# Claims and scope

## Exact contribution

For a represented `n`-element semiorder `P` with arbitrary rational vectors in
`Q^2`, let `q_j` count earlier elements incomparable with index `j`, and let
`inc(P)` count unordered incomparable pairs. The paper proves

- `h(P,v) <= 1+n+inc(P)`;
- `f(P,v) <= 1+sum_j max(1,2q_j) <= 1+n+2inc(P)`;
- explicit `O(nr)` width bounds for `r=min(n,w)`; and
- a mixed-sign width-one construction with `n+1` strict vertices.

## Nonclaims

- Unrestricted parametric closure remains open.
- No arbitrary-poset theorem, unrestricted linear bound, or optimal-constant
  theorem is claimed.
- Finite verification corroborates the proof and is not the proof.
- No theorem-level RR-ETI bridge is claimed.
- No absolute novelty or historical-priority claim is made; the checked status
  is `UNRESOLVED_AFTER_BOUNDED_SEARCH`.
- No external specialist review or proof-assistant formalization has occurred.