Boolean-product left-transfer audit

Exact statement

Exact enumeration checks 8,192 combinations of two-state one-letter transition structures, all eight Boolean policies on the supports $\{1\},\{2\},\{1,2\}$ , and discrete or universal component partitions. All 5,408 predecessor-compatible cases satisfy product predecessor compatibility and exact quotient/product commutation. An independent boundary audit also checks 56,448 saturated initial-set pairs and 86,528 final-set pairs.

StatusSource transition audit and independent initial/final boundary audit pass

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

Context

The source enumeration tests the predecessor argument on transition structures. The independent review adds the initial-set saturation required by left invariance and verifies final-block commutation separately.

Proof or evidence

For each admissible component partition, the checker compares every predecessor-block profile and every quotient transition with a product reconstructed from the component quotients.

Boolean-product exact audit →

Verification notes

All 5,408 predecessor-compatible transition/partition cases pass, together with 56,448 admissible initial-set pairs and 86,528 arbitrary final-set pairs.

Limitations

The computation is finite and binary; arbitrary arity and alphabet size come from the proof.

Open work

Retain this as an implementation audit; use the all-arity proof for the theorem.