One-shot Boolean-product overhead is a weighted matching count

Exact statement

For a graph $G$ , assign one letter $a_e$ and support $e$ to each edge, and give vertex $v$ the component expression $\varepsilon+\sum_{e\ni v}a_e$ . Useful canonical product states are exactly graph matchings $M$ , the state for $M$ has $|M|$ incoming signatures, and $\Delta(G)=\sum_M(|M|-1)_+$ .

StatusSelf-contained all-graph proof; exact product exploration audit passes

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

Context

The construction isolates the exact-search core using only size-two supports and components that accept epsilon or one incident edge letter.

Proof or evidence

An event consumes both endpoint components, so executable event sets are exactly matchings. Removing any selected edge gives one predecessor, making the incoming-signature count equal the matching size.

One-shot matching model →

Verification notes

All 1,099 simple graphs through five vertices and 256 deterministic random eight-vertex graphs agree on matching states, incoming multiplicities, and total overhead.

Limitations

The theorem is a restricted family used to expose the exact algorithmic core.
Novelty is plausible but unconfirmed; no external review is recorded.

Open work

Use the XCC compilation to enumerate matching receipts without constructing the canonical product.