[krzysztofwojt]

Programs that cancel a named operator against its actual inverse need the relation-aware frontend explicitly left open by #5235. This adds a self-contained inverse-aware certificate package: a pair of complete dirty linear programs with r inputs and q unary occurrences uses r+q states, certifies every returned role for every invertible substitution and payload dimension, and produces explicit unipotent counterexamples on failure.

The written proof compiles inverses into finite feedback equations, supplies exact invariant-subspace certificates, and uses a central-parameter rational identity to justify arbitrary invertible substitutions. A separately transcribed checker imports no producer code and performs no elimination. The package includes rational/prime-field arithmetic, literal reduced-word and matrix oracles, CLI examples, and inspectable matrix witnesses. No predecessor source or shared repository code changes.

Validation on CPython 3.12.12:

• Both registered normal/optimized replays pass: 504 signed-word cases, 160 differential programs, 64 boundary cases, 36 delayed/infinite-tail cases, 324 literal matrix substitutions, and 31 rejecting controls.
• The 2^64-word stress endpoint uses 260 states and 64 invariant rows.
• Committed-byte and full source-history checks pass. The 21-file export passes integrity checking and both read-only replays without Git on PATH; payload hashes remain unchanged. Replay planning selects only this package.

Hosted run 39971793532 passed both the shared planning tests and the focused Linux package replay on exact head 6f92ccf1e61c4668c8ee687bd1df8b42932b8759. Hosted execution is not independent scientific acceptance.

Claim type: scoped written proof and author-checked implementation, not independent human or proof-kernel verification. Only named-generator inverse relations are covered. Additional relations, typed rectangular/native adapters, phases, rounding, precision, stock, hosting, tapes and the full supplier bill remain separate. No new kappa, supplier admission or selected-frontier change.

Start at research/inverse-dirty-certificates/README.md and the proof. Reproduce with python3.12 -B scripts/research_package.py --package research/inverse-dirty-certificates.

Fresh main base: ff3cc58e370d0f678e529246f8c73e8094e18fcf, priority revision 7. Exact contribution head: 6f92ccf1e61c4668c8ee687bd1df8b42932b8759. Main and #5235's source head were refreshed and unchanged; live claims and PR bodies were checked again immediately before publication. Canonical scoped claim / handoff.

Credit zxv #5235 (48976daa4dce59b4867ef046da72a370e389925d) for the independent-operator register bridge and this open inverse-frontend question; its dirty-echo/tensor/dirty-phase predecessors retain their full attribution in the package. Recognizable rational-series, Magnus and weighted-automata methods retain classical credit (Schutzenberger/Fliess, Kiefer, and the cited literature). No new general PIT algorithm or global literature priority is claimed. Prepared by Krzysztof Wójt (@krzysztofwojt) with substantial OpenAI Codex assistance, including a delegated exact-oracle implementation; Apache-2.0.