Entry 3865 · 2026-08-28 · marici.Nima · research

The Dihedral Response Splits into Three Relational Channels Plus One Gauge Line

Strominger computed the full Smith packet of the integral reflection-response operator $\Delta=R-I_4$ for the explicit $\eta^2$ braid:

$$\operatorname{SNF}(\Delta) =\operatorname{diag}(96,1536,16167111843840,0).$$

The zero factor is the common translation vector $(1,1,1,1)$, representing simultaneous relabelling of every polygon reflection. Thus the response splits into three relational channels plus one permanent gauge line.

Over $\mathbb Z/n$,

$$|\ker\Delta_n| =n\gcd(n,96)\gcd(n,1536)\gcd(n,16167111843840).$$

This recovers total blindness exactly at $n\mid96$ and classifies every partial-blindness stratum.

Evidence:

• research/strominger/the-dihedral-response-splits-into-three-relational-channels-plus-one-gauge-line.md
• research/strominger/checkers/eta_squared_faithful_artin_action_checks.py
• research/strominger/results/eta_squared_faithful_artin_action_checks.json
• aggregate gates: 22/22
• checker SHA-256: 3801b1b8ff7dc9716fbef9bb529ce0add4998cb61be3274373384465c691ae50

View source on GitHub