[aliromman]

The PR5580 word already attains the best recursive moment for every frame path and public helper endpoint with its scalar contacts fixed, including arbitrary nonnested subspaces. The bound holds for every power tariff r^t with 0<t<1. Further endpoint-only or intermediate-frame detours cannot improve this word's kappa. No new kappa is claimed.

Scope, proof, exact checks, source pins, registered replay. Base: canonical main 5e0052ca0aa3036a3afa8b0438927377c8d97d53, priority revision 7. Contribution head: 627160c5e39501b69603c3a1e03bbfdc50a53a86.

The exact native frame price is the subspace distance dim(U)+dim(V)-2dim(U intersection V). Triangle inequality and concavity give a sharp cost floor between consecutive contacts and a sharp helper endpoint credit bound. All 3,453 nonzero contact intervals attain the complete signed-profile floor. The only unused helper, register 711, contributes a rank-five target and paid job that cancel. Main endpoints and scalar/owned contact frames are fixed. Changed contacts, scalar realizations and joint query interfaces remain outside the model. Canonical coordination is Discussion 5589.

Registered Python 3.12 normal and optimized checks pass. The credited scalar checker replays all 735 arbitrary public inputs and eight owned lifetimes. New checks bind all 2,921 source frame pairs, exhaust 4,770 small ordered subspace pairs, check three nonnested recipes including global phase, and reject changed scalar/contact and false dimension-difference controls. The interval certificate SHA-256 is 544092a4c732d94b7895689745b92c4ea0cafda665cdd6652b9bee352ffbb378.

python3.12 -B scripts/research_package.py --package research/p104-fixed-contact-ceiling

Python 3.12 and the standard library suffice. Committed-byte checks pass. This is a written proof with finite source binding, not a formal-kernel proof or a global P104 optimum. The full caller, ordinary budgets, precision/tape/compiler and outer ledger were not re-run. Existing framework assumptions retain their prior status. Full-history ancestry was not checked in the shallow checkout. Hosted status is unconfirmed at publication.

Credit Matarener PR5567 and Chris R/Clear1nsight PR5550 for the nested helper contract; this is not counted again. Credit DreamingOfClouds PR5561/5568, GamingPuzzled PR5569, thu-nmrc, Gareth Davidson, David Arias, Cinna Davis and the retained P104/native/Clifford/compiler lineage. The exact PR5580 source head is 6efa248. Imported source files and notices remain unchanged. Standard subspace geometry and concavity are not claimed as new general theorems.

Next: change a scalar contact or word and use this floor to reject unprofitable candidates before physical compilation. Respect the active changed-contact and basis claims. The selected frontier is unchanged.

Prepared by Ali Romman with substantial OpenAI Codex assistance; Apache-2.0.