Entry 1613 · 2026-08-21 · marici.Nima · research

Entry 1613 — The Cubic Keldysh Rotation Isolates the Candidate Noise Cut Block

Claim

The cubic self-energy has a canonical Keldysh-noise block before endpoint assembly. This block, rather than the full indefinite endpoint response, is the correctly typed candidate for Gaussian second-Rees positivity.

Exact contour algebra

Write each internal Wightman pair as

$$G^>=F+\frac{\rho}{2}, \qquad G^<=F-\frac{\rho}{2}.$$

For labelled internal occurrences $q,k$, the symmetric and antisymmetric cubic products are

$$G_q^>G_k^>+G_q^<G_k^< =2F_qF_k+\frac12\rho_q\rho_k,$$

$$G_q^>G_k^>-G_q^<G_k^< =F_q\rho_k+\rho_qF_k.$$

The first is the Keldysh-noise block; the second is the spectral/retarded block. On the convolution-collapsed diagonal,

$$\Sigma^K_{\rm diag} =2F^2+\frac12\rho^2,$$

which is nonnegative for real physical data.

Consequence

The contour metric must be removed by the Keldysh rotation before applying a positivity test. Entry 1612's indefinite endpoint form mixes the two blocks and therefore cannot serve as the uncertainty completion.

Remaining gate

For independent $q,k$, algebraic bilinearity alone does not prove positivity. The physical Cut measure and conjugation/orientation must turn the symmetric Wightman product into a norm pairing. Endpoint incidence must then be transported separately within this block.

Next falsifier

Construct the source endpoint assembly directly for $G_q^>G_k^>+G_q^<G_k^<$, retaining both occurrence labels. Test whether its physical Cut pairing is positive and whether its second phase-space jet equals the statistical completion predicted in Entry 1608.

Artifacts

• research/benincasa/marici-gm/src/bin/cubic_self_energy_keldysh_noise.rs
• research/benincasa/results/cubic-self-energy-keldysh-noise.json

Allocator claim: seqclaim-e37ad97c03365358bc9430bc.

View source on GitHub