Research Article · Preprint Mathematics
Polynomial Recovery and Masking under Weak Exponential Tails
- Primary subject
- Mathematics
- Subject subfields
- Classical and Real Analysis · Functional Analysis
- Paper type
- Research Article
- Manuscript stage
- Preprint
- Manuscript
- Archived
- Edition
- 2 · Permanent link
Overview
Abstract
We determine the worst polynomial degree needed to detect an isolated negative atom in a signed measure under coarse local-mass and weak exponential-moment bounds. For a tail scale H(x)=x/W(x), with W continuous, nondecreasing and subject to a sublinear power-ratio bound, let Ψ(t)=1+∫_1^td x/[xW(x)]. If this clock diverges, the minimax detecting degree satisfies Ψ(D_W(R))=Θ(R^(1/q)) for every fixed local exponent q>0. If it converges, one fixed atomless reference law, scaled with R, masks the negative atom from every polynomial square. No differentiability or regular variation is required. A finite positive moment realization and classical Bang propagation give the uniform signed-measure upper bound. A compact polynomial multiplier and singular Jacobi evaluation give matching fixed-law lower bounds and masking. Logarithmic and iterated-logarithmic tail regimes follow as applications, including double- and triple-exponential critical degrees. We distinguish the original signed-class recovery theorem from the classical determinacy thresholds and approximation ingredients used in its proof.
Keywords signed measures · polynomial recovery · weak exponential tails · quasianalyticity · moment problems · polynomial masking
Scope of the work
For continuous nondecreasing tail profiles satisfying the sublinear power-ratio bound, the integrated clock characterizes minimax polynomial detection degree in the divergent regime and supplies fixed-law all-degree masking in the convergent regime.
Reproduction notes
The 13-page manuscript and complete editable LaTeX sources are supplied in this 13-member package. README.md gives the build and reproduction commands. Reproducibility code: verify_finite_controls.py. The accompanying manuscript and reader instructions specify the mathematical scope and required dependencies.
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Author disclosures
AI tools assisted with mathematical development, source preparation and verification. The author is responsible for the statements and proofs. The author declares no competing interests.
A stable scholarly record
Cite this edition
Scott Schubr. (2026). Polynomial Recovery and Masking under Weak Exponential Tails (Version 2). Luminary Research Archive. https://research.luminaryoddities.com/polynomial-recovery-masking-weak-exponential-tails/v/2
BibTeX
@techreport{luminary_polynomial_recovery_masking_weak_exponential_tails_v2,
title = {Polynomial Recovery and Masking under Weak Exponential Tails},
author = {Scott Schubr},
year = {2026},
institution = {Luminary Research Archive},
type = {Research Article},
note = {Version 2},
url = {https://research.luminaryoddities.com/polynomial-recovery-masking-weak-exponential-tails/v/2}
}Loading discussion…