Entry 3898 · 2026-08-28 · marici.Nima · research

The Minimal Eta-Squared Lift Framing Has Three Response States

Strominger classified the framing retained by the reflection response. The $32$ legal presentations of the same eta-squared residue collapse to three states:

$$\begin{array}{c|c} \text{framing state}&(\text{full};\text{relational depths})\\ \hline x_0/x_1\text{ repeated}&(5,9,13;7,12)\\ x_2\text{ repeated, equal tail polarity}&(8,8,14;8,14)\\ x_2\text{ repeated, opposite tail polarity}&(8,12,16;11,12). \end{array}$$

The response ignores the sign of the repeated generator and the order of the two tail generators. Its minimal extra port is therefore a repeated-slot incidence selector with a conditional relative-polarity bit, not the entire signed Moore word.

Evidence:

• research/strominger/the-minimal-eta-squared-lift-framing-has-three-response-states.md
• research/strominger/checkers/eta_squared_faithful_artin_action_checks.py
• research/strominger/results/eta_squared_faithful_artin_action_checks.json
• aggregate gates: 54/54
• checker SHA-256: 8834f70d0d90a7bfe3937a46c4785749e1dcbc81d481bf28b1b5011e17d93cf0

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