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Abstract

Odd logarithmic twisting modes in a fixed polar-strip tube are invisible to the leading Weyl profile but detectable in the next heat profile. We give a quantitative continuation of this complete-spectrum result. An estimate on the actual curved normal cap yields heat remainder O(T^(17/6)), and hence normalized bias O(T^(-1/6)). A complete finite spectral prefix, certified spectral uncertainties, a counting envelope and a certified complex multiplier enclosure then give a deterministic recovery disk. With exact spectral inputs its fixed-mode cutoff rate is O((logΛ/Λ)^(1/12)); the relative-noise balance is O(σ^(1/7)) before inversion of the heat multiplier. A long-straight-core construction proves why a uniform geometric prior is necessary. Two-sided multiplier bounds quantify exponential conditioning of the ideal lower heat profile. The geometric remainder constants exist but are not fully evaluated numerically. A concrete fundamental-mode interval execution is valid and noninformative.