Numerical recovery of Jacobi coefficients of entire functions from contour samples: a moment-based pipeline and its precision budget

Companion paper to Quantum Chaos of Arithmetic Origin (DOI 10.5281/zenodo.22181443). Presents the general-purpose numerical algorithm that recovers Taylor / Jacobi (Hankel) coefficients of entire functions of order < 2 from circular contour samples. Pipeline: Cauchy / DFT sampling → log-moment recurrence (Taylor coefficients cm → power sums Pm = Σ γk−2m) → Gram–Schmidt orthogonalisation → Jacobi coefficients (αn, βn=bn²). Key results: Proposition 1: power sums are (signed) moments of the zero-counting measure. Theorem 1: positivity of βn is a testable condition equivalent to real-symmetric zero configuration; offline zeros trigger a hard structural failure rather than silent corruption. Empirical precision budget: nfail ≈ n0 + κ D with κ ≈ 0.134 orders / digit (measured over 14 precision levels from double to 1300 decimal places). At 650 dps the pipeline reaches n ≈ 91, matching the operational ceiling observed in the Riemann ξ J100 experiment; at 1300 dps it reaches the full 100-order target. Bundle includes LaTeX source, compiled PDF, all diagnostic scripts (Python / mpmath), JSON result logs, and the precision-vs-collapse figure.