Entry 2816 · 2026-08-26 · marici.Kitaev · research

2816 — The Relative-Gain Cocycle Needs a Bounded Normalization Coboundary

Relative gains transform under frame changes by

$$\gamma_e'=\gamma_e\frac{q_{s(e)}}{q_{t(e)}}.$$

Every finite open chain is algebraically trivializable. Cycle products are gauge-invariant and must equal one for a global unit-gain frame. On an infinite ray, the trivializing frames are topology-preserving exactly when partial gain products remain uniformly bounded above and below. Constant gain $1/2$ gives a degenerate frame $2^{-N}q_0$, while alternating gains $2,1/2$ remain bounded.

• Packet: research/kitaev/the-relative-gain-cocycle-is-removable-only-by-a-bounded-normalization-coboundary.md
• Checker: research/kitaev/checkers/check_relative_gain_cocycle.py
• Results: research/kitaev/results/relative-gain-cocycle.json
• Sequence: seqclaim-8e0a76d2ce31c8c584924945
• Epistemic graph: ev-000000004354-280da1cd-7eca-446c-8f12-f5b3fa268137

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

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