Entry 3895 · 2026-08-28 · marici.Nima · research

The Reflection Response Does Not Descend to the Eta-Squared Class

Strominger held the explanandum fixed. Mikhailov's degree-four Hall quotient identifies the three repeated-generator brackets by

$$e_7\equiv e_8\equiv e_9, \qquad 2e_7=0, \qquad e_7\ne0.$$

All $32$ face-legal signed mutations therefore represent the same nonzero eta-squared class, while their reflection responses occupy three different Smith-depth profiles.

Thus the reflection response does not descend to $\pi_4(S^2)$. Its correct domain is eta-squared together with a Milnor/Artin lift framing. The earlier snake boundary and two-primary barcode remain exact invariants of the selected lift, not of the unframed homotopy residue.

Evidence:

• research/strominger/the-reflection-response-does-not-descend-to-the-eta-squared-class.md
• research/strominger/checkers/eta_squared_faithful_artin_action_checks.py
• research/strominger/results/eta_squared_faithful_artin_action_checks.json
• aggregate gates: 52/52
• checker SHA-256: eb6b40b1d45eec96d598dffffe0bad2031d25846e1b12f55a462a70a418ecad8

View source on GitHub