schema_version: 1
title: Constructive Characterizations and New Families of van Dantzig Pairs
abstract: For symmetric nondegenerate U with M_U(t) finite for every real t, the manuscript
  characterizes existence of an independent V with M_U(t) phi_V(t)=1 by Fourier positivity
  and Hankel positivity at all sizes. It constructs pairs from every real polynomial
  positive on [0,infinity), using sufficiently large b followed by sufficiently large
  tau, and gives explicit families and parameter certificates. Entire-function mean-value
  identities require the stated integrability conditions; historical novelty and external
  class comparisons are not certified here.
field: Probability
license: CC-BY-4.0
type: paper
authors:
- eggtea
keywords:
- van Dantzig pairs
- Fourier inversion
- moment problem
- polynomial realization
main: main.pdf
takeaways: takeaways.md
verification:
- type: review
  path: verification/review.md
  status: materials-present-not-independently-verified
  model: Codex (GPT-6; current-session non-independent check)
  date: '2026-10-17'
  scope: Limited current-session claim/assumption and selected-proof consistency check
    of main.pdf SHA-256 fa94fb827f24f30a1d071797e61b11d7f9dfde6ea7e8d4bdf90cb2558090121d;
    includes executed formula checks; not an independent full mathematical review.
references:
- title: A new class of solutions to the van Dantzig problem, the Lee–Yang property,
    and the Riemann hypothesis
  authors: T. Konstantopoulos; P. Patie; R. Sarkar
  doi: 10.5802/aif.3600
- title: The Moment Problem
  authors: K. Schmüdgen
  doi: 10.1007/978-3-319-64546-9
- title: Contributions to a problem of D. van Dantzig
  authors: E. Lukacs
  doi: 10.1137/1113008