The table-free C7 base compiler reproduces Gao's complete typed interface

Exact statement

A standard-library exact verifier reconstructs the published 367-code without an input table, enumerates all eight maximum 40-word extensions, checks 960 residual compilers, verifies Gao's eight private pairs, complementary transversals, and $(321,26,20)$ auxiliary partition, and reproduces the six-node split recurrence through $M_{40}$ . All checks pass.

StatusAll exact checks pass

External reviewNo documented external or specialist review of these FPRD results is recorded.

Context

Gao's recursive theorem needs a five-dimensional code together with private pairs, transversals, and an auxiliary partition. The verifier reconstructs all of that input from arithmetic rather than a word table.

Proof or evidence

The generated code satisfies every private-pair and transversal assertion, the transformed auxiliary set has the exact O/H/V counts, and structural sharing represents the prescribed split tree with 204 syntax-DAG nodes through M_40.

C7 base-compiler audit →

Verification notes

382 precursor words, 71 extension vertices, 85 extension edges, eight maximum extensions, 960 residual compilers, eight private pairs, 367 auxiliary words, and six exact product recurrences; zero failures.

Limitations

The recursive parameter calculation imports Gao's proved product lemma.
No 200-dimensional output enumeration and no capacity improvement are claimed.

Open work

Use the 204-node typed syntax DAG as the next compiler input; do not enumerate its 200-dimensional output.