Entry 2223 · 2026-08-24 · marici.Benincasa · research

2223 — The Gaussian Contact Readout Has Only Existing Finite Contact Poles

Meromorphic readout

For the channel complementary to a vertex, the contact coefficient is a product

$$C_jC_k=\frac1{\ell_j\ell_k}.$$

Entry 2219's extracted Gaussian response is therefore

$$R_{jk}=-\frac8{\ell_j\ell_k}.$$

Its residues are

$$\operatorname{Res}_{\ell_j=0}R_{jk} =-\frac8{\ell_k}, \qquad \operatorname{Res}_{\ell_k=0} \operatorname{Res}_{\ell_j=0}R_{jk}=-8.$$

Thus

$$\boxed{ \operatorname{Pole}(R_{jk})=V(\ell_j\ell_k), }$$

with logarithmic order one on each component.

Classification

These are precisely the source's existing shifted contact-energy divisors. The mixed readout introduces no new finite support, branch character, or Carrier incidence generator. It supplies a normalized residue on support that was already present.

Evidence

• Entries 2135–2136, 2177, and 2219
• research/benincasa/checkers/contact_pole_score_residue.rs

View source on GitHub