# Claim 1

**Result: verified.** The authored Theorem 3.1 explicitly gives the
all-order polynomial statement. Native, from-scratch diagram merging and Wick
contraction compute exact rational `Y_s` polynomials through s=4. The boundary
control `F=H^-1 δ` has pure-target term `p/(2H²)` and is rejected because the
theorem requires a polynomial target.

This is not a fitted polynomial or a Monte Carlo surrogate. Finite execution
corroborates the identity-target specialization; the source theorem supplies
the arbitrary-order quantifier.

## Registered wording

Theorem 3.1 shows that for targets expressible as polynomials in parameters and Kronecker deltas, the coefficients of the formal power series expansion of the loss's time derivatives are themselves polynomials in the width H, the parameterization exponent p, and the initialization variance sigma^2 (Theorem 3.1).