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VALIDATION_V0.6.md

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Validation receipt — Version 0.6

Date: 2026-07-30 Base main: c31969c6fa4d40d9d9bf8effbe78800f77d1204d

Technical targets

  • Existing regression suite remains mandatory.
  • New adaptive-cutoff regression suite: 8 tests.
  • Native adaptive-cutoff receipt generation: required.
  • Structured and Markdown claim ledgers must contain SOH-L021 and SOH-N006.
  • Monograph Chapter 20 must compile without unresolved references or overfull boxes.

Mathematical PASS

  • The elementary tail inequality integral h <= h(U)/alpha(U) is proved for positive decay rate.
  • A coarse finite-section envelope is derived from explicit Hermite coefficient and row-sum bounds.
  • For every c>0, the schedule Q_N=exp(cN) gives log B_N(cN)=-c^2 N^2/(4w^2)+O(N log N).
  • Therefore the coarse adaptive envelope tends to zero.

Numerical PASS

Declared profile:

  • Gaussian width: 0.8;
  • base cutoff: 100000;
  • logarithmic slope: 2.0;
  • basis sizes: 1..20;
  • target: 1e-12.

Results:

  • all 20 sharp v0.5 certificates pass;
  • maximum: 3.280365246530569e-14 at N=5;
  • final-window coarse envelope is strictly decreasing;
  • arithmetic audit consumes no zeta-zero list.

Boundary

This closes an adaptive diagonal cutoff schedule, not uniformity at one fixed cutoff. Positivity of all infinite-cutoff sections, closure of the complete form, the null-space implication and SOH-C005 remain open. Version 0.6 does not claim a proof of the Riemann Hypothesis.