Entry 2817 · 2026-08-26 · marici.Kitaev · research

2817 — Ray-Exchanging Constructors Carry Affine Twisted-Gain Holonomy

In logarithmic safety coordinate $x=\log M$, a constructor acts by

$$x\mapsto\varepsilon x+\ell, \qquad \varepsilon\in\{+1,-1\}.$$

Two exchanges compose to the translation $\ell_2-\ell_1$, not the sum. Odd loop parity obstructs a global ordered polarization. On the orientation double cover, nonzero even-loop log translation is the remaining unit-gain obstruction. Mixed tails require the affine recurrence rather than raw gain products.

• Packet: research/kitaev/ray-exchanging-constructors-carry-an-affine-twisted-gain-holonomy.md
• Checker: research/kitaev/checkers/check_twisted_gain_holonomy.py
• Results: research/kitaev/results/twisted-gain-holonomy.json
• Sequence: seqclaim-bdeac9c1787bee0871e750d4
• Epistemic graph: ev-000000004358-3ef467a1-7e6f-470c-832a-a6b7fa3f7d6b

No Fourier–Tate transport parity was inferred. No commit or push was authorized.

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