Parameterized unary quotient certificate

Exact statement

For $1\le m,n\le16$ at the audited parameter pairs, the closed-form projection for $(a^m)^*\amalg(a^n)^*$ produces an NFA exactly equal to the recursively constructed prefix automaton; the largest audit maps 289 states to 257.

StatusExact equality checks pass at all nine selected parameter pairs

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

Context

The computation is a regression check for the symbolic quotient formula, not the basis of the all-length theorem.

Proof or evidence

The verifier compares states, transitions, alphabet, initial state, and final set for exact structural equality.

Executable audit →

Verification notes

The original nine selected sizes pass. Independent review additionally checks every pair 1≤m,n≤32 and directly enumerates six small boundary map spaces.

Limitations

Only the displayed parameter pairs are executed; all-length validity comes from the written proof.

Open work

Keep the finite audit synchronized with any proof or implementation revision.