Audit P104 relay floor with an explicit monotone-lifetime model

[kumagi]

Philippe Van Velzen's P104 correction screen reports a 208-helper floor, but using that number requires an explicit operation model and a distinction between helper lifetimes and simultaneous storage. This independent audit supplies a relay-safe proof and source-bound certificates for that implication. It credits the numerical floor to the original screen, pinned at 7dfc7a176d7de4e7eabaf553a0b187c1bd647546.

For each of 104 distinct terminal frames, the residual correction-source labels have binary rank eight, forcing at least two first arrivals from proper subspaces. One nested helper lifetime cannot visit two different terminal frames. This proves at least 208 monotone helper lifetimes with arbitrary same-frame linear relays, cancellation, independent dirty inputs and retiming preserving the source/target frame paths. It does not prove 208 simultaneous registers or an attaining construction.

The six-file package adds a written proof, eight-label rank witnesses and two-hyperplane covers for all 104 targets, an independent standard-library verifier, exact source pins and an opt-in replay hook. Two concrete boundary examples prevent overgeneralization: two arrivals may merge into one target writer, and the retained private descent at cut 2464 carries X8 with coefficient -2 into a frame excluding its label. Reusing the channel's descending/private values therefore changes a necessary premise.

Validation on macOS arm64:

• Registered CPython 3.12.14 replay and optimized CPython 3.14.7 replay passed; seven semantic/control groups.
• A separate AI-assisted implementation matched every target residual set and cover; a separate proof/model review found no blocking issues.
• A Git-free export passed optimized replay without changing any file. Modified source/receipt inputs and an occupied output path rejected.
• Metadata/source pins and git diff --check passed.

python3.12 scripts/research_package.py --package research/p104-monotone-relay-floor-audit
python3 -I -O -B research/p104-monotone-relay-floor-audit/verify.py

Scope remains a restricted logical lower bound. No native phase/full-channel replay, simultaneous-stock theorem, correction circuit, pricing interval, complete moment, global hosting, precision/tape, all-size admission or new κ is claimed. The two-hyperplane covers establish a geometric minimum, not global attainability. Selected/frozen files are unchanged; hosted CI is separate.

Base and refreshed canonical main: 0fdd7d82de03e43c9e5a1000dfbcd380d1b687d2, priority revision 4. Single chooser nonce a71071a87492501cab47b3076ccee844, complex-mechanisms / p104-side-correction; changed scope to a defined audit obligation. Final overlap refresh covered 561 open PRs and 1,073 Discussion records with complete pagination and no warnings, followed by a focused monotone/relay screen. This is distinct from the active early-prefix dimension and 41-contact chronological-lift tasks. Historical #1238 concerns the selected 112-port word's end caps, rather than this P104 correction model.

Canonical claim and handoff. Credit Philippe Van Velzen for the floor/screen; Rohan Arun/#1972, Chafik Boukhalfa/#1991, Adam Gall/#1940, Josie Elliston/#1071, Ali Romman/#1125 and the retained lineage. The neighboring pooled-space result is credited separately to Gonzalo Mier/#2173 and Gareth Davidson/#2251.

Prepared by kumagi with substantial OpenAI Codex assistance in proof, implementation, writing and parallel checking. No independent human review or formal proof assistant is claimed. Apache-2.0.