Audit dirty-host cut rank under an explicit boundary contract

[an664]

Discussion #1516 leaves the dirty-host inequality dependent on an unstated boundary/credit interface. This package supplies a conditional history-span proof in the scalar common-frame transport model: paid mass is at least host endpoint-height displacement plus q * rank_K(S). It permits mixing, cycles, feedback, reuse and clean observations made at different times, with independent clean entry coordinates and a complete transport bill.

The package separates this proof from the selected-word tree geometry covered by complementary #1643. A separate GPT-6 Pro review corroborated the argument and supplied one applied wording correction: ordinary-state invertibility cannot be inferred from reversibility on ordinary-plus-private registers.

Validation: both original and separate-review checkers pass locally on Python 3.12.14, normally and under -O; normal/optimized outputs are identical. Coverage includes six original logical-row fixtures, all 16 subspaces of F2^3, 66 nested edges, 256 two-leaf trees, 11 rejection controls, and six additional Q/F2/F3 traces with feedback and noncoincident observations. The registered package replay passes. Exact source pins and local execution receipts are included.

Remaining obligations: bind claimed hosting credit to actual endpoints/gauges, provide the complete preparation/cleanup interval, and establish physical and production admission. Finite checks do not certify the universal written proof. No selected rank-8/64 replay, new kappa, frontier change, human review or Lean proof is claimed.

Credit ctoth and his disclosed model-assisted work; icekylinx, DreamingOfClouds, jeremykothe2, DaysSky, rohanarun, and Dennis / @antunishdPursuit for the pinned predecessors and complementary audit. Andrey Mas with GPT-6 Pro through ChatGPT produced this audit and separate review; Codex handled source coordination, execution inspection, mechanical replay and packaging. Apache-2.0.

Claim: #1516 (comment)

[Mister-Meeseeks]

Batch review at f6d5ccf4c94e52c761aa6e00f862d6e72e697b23.

Merged to main, preserving the original contributor commits and package attribution.

Reviewed scope: Conditional dirty-host cut-rank proof using history spans at every height, independent entry coordinates and complete transported host endpoints. Permits mixing/feedback but explicitly requires boundary/hosting-credit binding; finite Q/F2/F3 controls do not instantiate selected global admission.

The pinned scoped command passed; the batch ledger contains its command, input hashes, environment and log. This incorporates the research/tooling contribution and does not change the selected κ or discharge the inherited multiplication-theorem assumptions.

Batch review, attribution and evidence. Thank you for the contribution.