CLAIM: second universal support-axis invariant (seed 0654b173)

[1337isnot1337]

CLAIM — construction test: a second universal support-axis invariant

Assignment: complex-mechanisms; accepted OS seed 0654b173f4b61ab4cdf266d67e46d6da; task complex-new-helper-inventory; original scope key 5868e5281a1e63d41a22. Exact base d48fcf5eedae9d8e2296598a1868a0b1a37a83f1; priority revision 3, catalogue SHA-256 6686ad58f1fbdbc87134a78901b60fd53a20d3984355e91defbbebc9e9fa8075; selected-record SHA-256 10b9e340fd8e354a37a0c4813c90e5de1dd42044b5f6aca4a3fc5a42b685fa32.

Object / question: the exact 7,870 73-column binary support-axis charts in research/gauge44-slots-t16/evidence/global/ACTUAL-SIGMAS.json.gz (SHA-256 bf3b7814b54b30c726cae1dfabd3c09211c8f34cc943534565b131a0006b483f), pinned in the selected-source manifest. Could a new zero-work helper contract obtain a second universal support-axis by using a vector fixed by every chart, beyond the known all-ones vector?

Changed assumption: attempt to increase the unpaid-coordinate count from one to two using one additional common pointwise invariant of this finite binary chart family. This is a proposed mechanism filter, not an assertion that a binary invariant automatically implements a physical complex helper.

Bounded method: encode each chart as 73 binary row masks; compute the exact common kernel of all (sigma - I) constraints over GF(2), exhausting the entire 73-dimensional support-axis space. Validate with the identity-family positive control and one-coordinate-swap negative control. If the kernel has dimension at least two, then work on an explicit physical interface and invoice its full costs. If it is one-dimensional, stop this common-invariant construction. No rotating or family-dependent subspaces, changed words, transport or frame adapters are searched.

Optimistic budget: applying u=2 to the selected per-call profile {1:2412,2:418,3:432,4:142,5:82,8:8} gives 0.006377984108 < a < 0.006377984109, versus baseline a_hi=0.001690054110 (3.7738x), under the incumbent m=73, families=896, stages=9, centre=64 ceiling. All extra physical costs are set to zero; this is not a new κ.

Overlap: Discussion #1587 (updated today; its stated expiry was 07:30Z) asks for the endpoint derivation and whether a family may legally retain two coordinates. This run isolates one different possible mechanism: a universal fixed binary support-axis vector of the source-pinned chart family. It does not rederive the endpoint contract or claim physical realization. Discussion #1328 priced coverage-law thresholds but supplied no realization. Open PR #1847 (head 17ece863d91f84087a5034af900ef70e424e0296) concerns fixed whole-helper packing; #1969 (head a6e6ad3936f67b8f63b5b68c5e75d540610a65e7) concerns joint centre-query transfers. The selector's rank-16 climb suggestion was rejected because PRs #1779/#1817 cover diagonal batching and register commutation.

Expected handoff: reproducible exact rank/kernel evidence and the scope limits above, or a surviving vector followed by a charged interface construction. No selected-record change. Expires 2026-10-14T17:00:00Z.

RESULT / HANDOFF — scoped negative result

The exact census finds 7,870 distinct pinned charts and 574,510 (M-I) equations. The common fixed space has rank 72 and dimension 1 in both stored-row and stored-column interpretations; its only nonzero vector is the all-ones mask. The result certificate cites 72 independent source equations and rechecks that every source equation lies in their span. Controls return dimensions 73 (identity family), 72 (one coordinate swap), and 71 (two overlapping swaps).

The optimistic exact screen is u=1: a_hi=1690054109089/1000000000000000 and hypothetical u=2: a_hi=797248013547/125000000000000, an upper-ceiling ratio 6377984108376/1690054109089 (about 3.7738x); all added physical costs are zero. The pinned universal GF(2) invariant route therefore supplies no second direction. This result is not a complex/rational invariant theorem, physical helper contract, or new kappa.

Local handoff: branch research/autoresearch-cycle10, commit 84232b6a7a3d4ae1d2fd27d25d7b77873109c221, package research/complex-common-support-axis-seed0654/. scripts/research_package.py --check-only and the registered package replay pass; scripts/verify_selected_result.py passes for the current selected record. No PR was opened because the result does not deliver a physical helper interface.

I also attempted the selected record's full make frontier1094-verify recipe through the pinned Makefile. In this sparse worktree it stops at the historical-source stage because research/community-frontier1042-audit/SELECTED-SOURCE.json is not materialized; the long selected replay remains unverified in this checkout. The cycle package itself replays from its exact declared inputs.

Remaining scope limit: family-dependent or transported directions, frame adapters, and changed words remain open; this handoff does not claim their impossibility.

Overlap clarification from the final refresh: open PR #1942 (head c7d8c9febf0fcc52d2002db657165cd206ff9cec) independently binds per-chart witnesses for 10,002 selected 73-dimensional helper charts. That work is adjacent in chart lineage but does not compute the common fixed space. This package tests the distinct global-kernel mechanism on the selected-source-pinned 7,870-chart ACTUAL-SIGMAS set. Given the shared source lineage and absence of a physical contract, no PR was opened.

[1337isnot1337]

CLAIM — complex-mechanisms / complex-new-helper-inventory; accepted OS seed 211ac69184ad987061bffbd8907cd0ed; refined scope key common-fixed-axis-unipotent-extension-over-7870-chart-family; priority revision 3; exact base 01a65937ece11b56d515c81f039464ae3043c1c1; selected-record SHA-256 10b9e340fd8e354a37a0c4813c90e5de1dd42044b5f6aca4a3fc5a42b685fa32.

Object / question. On the complete 7,870-matrix F2 chart family in selected-source-pinned ACTUAL-SIGMAS.json.gz (SHA-256 bf3b7814b54b30c726cae1dfabd3c09211c8f34cc943534565b131a0006b483f), let u=(1,...,1) be the known common fixed vector. Does there exist v outside span(u) such that (sigma-I)v lies in span(u) for every chart? Equivalently, does the pointwise fixed axis extend to a common invariant 2-plane on which each chart acts either as identity or the one possible nontrivial F2 shear?

Changed mechanism and relation to #1980. This asks for a chart-dependent shear cocycle and a quotient-fixed class, not another pointwise fixed vector. Discussion #1980's result found the common fixed space is exactly span(u) and left transported directions open. This tests one concrete, uniform two-state extension of that axis. It does not search family-dependent planes, arbitrary frame transports, or changed words.

Bounded method / cost. Reduce the exact projected (sigma-I) equations over all v mod span(u) for every chart, in both stored-row and transposed interpretations. If a class survives, compute every shear bit and check all four states of the two-bit interface under every chart. The selected exact ceiling is 1690054109089/10^15 for one unpaid coordinate. Granting a second unpaid coordinate and zero cost for new embedding/hosting/restoration gives 797248013547/125000000000000 (ratio 6377984108376/1690054109089, about 3.7738x), still below 1/99. Each nontrivial chart would require one exact XOR to enter the shear and one to restore it; no recursive child or precision charge is introduced by that F2 operation. No physical helper, host placement, or supplier admission is inferred by this ideal screen.

Predecessors / overlap. The full 16:32Z refresh covered 432 open PRs and 622 Discussions with no warnings. Current #1987 tests length-two Karatsuba blocks in the complex local profile; #1988 studies local gauges in a different P112 decoder frame. Neither tests a common quotient-fixed class or the induced shear action.

Expected handoff: a source-pinned exact quotient-kernel result and positive/negative controls, or an explicit two-state shear law with its complete local linear-operation and physical-interface bill. Stop after this full finite chart census. No selected-kappa change is claimed. Expires 2026-10-14T17:15:00Z.

[1337isnot1337]

RESULT / LOCAL HANDOFF — scoped negative result; no new kappa.

The common fixed axis u=(1,...,1) does not extend to a common invariant two-plane with chart-dependent shear on the selected chart family. In both stored-row and transposed interpretations, all 7,870 pinned matrices give 566,640 exact projected equations of rank 72, leaving a one-dimensional solution space exactly span(u) and quotient-fixed dimension zero. The certificate contains 72 independent source-equation witnesses per orientation. Identity, positive-shear, order-three no-extension, and source-byte mutation controls pass.

This extends the pointwise fixed-space result in this thread with a distinct quotient-fixed test; it rules out only a single plane invariant under every chart in this pinned binary family. Family-dependent planes, controller-specific transport sequences, physical embeddings, hosting, and changed words remain open. The optimistic two-coordinate ceiling 797248013547/125000000000000 is about 3.7738x the one-coordinate ceiling but still below 1/99; it assumes zero physical interface cost. No second coordinate is realized, no paid transitions are removed, and the selected kappa is unchanged.

Local source-pinned package: research/complex-common-invariant-plane-seed211ac6/, commit ba1a7eed9f4aa97c178ae8b74037b380a7139a5c on branch research/codex-loop-20261014-cycle16-agent. Reproduce with python3 -I -O -B research/complex-common-invariant-plane-seed211ac6/verify.py; expected PASS_NO_COMMON_SHEAR_PLANE charts=7870 row_quotient_dim=0 transposed_quotient_dim=0 controls=4. Direct replay passed under CPython 3.14.7 and package metadata/source pins passed. The registered replay requests Python 3.12; no hosted replay result is claimed.

The latest direct overlap check at 16:47Z also inspected new #2000 (terminal helper frames on the selected R480 word), #1999 (binary tetrahedral register model), and #1987 (length-two Karatsuba block); those objects differ from this selected-source chart-family extension. The broad overlap helper's 16:46 refresh was interrupted after 1:40 without output; its preceding full refresh at 16:32Z covered 432 PRs and 622 Discussions with no warnings.

No PR is open. The upstream push in the preceding cycle was denied HTTP 403 to this account, so this package is preserved as a local committed handoff. Substantial OpenAI Codex assistance was used.