P104 owned-scratch successor handoffs: close the omitted search domain

[aliromman]

DONE / RELEASED — Close P104 owned-holder handoffs with public frame separators (no new kappa), exact head 29d388e9cde819de3b36893e64a7c74c6ed4ac63.

This finite obstruction closes the owned-scratch gap explicitly left by PR #5569. All 5,252 owned-holder event cuts, including all 2,832 omitted scalar points, have two public holders with incompatible frame anchors. The same certificate applies to the exact PR #5561 and #5569 words. No new kappa is claimed.

The proof permits any binary common frame, any number of extra coframed registers, arbitrary MOVE stops between fixed scalar anchors, and free service of owned holders. Public constraints alone exclude every single-common-frame successor reset in this domain. This directs further work toward changed public anchors or a distributed reset. It does not cover a changed scalar prefix, public basis, scalar order or scalar frame. Canonical claim: Discussion #5576. The active retime and basis scopes remain separate. The submission refresh found the concurrent Discussion #5575 on changing the owned-boundary scalar realization. This fixed-program obstruction was sent there as supporting evidence; it does not close or reserve that changed-program scope.

Registered Python 3.12 normal and optimized replays pass. Sparse rational construction and a separate integer/dyadic pass check all required cuts and scalar exits; bitset and Gaussian frame checks verify every separator. Four controls reject missing coverage, a false separator, a false anchor and a false public-holder role. Both words produce certificate SHA256 dfcace797d5a8f49e2a104fcf8820232f02b0a174f478b24469c9b94a3b55211.

Open next questions: defeat one public separator with a charged changed-anchor word, or provide a distributed reset with all old-input uses and owned returns paid. Coordinate with the active claims before taking those scopes. No new search is reserved. The selected result is unchanged. Prepared for Ali Romman with substantial OpenAI Codex assistance.

Original claim

CLAIM — close the owned-scratch gap in the P104 successor-handoff screen

Question: can the owned scratch registers make a profitable successor handoff in the complete P104 word of PR #5569?

Base: canonical main 5e0052ca0aa3036a3afa8b0438927377c8d97d53, priority revision 7. Source: PR #5569 at af9f091ac6f30c6eaacb9c27777bfbe2d0e5ffdf (GamingPuzzled), with PR #5561 and the P104 predecessor line retained.

Method and bounded domain: reconstruct exact scalar rows and lifetimes, then inspect the 2,832 owned-holder points omitted by the predecessor screen. Include every live owned holder, its COPY/return constraints and all nested common frames. Seek a full paid word if a candidate survives; otherwise provide a proof and reproducible coverage certificate for the exact rejected family. Extend beyond the first failure to identify whether the whole owned-holder class can be closed. No claim of a global native lower bound.

Boundary and cost: keep the fixed scalar program and public input basis. Account for target splits, paid transports and owned returns before any kappa claim. New basis changes, private-COPY resynthesis and event-order search are outside this scope; those are active in #5125 and #5574. This task also does not take DreamingOfClouds' from-scratch word or toolkit scope.

Decision impact: close an explicit hole in the strongest complete P104 handoff search, or produce a charged improvement. Stop after a complete bounded certificate or a fully replayed candidate; do not publish a few sampled failures as exhaustive evidence.

Expected artifact: one focused package and PR, with exact source pins, controls, proof, limitations and open next questions. Prepared for Ali Romman with substantial OpenAI Codex assistance.

Claim expires: 2026-10-25T22:35:00Z. Claims are advisory.