Weighted dual-suffix carriers: conditional κ = 7.9961717358e-5

[rohanarun]

Full verification passed. Full repository verification passed on b054739841f9e106bc15064c79cbc958811a709c in 2435.331 seconds, completed 2026-10-09T00:40:51.103942+00:00: make -j1 verify (78 isolated test modules, 20 historical patch checks), fresh parent/selected producer and certificate regeneration, and ten adversarial controls. All 42 research-head GitHub checks passed, with no source drift. See research/weighted-dual-suffix/validation.json for commands and evidence hashes.

Under the inherited analytic, fixed-tape and PR104 stopped-product/odd-grid interfaces,
T(n)=O(n(log n)^(1−κ)) with κ = 39980858679/500000000000000 = 7.9961717358×10⁻⁵,
0.0986743% above PR108. These general interfaces remain written proof dependencies.

This keeps PR108's complete dual-suffix scalar graph and exact frames, but selects different legal carrier links using weights from the full rank-dependent cost. Both matchings have 15,422 carriers and 43,270 roles. The improvement comes from their width distribution, not omitted work: the strict complex saving rises from 7989584037/10¹⁴ to 7997468953/10¹⁴. The bit axis, all 24 retained centers, divisor21, copied-center corrections and all three row stocks remain unchanged.

The discovery step used numerical SciPy assignment. No weighted-optimality claim is made. The explicit link list is checked independently without SciPy:

• Regenerate PR104, PR107 and PR108 producers, retaining all scalar/frame/rational-scatter assertions.
• Recompile the inherited C++ matcher and verify every selected edge and paid histogram entry.
• Independently construct active GF(2) frames in Python, check nondegeneracy and operand nesting, then replay matching uniqueness, shared operands, strict carrier order, exact frame inclusion and the complete histogram.
• Check the exact assembly's 47 constraints and seven margins, plus rejection of the next complex and κ grid points.
• Ten controls pass, including duplicate links, invalid donors, out-of-range uses, corrupted frame ranks, unpaid cleanup, omitted retained loss, mass-preserving histogram mutation and exclusion of PR108 at this saving.
• All 344 source pins are tracked. The bounded search also tried six structural families and sixteen alternative coordinate layouts; none beat the selected unchanged graph. This is not a global search or optimality claim.

Run:

python3 research/weighted-dual-suffix/verify.py
python3 research/weighted-dual-suffix/test_controls.py
make verify

Written transfer and scope: research/weighted-dual-suffix/proof.md. Optional discovery tool: optimize.py (NumPy/SciPy); exact verification does not need those libraries. Dedicated focused CI covers Python3.11,3.13,3.14.

Credit: Rohan Arun with Anthropic Claude assistance for PR108; Rohan Gupta / gupt1156 for PR55 dual-suffix strips; icekylinx for PR104 rational centers and stopped products; the PR44 weighted-carrier work; and all inherited contributors in NOTICE/SOURCES. Prepared by Rohan Arun with OpenAI Codex assistance.

[Mister-Meeseeks]

Thank you @rohanarun. This contribution is now recorded on main in the scoped reconciliation review and contributor credits.

Contribution: Matching selection with independently audited binary frames.

Review and limits: Exact-head CI evidence. Float matching is only a proposal mechanism; actual eligibility and histogram nonnegativity are checked separately.

The complete original source, proof/research notes, notices and relevant replay/CI evidence are retained through the pinned source archive. The review distinguishes fresh runs, exact-head historical CI and prior integration evidence. Closing this historical PR as reconciled; its obsolete headline does not replace the current selected bound, and draft/retracted claims retain their explicit qualifications.

Reviewed head: 45389b383b31092d83d19007dd6faaa8543db961. Publication: b84ba67156a01f9c2cb34fe1e3cb1dcdeab00d9c.