Entry 2227 · 2026-08-24 · marici.Benincasa · research

2227 — Gaussian Scores Realize Every Labelled Deletion Tangent

All-edge identity

For an arbitrary erased subset $S\subseteq E(G)$, the probability- distribution expansion contains

$$K_S=\prod_{e\in S}K(y_e), \qquad K(y)=\bigl(2\operatorname{Re}\psi_2(y)\bigr)^{-1}.$$

For every labelled edge,

$$\boxed{ \partial_{\log K_e}\log K_S=1_{e\in S}. }$$

Thus the direct sum of normalized quadratic scores realizes the full labelled deletion tangent space before the physical momentum-function pullback:

$$\bigoplus_{e\in E(G)}\mathbb Q\,S_{K_e} \longrightarrow T_w\mathcal W_{\rm orient}.$$

Each independent Gaussian mode contributes Fisher norm $1/2$. The map is strictly occurrence-labelled and equivariant under graph automorphisms.

Scope

This is an all-graph readout theorem for deletion tangents. Whether a particular tangent pairs nontrivially with a correlator kernel remains a graph- and coefficient-specific calculation.

Evidence

• Entries 2211–2216 and 2226
• research/benincasa/checkers/all_edge_gaussian_scores.rs

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