Polynomial Recovery and Masking under Weak Exponential Tails
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Abstract
For H(x)=x/W(x), with W continuous nondecreasing and satisfying a sublinear power-ratio bound, the integrated clock Psi(t)=1+integral_1^t dx/(xW(x)) determines the worst polynomial-square recovery degree D(R): Psi(D(R)) has order R^(1/q) when the clock diverges. A finite clock gives one fixed atomless law masking every polynomial square. The original class permits arbitrary signed backgrounds and every q>0. No smoothness or regular variation is required; an explicit irregular example and logarithmic double- and triple-exponential critical scales are proved.
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Research details
- Subjects
- Mathematics · Classical and Real Analysis · Functional Analysis
- Keywords
- signed measures, polynomial recovery, weak exponential tails, quasianalyticity, moment problems, polynomial masking
- Manuscript date
- 2026-10-25
- Reader reuse
- No additional permission granted
Scope
Fixed declared class constants and every q>0, with continuous nondecreasing W satisfying the stated sublinear power-ratio hypothesis. Recovery is an order law in the integrated clock; finite-clock masking uses one fixed law for sufficiently large contrast.
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.
Reproduction
The complete package contains editable LaTeX, references, compilation instructions and a standard-library exact rational verifier. Finite Jacobi moment and singular-power kernel controls corroborate algebra; analytic proofs establish the all-degree and asymptotic results.