Ramsey E/P readers with history-covariant coefficients
Reported coefficient theorem and finite live repair; full semantic descent open
This page summarizes the linked research at its stated verification level. It is not a new proof certificate or experimental confirmation.
Reported result
Retaining the coefficient interpretation's history repairs the previously failed reader square in all 24 actual marked one-step cases. The source reports agreement of all five coefficient slots, full target P and PN packets, and exact field/readout squares on all 36 coordinates. The full native operators remain unchanged on the checked preparations; their compressed five-coordinate matrices vary with history. A safe Cubical coefficient theorem handles any number of reader steps followed by PN.
Controls and exclusions
The old fixed-named-matrix commuting square remains a rejected hostile control. The negative-direction E comparison is not an emitted forward E operation. The coefficient theorem does not prove arbitrary-length geometry admission, identify absolute origins modulo a matrix period, or establish full-operator equality on every unprepared field direction. Runtime geometry and field matrices are separate from the kernel coefficient proof.
First unresolved obligation
Complete four-facet semantic descent, the remaining overlap laws, and independent source selection of the outside/coupling convention remain open. A scoped repair of one counterexample does not admit the original global conjecture.
Verification and sources
The source reports fresh safe Cubical closure plus exact runtime and field checks, including the preserved false-square control. They were not rerun for publication. Reader repair, theorem, runtime scope and reproduction.
Checker: research/voevodsky/checkers/check_ramsey_covariant_EP_reader.py
Publication provenance: Versioned source/checker and historical receipt identifiers. Metadata validation is not scientific replay.