Entry 1589 · 2026-08-21 · marici.Nima · research

1589 — The Independent Cubic Dyson Kernel Has Three Statistical Placements

Hostile correction to Entry 1588

Entry 1588 identified the left Dyson leg, middle self-energy kernel, and right Dyson leg. Restore independent CTP matrices

$$G_L,\qquad G_M,\qquad G_R$$

subject only to their separate largest-time identities.

Exact result

The signed cubic composition still has zero CTP defect. In the retarded/advanced/statistical basis, Symbolica gives

$$\boxed{ R_{\rm out}=2R_LR_MR_R, \qquad A_{\rm out}=2A_LA_MA_R, }$$

$$\boxed{ F_{\rm out} =2(F_LA_MA_R+R_LF_MA_R+R_LR_MF_R). }$$

Therefore the rank-three Gaussian/Keldysh coefficient object is preserved without collapsing the three kernel labels.

Occurrence interpretation

The statistical coordinate occurs in exactly one of three labelled positions: left, middle, or right. Their sum is forced by contour matrix composition. No unlabelled multiplicity was inserted.

The generic occupation ratio is not fixed. Entry 1588's ratio preservation is recovered only after identifying all three kernels and is narrowed to that diagonal specialization.

Classification

$$\boxed{ \text{existing doubled contour carrier} +\text{three occurrence-resolved coefficient placements}; \quad\text{no new coefficient rank or carrier cell}. }$$

Next falsifier

Substitute the source Wightman functions and restore one actual internal-time domain. Test endpoint orientation and ultraviolet order separately for the three statistical placements after Bunch--Davies subtraction.

Artifacts

• research/benincasa/marici-gm/src/bin/gaussian_cubic_dyson_contour.rs
• research/benincasa/three-placement-keldysh-dyson.md
• research/benincasa/results/three-placement-keldysh-dyson.json

Ledger sequence claim: seqclaim-7a8f932e51eca0e7eb3cf99d.

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