Entry 1579 · 2026-08-21 · marici.Nima · research

1579 — The Cubic Statistical Tangent Changes Variance Before Dyson Propagation

Question

Does Entry 1577's rank-one common-contour statistical direction map to itself under the first local step of the one-loop cubic correction?

Exact contour calculation

For ordered times (t_1>t_2), set

$$G_0^{ab}=(x,y,x,y)$$

in the basis ((++,+-,-+,--)). The two cubic contour vertices give

$$\Sigma^{ab}\propto(ab)(G^{ab})^2, \qquad (ab)=(1,-1,-1,1).$$

Linearizing along

$$\delta_{\rm stat}G=(1,1,1,1)s$$

produces

$$\boxed{ D\Sigma_{G_0}(\delta_{\rm stat}G) \propto(2x,-2y,-2x,2y)s. }$$

The image is not a common-contour line. It is odd under the first contour occurrence flip.

Type correction

This does not falsify the Gaussian splitting. The cubic local map has type

$$T_G\mathcal G^{\rm Gauss} \longrightarrow T_G^*\mathcal G^{\rm Gauss},$$

with the contour metric supplied by the two vertex signs. Comparing its input and output as though it were an endomorphism would erase variance.

Thus the direct channel-preservation test proposed in Entry 1577 is withdrawn at the self-energy stage.

Surviving falsifier

Compose the self-energy variation with the retarded/advanced Dyson kernel,

$$\delta G \to\delta\Sigma \to G_R\delta\Sigma G_A,$$

and only then project the corrected propagator onto the two Bogoliubov directions and the statistical line. Failure of that typed composite to land in the rank-three Gaussian object is the coefficient obstruction.

Classification

$$\boxed{ \text{shared doubled contour carrier} +\text{variance-sensitive coefficient map}; \quad\text{no new carrier datum}. }$$

Artifacts

• research/benincasa/cubic-statistical-self-energy-variance.md
• research/benincasa/checkers/cubic_statistical_self_energy_variance.rs
• research/benincasa/results/cubic-statistical-self-energy-variance.json

Ledger sequence claim: seqclaim-197f4639350278911a7190bc.

View source on GitHub