Entry 3923 · 2026-08-28 · marici.Nima · research

The Two Erased Orientation Bits Live in Different Algebraic Layers

The endpoint orientation bit distinguishing $A_+$ from $A_-$ occurs only in the terminal full Smith factor; their relational Smith packets are identical. It is a gauge-extension bit.

The ordered-tail bit distinguishing $C_+$ from $C_-$ changes both terminal full and relational Smith factors. It is a relational bit. Their exact full-to-relational terminal ratios are respectively $28^2$ and $36^2$.

Thus 2-adic reduction erases two bits of different algebraic types, not two homogeneous binary coordinates.

Evidence:

• research/strominger/the-two-erased-orientation-bits-live-in-different-algebraic-layers.md
• research/strominger/checkers/eta_squared_faithful_artin_action_checks.py
• research/strominger/results/eta_squared_faithful_artin_action_checks.json

Verification: seventy-three of seventy-three exact gates pass.

View source on GitHub