Finite bit construction: five-helper cycle saves 12 R439 ADDs (no new kappa)

[1337isnot1337]

Result

This adds a five-helper cyclic basis change to the source-pinned R439 D word. Applied after the existing helper preparation, it uses injection J0 H1^-1 and the reverse cycle before the existing helper restoration, preserving the D map for arbitrary dirty helper and target inputs.

The selected support is [21,25,59,129,148] with directed edges 59 ^= 148, 148 ^= 21, 21 ^= 129, 129 ^= 25, 25 ^= 59. The exact injection weight falls by 22 ADDs; charging all five preparation and five restoration ADDs leaves a 12-ADD complete-word reduction, 11,500 to 11,488. The bounded search covers all 1,860,480 five-edge sweeps on the top 20 overlap-ranked helpers; 56 give a positive net saving and four tie at the maximum. Its favorable fully charged ceiling was 109 ADDs.

The paid rank profile and mass 5,129 are unchanged, so there is no recursive-moment or κ improvement. The selected conditional result and supplier are not changed; the selected complex side remains binding.

Verification

• python3 -B research/r439-five-cycle-seed9f01/verify.py — passed the full search, exact dirty D map, all 661 formal columns in both directions, H1–H5 owner checks, unchanged paid profile, exporter agreement, exact precision bounds, and five negative controls.
• python3 -B scripts/research_package.py --package research/r439-five-cycle-seed9f01 --check-only — passed metadata and source pins.
• Local runtime is Python 3.14.7; Python 3.12 is not installed here, so the registered package runner was not run locally. The registered replay is included for CI.

The certificate gives F=27,061, B=5,921,344, 64 F^3 B^2 < 2^104, and 2^18 F^5 B^4 < 2^192. Native C++ replay, supplier adoption and outer assembly replay remain unrun.

Task and provenance

Accepted seed 9f01e96180d88ff08d00037f7d9b9abc, task bit-helper-contract refined to a distinct five-helper cycle, priority revision 3. Exact base: 0b1cccf86e2f5132ed286a26ef0a681a495740ea; selected-record SHA-256: 10b9e340fd8e354a37a0c4813c90e5de1dd42044b5f6aca4a3fc5a42b685fa32. The claim and correction are in Discussion #1695.

The pre-submit overlap refresh at 2026-10-14 07:30 UTC covered 396 open PRs and 352 Discussions with complete pagination and returned no match for the five-helper cyclic scope. The package retains the R439 lineage from #941, #967, #923, #1015 and #1040; their source data and checkers are pinned and reused unchanged. Nearby #1333 and #1662 use different address objects and are not imported.

Prepared by Cinna Davis with substantial OpenAI Codex assistance in the derivation, search, implementation, checking and writing. No independent human review is claimed.

[Mister-Meeseeks]

Batch review at 340e3babf1775f79131d2f4d4633a1241e1ad8c1.

Merged to main, preserving the original contributor commits and package attribution.

Reviewed scope: Full 1860480-word bounded five-helper-cycle search saves twelve ADDs after preparation and restoration on the pinned R439 word. Both dirty directions, retained frame checks and guard expressions pass; unchanged paid profile means no exponent gain.

The pinned scoped command passed; the batch ledger contains its command, input hashes, environment and log. This incorporates the research/tooling contribution and does not change the selected κ or discharge the inherited multiplication-theorem assumptions.

Batch review, attribution and evidence. Thank you for the contribution.