Certify all-subset exposure bounds for 273 fixed BIT planes

[RossRichardson]

Summary

For each of120 pinned E8 root lines and153 actual rank-two R438 frames, certify dim(E)*nullity_F2(D_S) <= 8*|exposure_E(S)| for every subset S of438 helpers. Complete colored partitions turn finite certificates into this all-subset statement without enumerating2^438 subsets or trusting augmentation optimality.

The new independent checker reconstructs the semantic111-by438 dirty map with reverse adjoints and causal masks with forward helper-seed propagation. It imports no producer mathematics. A separate proof review checks the counting argument and its exact model.

Scope and limits

One package, research/bit-fixed-plane-exposure. It covers exactly273 specified planes, full semantic D, unchanged causal common-E promotion,111 target resources and nine copied-total resources, and private copied fields keptZERO. Both capacity-eight batch optima are zero, attained by S=empty. Eight is the least integer common coefficient: frame116 with all438 helpers has nullity327 and90 exposed resources, so654>7*90. This does not determine the best real coefficient.

Eight is an auxiliary partition capacity, not the actual one-rank charge of a reached resource. The inequality is not net deficit or an all-rate rejection. Source paths, pivot promotion, owner credits and complete moments need separate bounds. Mixed E, cold-target quotients, new private cuts, changed words and arbitrary rational planes are outside it. No native selective supplier, rounding/tape implementation, selected-frontier change or new κ is claimed.

Historical individual-plane examples and other weights are retained as provenance, not silently included in this replay. The earlier paired-helper package uses a different private-at-E convention and has its own caller assumptions.

Test plan

• Full registered Python3.12 replay: both complete batch producers, both historical certificate verifiers, the fresh independent checker and integrity controls.
• Independent D rank111/nullity327; all273 exact plane bases and119574 helper exposure masks; every colored partition, capacity, incidence and owner.
• Separate written all-subset proof, precise chronology/private assumptions and countermodels to cold-quotient or shared-resource mixed-plane extensions.
• Source authentication, complete typed receipts, plane/partition/mask omission and corruption, normalized-path collision and demonstrably poisoned nested-cache controls in normal/-O and committed export.
• Metadata/source-history preflight and automatic exact-head GitHub CI passed at 304c4e0778d0bf864b7d09c163a837d7eb4fa455, including all five mathematical stages, integrity controls and unchanged inputs; no manual rerun requested.

Sources and credit

Scientific pin 20ecf2891d80b5acf18d980b2164fb44ea7faa90. Retain Sagar Thakrar's R438 transport and the eumemic/DreamingOfClouds/Ali Romman E8/BIT ancestry. The causal promotion experiment and dirty-map construction are predecessor lane work; generic colored-partition counting is not claimed as a new theorem. Related compensation-kernel/paired-helper work retains the PR2857/2908 and PR386 lineage; PR4058 contains the separate fixed-word paired-boundary package.

Prepared by Ross Richardson with substantial OpenAI Codex assistance and separate AI computational, proof and integrity reviews. Apache-2.0; all original bytes, source pins and notices retained. No independent human or formal-kernel certification.