[petalas]

Summary

 fixed selected PR1094 word, 144 calls and complete physical invoice
- PR3338 idle ranks (2,1,0), kappa = 0.001673619538656538
+ three-helper cycle (3,0,0), kappa = 0.001673620586419375

Rows 1811, 2977 and 531 cycle between three occupied T16 bins across calls 3, 6 and 1. Three helpers relocate and four other offsets change. Strict concavity proves the moment gain; complete finite admission prices an exact increase of 1047762837/10^18 over PR3338 and 960389342457/10^18 over the selected headline. Complex still binds.

The isolated research/t16-three-helper-cycle/ package contains the proof, complete canonical predecessor payload reconstruction, exact sources, generator, failure controls and actual replay/invoice receipts. It answers PR3338's explicit three-bin open question. No solver or unmerged commit object is required. No packing optimum or global-best claim is made.

Canonical finding and handoff: Discussion3355.

Evidence

• Before: authenticate the complete PR3338 owner payload from canonical PR2169 bytes and a 169-row patch. After: rebuild the literal cycle and independently audit all 69,120 roles. Exactly -H1-H2+H3 changes in the paid profile; rank mass and deficit remain fixed.
• The unchanged eleven-stage PR1087 strict replay passes, including both supplier endpoints, both seven-step bootstrap paths, all 47 strict outer inequalities per tariff path and controls 69/12/6/15. The independent owner auditor adds eleven controls.
• Entire typed JSON invoice equality retains every cost and unknown key, excluding only three rebound source identifiers. Actual chart count remains 10,008; prefix 397 is paid at 512; physical row coefficient remains 16,469. Ten construction/invoice groups pass normally and optimized, including partial/reversed cycles, corrupted predecessor data, type changes, unknown keys and array order.
• Registered replay, Git-free source-closed replay, Ruff, metadata/pins and exact committed-byte/source-history preflight pass on CPython 3.12.15/macOS arm64. Reproduce with python3.12 -Werror -B scripts/research_package.py --package research/t16-three-helper-cycle.
• The fixed-word cap is 1690054109089/1001690054109089; this witness attains about 99.1949954%. Canonical refresh remains 6f100d4bb5083f8c35d96fd95a539811c62f245c, priority revision 6. PR3338's live receipt-serialization successor leaves the pinned scientific map/PLAN/SPEC/replay/swap blobs identical.

All selected all-size/compiler, common-label/mutable-source, whole-call hosting, precision/tape, exact recovery, analytic and bit H1-H5 assumptions remain. Native local ancestry is source-bound reuse, not a fresh cold native rebuild. No formal-kernel or independent human review is claimed. The selected manifest is unchanged. Hosted checks are separate from the local receipts.

Credit Nick Petalas/PR3338, Gonzalo Mier/PR3308, Philippe Van Velzen/PR2169, George Lydakis, Rohan Arun, Jeremy Kothe, Josie Elliston, Hao Yan and the retained compiler/native/bit/moment lineage. Open next questions are scoped in the package.

Merge Danger

Door: two-way. This adds one isolated research package.

Blast radius: package. It does not modify shared scientific code or select a frontier.