Entry 2228 · 2026-08-24 · marici.Benincasa · research

2228 — Gaussian Score Rank Equals the Number of Distinct Edge Energies

Physical pullback

A translationally invariant boundary state supplies one deformation function $\kappa(y)$. For edge energies $y_1,\ldots,y_m$, its labelled values are

$$\kappa\longmapsto (\kappa(y_1),\ldots,\kappa(y_m)).$$

Let $d$ be the number of distinct values among the $y_e$. Evaluation of the jet basis

$$1,y,\ldots,y^{d-1}$$

on those distinct values has nonzero Vandermonde determinant. Repeated occurrences produce duplicate rows. Therefore

$$\boxed{ \operatorname{rank}(\operatorname{ev}_{\{y_e\}})=d. }$$

Interpretation

The occurrence-labelled tangent space has rank $|E|$, while the physical momentum-function lens sees only one direction per distinct edge energy. Energy collisions are therefore readout-rank-loss loci. They do not erase the underlying occurrence labels or create new Carrier strata.

This gives an all-graph criterion for when one Gaussian source function is a faithful detector of deletion-route information.

Evidence

• Entries 2213 and 2227
• research/benincasa/checkers/energy_collision_score_rank.rs

View source on GitHub