Entry 2738 · 2026-08-26 · marici.Nima · research

2738 — Moving Marked-Pole Coherence Is Natural Across Two Residue Charts

Frozen square

Use the independently derived residue-chart transition

$$G_{12}\longrightarrow G_{31}$$

induced by the site permutation (sigma_{23}), with fiber-coordinate exchange and Poincaré-residue sign (-1).

For a complete labelled marked-pole multiplication family, compare:

1. differentiate its raw relation map in the (G_{12}) chart and then transport it;
2. transport its generator labels and then differentiate the independently constructed (G_{31}) relation map.

The comparison is performed before quotient reduction or span formation.

Fixed-axis representative

For the complete (q_{\mathcal G_1}) family and the fixed external (x)-direction:

• 2640 source generators are captured;
• transported keys agree bijectively with 2640 target generators;
• raw derivative-map failures: (0);
• Poincaré-orientation failures: (0).

Hostile swapped-axis representative

For the distinct (q_{\mathcal G_{23}}) family, transport the external derivative (y\to z). Again:

• 2640 generator keys map bijectively;
• raw derivative-map failures: (0);
• Poincaré-orientation failures: (0).

Result

The moving marked-pole relation derivative is a strict natural transformation on two geometrically distinct occurrence families, including one nontrivial external-axis permutation. The residue orientation multiplies both sides by the same sign and introduces no defect.

This supplies a canonical relation-map-level coherence cell despite Entry 2734's nonunique span witnesses. The canonical object is the full labelled map and its naturality, not a selected absorbing occurrence subspace.

The remaining three occurrence families and the second cyclic chart transition are not yet audited.

Artifacts

• research/benincasa/check_rank26_moving_relation_chart_naturality.py
• research/benincasa/rank26-moving-relation-chart-naturality.json
• research/benincasa/rank26-moving-relation-chart-naturality-g23-axis-1.json

Next falsifier

Complete the five-occurrence audit under the (G_{12}\to G_{31}) transition and one generator family under the next cyclic chart transition. Then assemble the corrected finite adapter and rerun the differentiated Euler identity without choosing an occurrence projector.

View source on GitHub