Unique incoming signatures exactly characterize marked agreement

Exact statement

For a fixed flat Boolean-product expression with marked ordinary components, the natural prefix automaton is isomorphic to the useful canonical component-prefix product if and only if every noninitial useful product state $q$ has exactly one incoming event signature. If some $q$ has two signatures, the natural marked automaton is strictly larger and cannot be a quotient of the product.

StatusImmediate exact consequence of the event-signature expansion

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

Context

The criterion isolates the precise expression-specific seam before position marks are erased.

Proof or evidence

FPRD-SH-T12 gives one natural state per incoming signature. Equality of state counts and the projection isomorphism therefore occur exactly at one signature per useful target.

Unique-signature criterion →

Verification notes

The signature-expansion checker verifies that every split edge projects to its canonical product edge across all 16,448 audited policies.

Limitations

For a particular unmarked expression, erasing positions may merge different signature copies; the marked converse must not be silently transferred.

Open work

Use the signature count as the exact state-overhead statistic for algorithmic bounds.