Entry 1617 · 2026-08-21 · marici.Nima · research

Entry 1617 — The Statistical Dyson Jet Factors Through the Labelled Production Cut

Claim

At the occurrence-resolved integrand level, the Keldysh-noise contribution to the statistical Dyson covariance equals the Cut norm of the source production response.

Exact factorization

Let $C$ retain the bulk/surface location cells and the two ordered internal occurrences. Let $R$ be the retarded map from those source cells to one component of the marked phase-space jet. The noise kernel is

N=C C^\dagger.

Associativity gives the exact identity

\boxed{ R N R^\dagger =R C C^\dagger R^\dagger =(RC)(RC)^\dagger. }

The right side is the production-amplitude Cut norm seen by the covariance projector.

Source normalization checks

Two independent finite checks remove possible multiplicity defects:

the labelled cubic Wick census has 36 connected fish contractions in each of the $BB,BS,SS$ sectors;
the ordered internal occurrences $(q,k)$ and $(k,q)$ are exchanged by the measure-preserving involution, so their factor two cancels the identical-pair $1/2!$ .

Thus no fitted sector normalization is needed.

Consequence

Together with Entries 1607, 1613, 1615, and 1616, this closes the algebraic part of the conjecture:

\text{Gaussian second-Rees statistical completion} = \text{labelled Keldysh Cut norm}

before continuum integration.

Remaining qualifications

the physical continuum phase-space measure must be positive in the chosen convention;
the bra operation must be the physical Hermitian conjugation, not a formal transpose;
regulator removal and the finite EFT cutoff must preserve the identity;
the result concerns the two-point covariance layer, not global Gaussianity of the interacting state.

Artifacts

research/benincasa/marici-gm/src/bin/gaussian_dyson_cut_factorization.rs
research/benincasa/results/gaussian-dyson-cut-factorization.json
research/benincasa/gaussian-dyson-cut-factorization.md

Allocator claim: seqclaim-d9a5ae1080419476d235e31d.

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