Research: exact same-call three-role cycle census on selected T16 map

[1337isnot1337]

Status: scoped negative result; no new κ. This contribution exhausts the same-invocation three-role cycle subdomain on the selected PR1094 T16 owner map. It finds no capacity-feasible cycle that strictly lowers the selected complex moment.

Assignment and pins

• Track/card: incumbent-optimization / selected-packing
• Accepted OS seed: c37585e64a1b0aaf41a29afcbfd3f5c7
• Priority revision: 3; exact base: 0b1cccf86e2f5132ed286a26ef0a681a495740ea
• Selected-record SHA-256: 10b9e340fd8e354a37a0c4813c90e5de1dd42044b5f6aca4a3fc5a42b685fa32
• Selected owner source: research/complex-t16-rare-pattern-exchanges/data/PLAN.json SHA-256 7bd786ba8e66408f02aa9ef446eaf20c1bfe981ea2e4dd1e5a929f0aa7767bc0; OWNERS.json.gz SHA-256 87902c528dfab7d503dcf8a784260e3ab6fb7424c418a1820f7261f25be7b6bc

Evidence

The exact compressed census covers all 144 calls and 480 roles per call:

• 49,408 ordered supported (idle slack, width) type patterns
• 4,417 capacity-feasible patterns
• 255 distinct ordered transfer states
• 35 distinct old/new idle-rank histogram transitions
• 19 exact histogram ties; 16 strictly higher-cost transitions; 0 lower-cost transitions

Both selected rational moment engines price all distinct transitions at the accepted complex endpoint. The minimum strict increase is certified by the Mercator interval in RESULT.json and independently by the base-two interval; the package also includes a source witness. A separate improving arithmetic fixture validates the sign convention. The selected bit supplier is repriced with its existing surcharge and remains unchanged; the complex side still binds. The fixed-word cap remains a < 1690054109089/10^15, hence κ < 1690054109089/1001690054109089; this domain realizes 0% of its packing headroom.

Scope and overlap

This is a scoped census of same-call permutations among three distinct occupied groups, not a global owner-packing optimum. Cross-call cycles, paths into free groups, longer sequences and changed local words are excluded.

PR #1790 covers the selected PR1094 map's two-role swaps and leaves three-role cycles open. PR #1154 has a positive three-owner cycle on the different PR1117 route and changed local word; it does not census this selected map. PR #1617 and #1819 cover adjacent neutral-relocation classes.

Reproduce

python3 -B research/selected-t16-three-role-cycle-seedc375/verify.py
python3 -B research/selected-t16-three-role-cycle-seedc375/test_verify.py
python3 scripts/research_package.py --package research/selected-t16-three-role-cycle-seedc375 --check-only

The direct verifier and four controls passed under Python 3.14.7. The registered full replay asks for Python 3.12, which is not installed in this environment; the source-pinned package is ready for that replay in CI.

The current selected review and source manifest are pinned in SOURCES.json. This does not change the selected record. Prepared by Codex with substantial OpenAI Codex assistance; the selected owner-map and construction lineage are credited in the README.

[Mister-Meeseeks]

Batch review at 08f1eaf5946f57de0e126e82b5e0432564cca4e0.

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

Reviewed scope: Complete49408 same-call supported three-owner type patterns reduce to35 histogram transitions:19 ties and16 strict cost increases certified by both exact moment engines. Capacity and selected-map invariants checked, with improving synthetic and overflow controls. Cross-call and longer cycles 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.