwap#2973 correction reports that the retained PR2542/PR2634/PR2691 word engines group prefix states by coordinate bit 0 while applying a collision budget derived for Hamming-weight parity. That report singles out bit 0. This package tests the changed hypothesis that the substitution is not a bit-0 artifact but a property of the L/2 substitution for any functional other than the parity one. It recomputes the 01021323 fixture from scratch, then classifies all 2^n - 1 nonzero linear functionals on nine small singleton prefix-walk domains with n <= 7 and L <= 14. At (4,10) and (5,12) the substitution falsely prunes a universal word for every functional of Hamming weight <= n-2 and for none of weight >= n-1. At (4,8) the same holds except for one weight-2 functional. Bit 0 is the first member of that class, not a special case. The package also proves and machine-checks the alternation lemma l(q_{i+1}) XOR l(q_i) = v_{w_i}, which identifies the all-ones functional as the only one whose class value alternates with time and therefore the only one for which the L/2 substitution has a justification. Scope: finite certificate on a stated small domain plus one scoped lemma. The seven-label decision regime (7,18) and (7,20) is not reached; the only seven-label domain here is vacuous. No new f(7) bound, no kappa, no selected-frontier change, and no claim that any old exclusion is right or wrong. Co-Authored-By: Nick Petalas <petalas@users.noreply.github.com>
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…,7), (10,8), (11,8) Extends the #2973 corrected word-census engine to length 22 by changing only its compile-time gate (three header/gate lines; all counters stay within their exact types). Validates the extension against the pinned predecessor: its math check, its brute-force small-domain cross-check in all four budget modes, and node-exact reproduction of all six recorded L20/L18 receipts (590371593 / 244301902 / 14450133 / 67643567 / 35241 / 951416 nodes). Runs capped censuses at the nine open length-22 splits of the PR #3708 split domain with both proved necessary budgets. Three splits complete with complete=true and zero hits - finite exclusions of (11,7) at 8,784,744 nodes, (10,8) at 597,933,297 and (11,8) at 1,349,702,650. The six loose-budget splits abort at the 2e9-node cap and are recorded as tree-size lower bounds only. With the imported #2773/#2870 exclusions, the length-22 domain narrows from nine splits to six. No hits anywhere; f(7) in {22,24} is untouched; no kappa, supplier or frontier change. Supplies the node-budget measurement named as the blocker of the #3708 handoff (open question 1). Fresh CI replays compare against the committed RESULT.json receipt; node equality is deterministic, timing excluded.
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…split Ports the completion bound already proved in the merged independent census #3005 into the corrected seven-label census engine of #2973. The bound uses the union of the two same-parity pair supports and dominates the predecessor's even excess budget. The engine delta is committed as a zero-context diff against the pinned source; the length gate extension to 22 is the same one recorded in PR #3731. Validation: the predecessor's raw-product brute force passes for all small splits and all four budget modes, a union-only mode matches the brute-force universal counts, and the six recorded L20/L18 receipts replay complete with zero hits (node counts intentionally not compared). Length 22: the (9,9) split completes with zero hits at 388,563,293 nodes, a new finite split exclusion. The other five splits have measured sharded-node floors only; capped shards are never treated as exclusions. No kappa, supplier or selected-frontier change, and no length-22 decision.
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Show the fixed L/2 firing set is not monotone in length (no new κ)
unpaidmoon/integer-mult-bounds#61
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The word-census engines in #2542/#2634/#2691 use bit-0 state groups with budgets derived for Hamming-weight parity. This can falsely prune universal words: the simple balanced n=4, L=8 word
01021323covers all 16 masks but has bit-0 excess 8 against the incorrectly substituted budget 5. Historical count agreement therefore did not establish the claimed exclusions.Adds an isolated corrective package with a weight-parity, revisit-aware C engine, proofs for both necessary collision budgets, independent direct/brute Python controls, and full fresh enumerations:
Each run completed from the empty prefix without a cap, exit 0,
complete=true. Candidate leaves are not reported as all restored words. Exact split classification, parity-swap symmetry and padding of shorter restored words prove 22 <= f(7) <= 24 within the PR943 singleton prefix-walk model; the known Gray length-24 witness is checked directly. No supplier, tariff, selected-frontier or kappa change. This is a finite computational exclusion, not a formal-kernel proof.Validation: 164 small full-domain C/brute comparisons across four budget modes; 12 cap/input/output controls; 36 capped n=7 exact C/Python comparisons; independent mathematical checks; then a second complete six-case replay from the integrated package. Both production and integrated counts agree. The independent n=7 Python check is capped, not a second full n=7 implementation replay.
Observed:
PASS_F7_WEIGHT_PARITY_FULL ... f7_lower=22 f7_upper=24;PASS_PACKAGE_METADATA_AND_PINS. ~1 minute for the C traversals on the recorded Apple arm64 host; standard-library Python 3.12 and Clang/GCC required. Quick mode runs fresh controls and checks stored receipts, and explicitly does not claim a fresh complete census.Frozen predecessor packages are unchanged. Bit 0 remains valid in set-level searches using actual group sizes; later #2773/#2870/#2911/#2933/#2961 results are scoped separately in MATH.md. Also corrects the previous local session's overstrong “zero slack” implication. Scientific base a23bdc1; refreshed main ec1f08b has unchanged pinned engines and selected record. No new competing correction found in the checked live PR/discussion corpus.
Continuation CLAIM: #2691 (comment) ; coordination: #1166 (comment) .
Contributor: Nicholas Stone, with substantial OpenAI Codex assistance including three complementary agents; no independent human review claimed. Credit Ross Richardson (PR943 model), Douglas Colkitt (PR1185 record), Aaron Wang/opencode (#2542/#2634 and later set-level work), Nicholas Stone (PR2691 predecessor engine). Apache-2.0. Open next questions: independent complete implementation replay and length 22 versus 24.