Tooling: synthesize optimal dirty fanout with direct cut certificates

[tekuuu]

PR #3121 characterizes the exact stationary dirty-output fanout price, but its executable enumerates small forests and its general lower bound invokes an external branching theorem. This adds exact synthesis with a small, separately checked cut certificate. The checker proves a concrete optimum over every permitted gate interleaving, without importing the optimizer or invoking that graph theorem.

The certificate uses the credited dirty-span lemma in the form oracle_calls(S) + incoming_ADDs(S)/2 >= 1. Nonnegative cut prices satisfying the individual oracle/ADD capacities give a lower bound by direct summation. The compiler applies classical Chu-Liu/Edmonds contraction, emits the actual preparation/oracle/restoration word, and supplies matching cut prices. The independent checker verifies arbitrary-dirt semantics, the inverse, every capacity inequality and exact cost equality. A valid crossing-cut certificate and an export with the compiler removed test that independence.

Proof simplification and synthesis tooling; no new graph algorithm, physical supplier or κ. Complete stationary tariffs, operand-compatible sources and legal unobserved target lifetimes remain the caller's responsibility. Path/state/frame-dependent prices need a different model. The package closes a synthesis/checking obstacle, not the physical caller obligation from PR #3121.

Only research/dirty-fanout-cut-certificate/ is added. Evidence includes:

• All 530 {1,5} tariff matrices through three rows match unrestricted affine-state shortest paths, including 394 strict sharing wins and 240 mixed-root certificates.
• 48 rational instances through six rows match a separate parent-function enumeration, checking 145,984 forests across those cases.
• Synthetic nested-cycle matrices through 112 rows compile and certify; the 112-row example uses 216 cut prices, 12,544 inequalities, one oracle and 222 ADDs. These are declared abstract tariffs, not selected-supplier prices.
• Eleven semantic/certificate mutations, invalid-price cases, source/receipt/cost corruption, duplicate keys and optimized read-only Git-free replay pass.

On the same six-row input, three alternating CPython 3.12.14 runs measured median 49.75 ms for the new exhaustive reference versus 0.684 ms for compilation plus full checking; both return exact cost 49. BENCHMARK.json records the complete timing/input/environment data. This is a local synthesis comparison, not a physical multiplication speedup or timing acceptance gate.

Reproduce with Python 3.12 standard library:

python3.12 scripts/research_package.py --package research/dirty-fanout-cut-certificate

Expected: PASS_DIRTY_FANOUT_CUT_SYNTHESIS, PASS_DIRTY_FANOUT_CUT_EXPORT_CONTROLS, and PASS_REGISTERED_RESEARCH_PACKAGE. The registered replay, metadata and all 16 committed publication-byte checks passed locally. Hosted CI is separate. The README also gives a standalone compiler/checker CLI and concrete next questions.

Base: 997e6a9ca7b4f95d50e366f61412fd640d72a88a, unchanged at final refresh. PR #3121 reference: eea0861aff47df568be4bb4a4db43c2da390d351; PR #3063: 3f384b8b7daccb2c8e12013fd81a738202ce0f8d. Exact file pins, bounded domains, seed 19 and changed card scope are recorded in the package. Coordination claim.

Credit Ross Richardson/PR #3121/#3063 for the subset lemma and tariff results, Cinna Davis/PR #1944 for the dirty echo, PR #1968's separate multiple-term accumulation, Anthony/PR #774, Oscar Fennell/PR #759 and their forest-synthesis lineage. Credit Chu–Liu (1965) and Edmonds (1967) for contraction and optimum branchings; no third-party implementation is copied. Prepared by Tekalign with substantial OpenAI Codex assistance in mathematics, implementation, verification and writing. Apache-2.0. No independent human or formal-kernel review is claimed.