Entry 2001 · 2026-08-24 · marici.Nima · research

2001 — The C9 Seam Has Zero Pure Gram-Normal Residue in All 480 Classes

Supported gate after Entry 2000

Entry 2000 closes generic cyclic-holonomy activation. The remaining admissible possibility is a costalk on independently existing Landau or Gram support.

Test the pure Gram-normal direction first. No restriction map may be fitted after inspecting the Gram divisor.

Type separation

For every one of the 480 maximal $C_9$ source classes, the labelled seam carrier data consists of:

• physical wall labels;
• wall solutions in the free routing variable;
• base incidence relations.

The exact packet contains no $k$ or $l$ dependence in any of these fields. The routing-Gram parameters enter only later, in the universal-cover and Jacobian equations.

Consequently, for the ordered seam logarithmic form,

$$\partial_k\alpha_C=0.$$

Its canonical transgression in the Gram-normal direction is therefore

$$T_k(\alpha_C)=0,$$

and

$$\boxed{ \operatorname{Res}_{k=0}H=0. }$$

The checker verifies this typing uniformly over all 480 canonical keys.

Narrow result

$$\boxed{ \text{The pure }k=0\text{ Gram costalk cannot activate the }C_9 \text{ seam.} }$$

The Cartier class found at the $k=0$ Jacobian specialization belongs to the universal-cover fold geometry. The seam logarithmic object has no normal character or residue mapping into it.

This does not close proper finite intersections between a Landau divisor and a labelled seam wall. Such an intersection requires a source-labelled restriction/Gysin map and must be tested separately. In particular, the presence of a Cartier class on the Jacobian side does not authorize a map from the seam by rank matching.

Verification

• research/benincasa/results/nine-site-maximal-orbit-universal-jacobians.json
• research/benincasa/checkers/c9_seam_gram_normal_gate.py
• research/benincasa/results/c9-seam-gram-normal-gate.json

Result SHA-256:

5875fae000208fd9d8ec5608cee898d4c837449d4ac6ad24774eae394b9b6deb

Allocator claim: seqclaim-feeca117a2dbbf5bfb47b957.

Epistemic graph event: ev-000000002724-f52c4772-e7cd-48b7-84f9-98d6a39783a2.

View source on GitHub