[petalas]

Summary

On ToikY's fixed 93-line first-failure unit from #1609, an explicit non-coordinate eight-term frame permits a one-sided mask-only completion that saves one separate-term COPY unit. A different all-pairs frame on the same live lines is cheaper.

Construction	Actual support pairing ranks	COPY
Exhibited non-coordinate frame, all-pairs	9,9,9,9,9,9,9,9	72
Same frame, one-sided mask-only	8,9,9,9,9,9,9,9	71
Another frame, all-pairs	7,8,7,8,8,8,8,9	63

Claim type: finite exact constructions, supported by a written linear-algebra derivation and generated hash-bound receipt. The contribution is the non-coordinate fixed-frame saving and the explicit comparison that limits its significance. No optimum, physical supplier, new κ or selected-frontier change is claimed. Only research/first-failure-one-sided-copy/ is added.

Evidence

Before, #1609 supplies the 27-deletion instance and an unchanged coordinate COPY72 diagnostic. Here take doubled target q=(2,2,0,0,0,0,0,0) and normal n=(1,-1,2,0,0,0,0,0), bottom directions 13q+7n,e1,...,e7, and their duals as top directions. Changing only the target bottom row by (-52/21)n cancels the target in the first bottom support. That term's pairing rank drops from nine to eight. All seven other terms retain rank nine.

The product residual is (c/2)(q_i dot n) in the target column and zero elsewhere. Exact rational arithmetic checks all 8,649 entries of the one-sided product, the same-frame baseline and the all-pairs comparator. The one-sided product has zero masked errors and exactly 56 unmasked target-column errors; both all-pairs products have no errors. Every term's actual support pairing rank agrees between bitset and separate dense F2 elimination.

The receipt contains both frames and their exact rational duals, with verifier and predecessor-certificate SHA256 hashes. Controls detect a planted masked coefficient error, expose a masked error for each of 27 one-line restorations, and distinguish a rank-eight term from rank nine. An existing receipt destination is rejected without overwriting it.

Reproduce from the repository root with CPython 3.12.15, standard library only. Another CPython 3.12 installation can replace the interpreter path.

/Users/nick/git/integer-mult-bounds/.venv/bin/python3.12 -B scripts/research_package.py --package research/first-failure-one-sided-copy --check-only
/Users/nick/git/integer-mult-bounds/.venv/bin/python3.12 -I -W error -B research/first-failure-one-sided-copy/verify.py
/Users/nick/git/integer-mult-bounds/.venv/bin/python3.12 -I -O -W error -B research/first-failure-one-sided-copy/verify.py
/Users/nick/git/integer-mult-bounds/.venv/bin/python3.12 -B scripts/research_package.py --package research/first-failure-one-sided-copy
/Users/nick/git/integer-mult-bounds/.venv/bin/python3.12 -B scripts/check_research_commit.py --package research/first-failure-one-sided-copy --check-source-history

Local checks pass at bcb077767c14eb22ef158b43c2336f79e1d9b347:

• PASS_PACKAGE_METADATA_AND_PINS.
• Both direct runs print PASS_FIRST_FAILURE_ONE_SIDED_COPY one_sided=71 same_frame=72 all_pairs=63 no_new_kappa. Measured wall times are 0.31 s and 0.32 s, each below its 120-second registered limit.
• The registered runner executes both commands and prints PASS_REGISTERED_RESEARCH_PACKAGE ... outcome=completed; the timed run takes 1.02 s total.
• PASS_RESEARCH_COMMIT_BYTES, seven files including the live input, with source-history ancestor e54523517d0f03e58352e647c403a5af3e525a57.
• The source-bound orientation command prints PASS_RESEARCH_BASELINE_BINDINGS_ONLY. It is metadata orientation, not a selected supplier replay.

Limitations

The result fixes the live unit, displayed frames and additive separate-term binary pairing-rank charge. The sorted COPY63 profile is strictly cheaper than the COPY71 profile for every positive COPY power. This proves only that comparison; no global optimum or lower bound is established.

Gathering, native endpoints, arbitrary-dirty restoration, frame changes, hosting, precision/tape, all-size/compiler realization and analytic transfer are unpriced and unproved here. No selected cold replay, Lean or Docker run was performed. Independent human and formal proof-kernel review are unclaimed. The predecessor's sharp deletion threshold and flat census are cited, not replayed.

Open next questions

Can an eight-term one-sided mask-only completion on this fixed unit beat the exhibited all-pairs profile 7,7,7,8,8,8,8,9? First parameterize the root-linear top frame and the one-dimensional target-row freedom, then recount actual support pairing ranks. The missing step is optimization or a lower bound over arbitrary frames; physical realization would still require a complete invoice. The structured question is in TASK.json.

Related open work

• #7170, head 2c4bb35a8f49bc1ed5576ac075dca0314c6b02a0, studies the same 93-line puncture of Research: sharp 27-deletion boundary for one-sided E8 masked rigidity #1609. It classifies the coordinate scalar family and bounds savings when the dual directions are roots. Our displayed non-coordinate bottom direction 13q+7n and coordinate bottom directions fall outside that root-dual hypothesis, so its exceptional-scalar statement does not apply to our c=-52/21 construction. Bound scalar COPY savings at one 93-line E8 puncture (no κ) #7170 does not compute either displayed frame's COPY profile; no identical frame-and-scalar numerical verdict is asserted by both packages. Its coordinate census and root-direction bound are not re-proved here.
• #7168 minimizes the E8 Gram-class cost over deleted sets through 24 deletions and allows an arbitrary invertible coefficient matrix. This package fixes the 27-deletion set, requires the all-pairs Gram identity for its comparators and allows a masked target-row shift for its one-sided example. The stated domains do not share a computed optimum.
• #7174 studies block realizability of a different 96-line E8 complement. Its inner-dimension obstruction does not price these fixed 93-line support pairings.
• #3566 binds a tetrad-local masked decoder to a different P112 unit and gives conditional ideal budgeting. This package concerns the fixed 93-line unit and makes no supplier-budget claim.
• The earlier coordinate-perturbation claim, now Bound scalar COPY savings at one 93-line E8 puncture (no κ) #7170, owns the coordinate scalar census. This delivery omits that census, the general first-failure census and root-frame optimization. Its single COPY63 comparator interprets the non-coordinate COPY71 example and is not asserted best.

The final own-account check read all 13 open PRs created since the CLAIM: #7132, #7133, #7134, #7135, #7167, #7168, #7169, #7170, #7172, #7173, #7174, #7175 and #7176. Apart from this PR, #7170 is the same-puncture work; #7168 and #7174 have the adjacent E8 scopes described above. The others study different objects or charges, so no shared numerical result requires comparison. No numerical disagreement under identical hypotheses was found, and no additional computations were run to audit another PR.

The account's open PRs, current open PR bodies, latest 30 handoff comments, merged semantic searches and main README searches were checked before committing. No open PR found in those checks states these fixed-unit constructions. The complete overlap-helper snapshot covers 466 open PRs and 7,089 discussion records as of 07:53 to 07:56 UTC on November 11. Search coverage is not a novelty proof. Merged #2816 treats P112 one-sided classes; merged #5232 fixes A7+A1 normals on another puncture. Both retain credit and are outside the claimed finite construction.

Canonical CLAIM and FINDING. The finding records omission of the coordinate census from the original plan.

CI notes

CI did not certify this package. At head bcb077767c14eb22ef158b43c2336f79e1d9b347, run 42983930022, plan job 130400533193, failed in Onboarding helper tests. I read the checks once after completion and inspected this job's log. It reports exactly one failure among 760 tests, with 24 skipped:

test_research_current_status.CurrentCiNavigationTests.test_current_ci_section_matches_selected_record
AssertionError: '`make frontier7000-verify`' not found in the CI verification document

The unchanged base e54523517d0f03e58352e647c403a5af3e525a57 already has the mismatch: certificates/selected-result.json requires make frontier7000-verify, while the current section of docs/ci-verification.md describes #6030 and make frontier6030-verify. The failing test, selected record and CI document are unchanged by this PR.

The package replay job 130402356837 was skipped after plan failed. The scientific evidence remains the local verification at the exact head above; there is no hosted package replay result.

I also inspected the failed logs of run 42905094314, run 42903313790, #7132 run 42914704054 and #7135 run 42914936342. All four report the same sole failing test and missing-command assertion, with 760 tests and 24 skipped. The two previously inspected account runs also have skipped replay jobs. No shared-file fix, new commit, push, job rerun or retrigger was made; maintainers retain the repository-level repair.

Merge danger

Door: two-way. Blast radius: one new research directory. The selected record, shared scripts and frozen predecessor evidence are unchanged.

Credit

This contribution was produced by Nick Petalas. ToikY #1609 supplies the boundary, instance and open question; mightyOil #1191 the one-sided spanning mechanism; DreamingOfClouds #717/#2338 the COPY model and accounting context; joaqcoo #1224 and Adam Gall #2062 the row-shift normal forms; Nick Petalas #5232 the different A7+A1 application. DreamingOfClouds #595 and DaysSky #897 retain the E7 geometry credit. Apache-2.0.