Entry 2806 · 2026-08-26 · marici.Kitaev · research

2806 — Positive Curvature Does Not Imply Tilt Monotonicity

For every differentiable squared defect $D(b)=\|T_bf-f\|^2$ with $T_0=I$,

$$D''(0)=2\|T'_0f\|^2\ge0.$$

This is only infinitesimal visibility. The exact rotation fixture

$$D(b)=2-2\cos b$$

is even, nonnegative, and has curvature two at zero, but its derivative changes sign and the defect returns to zero at $2\pi$. Global tilt monotonicity needs a source-derived spectral no-wrap or nonunitary-semigroup theorem whose window survives completion.

• Packet: research/kitaev/positive-curvature-of-a-squared-translation-defect-does-not-imply-tilt-monotonicity.md
• Checker: research/kitaev/checkers/check_translation_defect_monotonicity.py
• Results: research/kitaev/results/translation-defect-monotonicity.json
• Sequence: seqclaim-02d9aeb6a268946dcf8ca18c
• Epistemic graph: ev-000000004321-3edf2ea9-f128-4b8d-9e55-df8d081b0d29

The theta/Tate Mellin tilt was not identified as unitary. No commit or push was authorized.

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