[petalas]

Summary

A free choice of existing physical carrier exposes no further independent helper split on Ali Romman's final PR5708 G20 word. All 1,981 newly admitted group/frame contexts have zero boundary pairing, including 46 with two nonzero eligible kernels and 45 with a nonzero internal pairing.

- The cut bank must contain a role from the helper endpoint group.
+ Any role in the existing common-frame bank may carry the split coordinate.

Claim type: finite exact certificate with a scoped algebraic proof. This answers the common-frame part of PR5679's different-physical-role open question. No new kappa, supplier admission or complete multiplication theorem is claimed. The first verified expanded-domain result ended the search.

The six-file package is research/g20-free-carrier-split-obstruction. The new contribution was produced by Nick Petalas. Credit Ali Romman for PR5679's construction and open question, PR5708's exact final word and helper-pivot census, and PR5609's older-word cut method. Retain Dugongue, ai-nanachi, compact436 and all native/controller/helper/ordinary/stock source credit. These predecessor results are cited, not audited as the deliverable. Gaussian elimination and rank-nullity are classical.

Evidence

• Before, the published final-word census required a physical helper-group pivot. After, the complete eligible spaces in the 1,981 added contexts are certified orthogonal at the boundary. The obstruction excludes a necessary independence equation even when the cut carrier and boundary pivot are different physical roles.
• The standalone check imports no predecessor executable. It covers 14,795 event cuts, 685 fields, 645 rational frame classes and 7,870 distinct exact contexts. All boundary matrices are zero. The helper-pivot cases provide context for the expansion, rather than a separate audit contribution.
• All kernels receive equation, independence and opposite-pivot rank-completeness checks. All 516 controls pass, including 512 literal exhaustive kernel inputs and a positive example with no helper in the cut bank. Normal and optimized warning-strict direct checks pass in 0.712 s and 0.713 s locally on CPython 3.12.15, macOS arm64. Each registered command has a 120 s limit.
• Both registered commands, package metadata, committed-byte/source-history/mode preflight, official export/input integrity, and a read-only optimized export replay with Git absent from PATH pass. The nine-file export is unchanged after replay. Generated receipts bind the exact package file hashes. No receipt is hand-written.

Exact reproduction from the repository root:

/Users/nick/git/integer-mult-bounds/.venv/bin/python3.12 -I -W error -B research/g20-free-carrier-split-obstruction/verify.py
/Users/nick/git/integer-mult-bounds/.venv/bin/python3.12 -I -W error -O -B research/g20-free-carrier-split-obstruction/verify.py
/Users/nick/git/integer-mult-bounds/.venv/bin/python3.12 -B scripts/research_package.py --package research/g20-free-carrier-split-obstruction
/Users/nick/git/integer-mult-bounds/.venv/bin/python3.12 -B scripts/check_research_commit.py --package research/g20-free-carrier-split-obstruction --check-source-history --check-modes

Any CPython 3.12 interpreter may replace the local absolute path. Only the standard library is needed. Expected markers are PASS_G20_FREE_CARRIER_SPLIT_OBSTRUCTION, PASS_REGISTERED_RESEARCH_PACKAGE and PASS_RESEARCH_COMMIT_BYTES. The deterministic context-summary digest is ba0e0a6915ab530a5f4f31c8ddcf54055325aaa1521bc7057b776f92d085b276.

Limitations

The claim fixes the normalized word, its existing common-frame banks, one helper endpoint group at a time and address-independent binary bases. Zero boundary pairing also persists under characteristic-two scalar extension. Paid mixed-frame interfaces, mixed endpoint groups, changed contacts, new producers and address-dependent recoding are outside the result. The source's native frame induction and normalized helper endpoints are cited premises. No full native/caller replay, recursive price, compiler, precision, tape, outer assembly, selected cold replay or rounded multiplier was run. The five framework assumptions remain. Independent human and formal proof-kernel review are unclaimed.

Open next questions

1. Can a paid multi-frame boundary expose a nonzero pairing on this word? Specify one frame conversion and inverse at an exact cut, then price all queries, targets, routes and restoration. No such channel or complete bill is supplied here.
2. Can one changed contact expose a nonzero pairing in one of the 46 new contexts with both kernels nonzero? Inspect one exact support pair, prove the changed independent endpoint and account for its full bill. Moving the carrier inside the unchanged bank cannot suffice.

Related open work

• #5955 independently audits PR5679/5708's endpoints, caller and ordinary admission. This contribution answers the untested physical-carrier extension of their split domain; it does not replay that audit or compute a competing ordinary saving.

• #5942 proves a scalar ADD floor for a different G20 boundary chain/exchange component. This contribution concerns helper splitting in the PR5708 word; no common numerical minimum is compared.

• #5985 improves the literal G20 quarter-carry leaf dispatcher. It does not change the PR5708 helper-split word or compute a competing boundary pairing or split count.

The completion refresh inspected the ten other open account PRs created since the advance CLAIM: #5981, #5982, #5984, #5985, #5986, #5987, #5988, #5989, #5990 and #5992. They concern Gaussian stages, Walsh tape travel, the selected outer ledger, G20 carry dispatch, Gaussian inverse locality, chirp movement, frame-span call floors, reciprocal guards, fused connector reads and pooled R437 moments. None reports a competing helper-split count on this word. No additional mathematical computation was run to compare those contributions.

CI notes

Both hosted checks passed at exact head 795c4f59aa9e7ca7e133bea6e3ea21837c5849dd: plan in 7m15s and replay (research/g20-free-carrier-split-obstruction) in 6m52s, in run 40570621490. The completed check list was read once, and the run head matches the PR head. Hosted replay certified the registered normal and optimized finite checks. Local scientific, metadata, committed-byte/source-history/mode and portable-export checks also passed. CI does not establish independent human or formal proof-kernel acceptance or the out-of-scope supplier obligations.

Merge Danger

Door: two-way. Only the isolated research package is added.

Blast Radius: package. No shared code, frozen input or selected record changes.