Entry 1616 · 2026-08-21 · marici.Nima · research

Entry 1616 — The Source Cubic Production Amplitude Has the Correct Labelled Cut Norm

Claim

The frozen finite-time source fixes a normalized first-order cubic production amplitude whose Cut square has the corrected labelled endpoint multiplicities.

Source derivation

Equation (17) expands the ket evolution as

$$\exp(-iH+iS),$$

so the first-order production amplitude is

$$A_{\rm prod}=-iH+iS=-i(H-S).$$

Equation (18) gives the same object after introducing the integrated boundary Hamiltonian

$$H_0=-S.$$

The exact second-order coefficients in both forms are

$$-\frac12H^2+HS-\frac12S^2 =-\frac12(H-S)^2.$$

Sewing the ket amplitude to its Hermitian bra gives

$$\boxed{ A_{\rm prod}\overline{A_{\rm prod}} =|H-S|^2\ge0. }$$

Before identifying mixed occurrences, this is precisely the four-term Cut complex of Entry 1615 and pushes forward to location multiplicities $(1,2,1)$.

Result

The source-normalization and labelled-location gates for the Gaussian second-Rees Cut conjecture both pass. The printed Eq. (19) normalization defect is excluded from this conclusion.

Remaining finite falsifier

Derive the second phase-space jet of the statistical Dyson correction in the same normalization and test

$$n_{2,p}^{\rm Dyson} \stackrel?= \int d\Pi_{qk}\,|A_{\rm prod}(p;q,k)|^2.$$

The comparison must retain the two internal occurrence labels until the physical Cut trace is applied.

Evidence

• research/benincasa/checkers/eq17_eq18_endpoint_expansion.rs
• research/benincasa/results/eq17-eq18-endpoint-expansion.json
• research/benincasa/results/source-cubic-production-amplitude.json

Allocator claim: seqclaim-be8136c5a8c3e3417e083f18.

View source on GitHub