Selected PR1094: one neutral move opens a strict two-step packing gain

[1337isnot1337]

Scope

One explicit two-move, three-bin positive witness on the selected PR1094 owner map. The chooser seed is 893dae841093010f4e6385353a3c2714 (incumbent-optimization, selected-packing, priority revision 3); exact base main is 0b1cccf86e2f5132ed286a26ef0a681a495740ea, and selected-record SHA-256 is 10b9e340fd8e354a37a0c4813c90e5de1dd42044b5f6aca4a3fc5a42b685fa32. Coordination claim: #1166 (comment).

This is complementary to open PR #1790: that package censuses simultaneous two-role swaps and explicitly leaves sequential neutral-then-improving paths open. This PR gives one exact legal witness. It does not enumerate the open path class or replay #1790.

Construction

1. Move width-7 helper (stage=7, replica=2, helper=230) from (1,14,57) to (13,15,14). Free remainders change (0,7) -> (7,0), preserving the full idle histogram. Event position 268 lies strictly inside the destination window (255,430).
2. Move width-7 helper (stage=1, replica=15, helper=226) from (11,8,103) to (1,14,57). Its event position 181 lies inside (92,272). This landing is window/family legal initially but cannot fit the initially full bin; after step 1 its remainder is 7. The remainders change (1,7) -> (8,0).

Strict concavity of t^(1-a) for every real 0<a<1 proves the first move is neutral and the second strictly improves the idle moment uniformly on that interval. The final idle profile is {1:2275, 3:377, 7:6, 8:1, 48:4866}. The complete 69,120-role owner audit accepts the map, including source-event windows, family uniqueness, occupied prefixes, rank mass and halving guard.

Pricing and scope

The exact outward-rounded complex-moment root rises from the certified bracket around 0.001675462676808 to the bracket around 0.001675464332527; certified gain is at least 291277/175921860444160 (about 1.66e-9). The unchanged bit endpoint is 1733427039589844234749/1000000000000000000000000, still above the new complex endpoint, so complex remains the binding primitive in the retained supplier comparison. The fixed-word packing cap remains a < 0.001690054109089; the constructed endpoint is about 99.14% of that cap and closes about 0.0114% of the remaining gap.

This is a conditional fixed-word packing improvement, not a source-bound supplier rebuild, invoice, new supplier endpoint or new kappa. The selected record is unchanged. Exact before/after brackets, source pins, the owner audit and limitations are in research/selected-neutral-path-seed893/.

Verification

Passed locally under CPython 3.14.7:

python3 -I -O -B research/selected-neutral-path-seed893/verify.py
python3 -I -O -B research/selected-neutral-path-seed893/test_verify.py
python3 -B scripts/research_package.py --package research/selected-neutral-path-seed893 --check-only
python3 -B scripts/verify_selected_result.py
python3 -B -m unittest discover -s tests -p 'test_research_*.py'

The tests include the legal positive path, the direct-move capacity failure before the neutral step, an invalid-window control, a family mutation rejected by the full owner checker, exact uniform moment signs and certified endpoint increase. The registered package runner requires Python 3.12, which is unavailable locally; its package metadata/pins check passed and direct replay/tests pass on 3.14.7.

Credit

Selected owner construction: Rohan Arun (PR #1094). Owner audit and geometry: Josie Elliston (PR #1091). One-role relocation model: research/frontier1094-single-relocation. Packing ceiling: Douglas Colkitt / PR #1240 lineage. Prepared by OpenAI Codex with substantial AI assistance in derivation, implementation, verification and documentation.

[Mister-Meeseeks]

Batch review at eb519ed5b0013e03f4d9657730d57acee65cafd4.

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

Reviewed scope: Explicit neutral then strict whole-helper relocation passes the complete retained69120-role owner audit and exactly changes idle(1,7) to(8,0). Concavity and rational endpoint brackets certify a conditional fixed-word moment improvement. Controller reconstruction, full invoice and supplier/selected admission remain open.

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.