DONE: signed record-phase encoding to the selected tensor action

[bitplane]

DONE / 2026-10-15 UTC. Claim released.

Published #2422 at 0df268def5a3ce9e7e077ed8166eec545c3b8c25.

The new Lean bridge composes PR2378 signed words and full-array tensor semantics for every Gaussian coefficient field, with exact width/headroom, a common grid scale and guarded inverse. It retains AAAmirinu's PR2378 and Jose Manuel's PR2250 sources unchanged. PR2378 already covers packed finite records; the new contribution is formal composition.

Fresh Lean build: 46 actual axiom reports, standard axioms only; three mathematically false proofs rejected. Actual interpreter: 33,280 phase cases, three complete 4,096-record arrays with 1/3/5 fields, six semantic controls. Registered CPython3.12 and nine package controls pass. A read-only Git-free 38-file execution export passes a fresh kernel build and all controls under CPython3.14 with identical receipt and unchanged files.

Completed physical address primitives, Python/tape-to-model correspondence and caller width/headroom remain explicit. No selected frontier or exponent claim. The generic Python replay does not execute Lean; a dedicated workflow does.

Next: prove one actual completed Compact/digit ADD endpoint, or bind one caller precision ledger to the every-field guards. New work by Gareth Davidson with substantial OpenAI Codex assistance; predecessor and LemmaG notices retained. No independent human review claimed.

[JoyboyBrian]

R9 task 09 — source coverage gate: no new PR

JoyboyBrian; local read-only audit at base 81e9bd69e4a5b00ba9c713a1620e36d576d5522e.

The claimed source-level pooled completed-record phase-guard binding is already covered by the existing written proof composition. PHYSICAL-BRIDGE.md, “All-width local refinement lemma”, fixes all six authenticated providers, every positive outer row/coefficient count, all 73 vector fields, all three Compact fields, arbitrary complete spectators, and every f≥1. It explicitly evaluates inverse phases on recovered source addresses and retains the f-fold constant phase. PHYSICAL-GLOBAL.md, “An explicit safe coefficient guard”, supplies a single whole-invocation grid and signed width covering every exact half and signed prefix.

Substituting the signed width into the guard predicates adds no new source-level mathematical implication. The remaining formal bridge is a distinct task: RecordBridge.lean uses its fixed selected recipe and primitive hypotheses. This audit neither generalizes that Lean development to the pooled ABI nor discharges its assumptions in the kernel. No Lean build was run or proposed. Renaming existing guard consequences ForwardFits/BackwardFits would not justify a separate research package.

Decision: release this claim as covered at source-proof scope; no implementation, checkout change, commits, or PR. This is a coverage decision, not new proof-assistant acceptance or independent verification of the inherited primitive contracts.

Exact inspected sources:

• research/complex-pooled-full-admission/PHYSICAL-BRIDGE.md SHA256 2fa75b9af51d31f68b818aeca7f2cb9e9f9d940ebe509fdb29d77053e05f8218.
• research/complex-pooled-full-admission/PHYSICAL-GLOBAL.md SHA256 1d1f06c714f0f3e5e6ab660084191a080ce4a86c0dfef8022b57c00778085b97.
• research/lean-record-phase-bridge/lean/RecordBridge.lean SHA256 b9d648d50f620ebd92cc7065330a20371bd8445a01f671a6d572c3a501f9da32.

Prepared by JoyboyBrian with substantial OpenAI Codex assistance. The result and provider contracts remain credited to the authors of the linked pooled-admission and record-phase-bridge packages; this is a coverage audit, not a new theorem.

{
  "schema": "integer-mult-coordination/v1",
  "kind": "HANDOFF",
  "task": "formal-interface-lemma",
  "base": "81e9bd69e4a5b00ba9c713a1620e36d576d5522e",
  "scope": "Does the actual pooled T74 coefficient layout and whole-invocation common-grid height allocation imply every-field ForwardFits and BackwardFits at every emitted monomial call, including inverse phasing on recovered input addresses, both orientations, every active provider and all positive column counts? The target is source-level theorem/ABI binding, not a Lean build or another primitive-prefix proof.",
  "artifact": "https://github.com/CrocSwap/integer-mult-bounds/discussions/2417#discussioncomment-19142355",
  "expiry": null
}