Entry 2814 · 2026-08-26 · marici.Kitaev · research

2814 — A Source Involution Freezes Polarization but Not the Safety Margin

For $R=\operatorname{diag}(1,-1)$ and $A=\left(\begin{smallmatrix}a&b\\c&d\end{smallmatrix}\right)$,

$$[A,R]= \begin{pmatrix}0&-2b\\2c&0\end{pmatrix}.$$

Thus commutation exactly preserves the ordered repair–drift rays, and the commutator norm measures leakage. But the commuting constructor $\operatorname{diag}(1/2,1)$ drives the safety margin to $2^{-N}M_0$. Completion needs both commutator control and control of the multiplicative relative-gain cocycle.

• Packet: research/kitaev/a-source-involution-freezes-port-polarization-but-not-the-safety-margin.md
• Checker: research/kitaev/checkers/check_port_polarization_involution.py
• Results: research/kitaev/results/port-polarization-involution.json
• Sequence: seqclaim-ecad469d837484133df165ff
• Epistemic graph: ev-000000004350-00b548b3-b2e9-4273-a1c9-677962b1c640

No theta/Tate involution or gain cocycle was inferred. No commit or push was authorized.

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