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Cubic augmentation of a two-moment model: an exact finite absorption theorem and its limits

Primarily AI-generated textHuman understanding: some partsmath.NT — Number Theorymath.OC — Optimization and Control

Contributed by Kunal Tyagi

Version 2 / Oct 15, 2026 / CC BY 4.0

Abstract

We study adjoining a half-bandwidth signed cubic trace and a spectral count ladder to a bandwidth-one trace/Frobenius model motivated by zeta-zero certificates. In a finite circle model with mass N = 64, flat windows, and explicit budget centers, we prove exact absorption over the full atom-only class: the augmented and baseline optima agree for both the distinct-count and simple-fraction objectives. Three explicitly specified integer-marked grid columns attain the lower bounds. Their mixing weights are defined algebraically, and an Arb certificate proves all strict feasibility and inertia inequalities. The witness satisfies the ladder at every positive threshold, not just on a finite threshold grid. We also give the exact conjugate-pair spectrum, the isolated-block cubic identity, grid Parseval, and the sharp conditional spectral-capacity constant 2 sqrt(2). The result is a finite model theorem, not an unconditional statement about zeta zeros. Version 2 corrects an infeasible witness, a cubic-tolerance mismatch, and an incorrect rationality claim in version 1. Global absorption in the pair-containing or pinned classes remains unproved; equality on a searched column dictionary and heuristic pricing do not establish it.

Provenance statement

Original version prepared with Claude (Anthropic); revised manuscript, mathematical audit and companion checks prepared with OpenAI Codex under Kunal Tyagi's direction. The revision explicitly corrects the scope of the earlier paper. The new finite atom-only witness is certified by Arb with exact integer inputs and algebraically defined weights; no full-class LP theorem or new Lean verification is claimed. No independent human expert review of the revision is claimed. Original publication artifacts are at https://github.com/x67ai/riemann-rh-program; all new source and checks accompany this version. Zenodo concept DOI 10.5281/zenodo.22171688.

Tools used

Anthropic
Claude OpusVersion 4.x (agents), August 2026
OpenAI
CodexVersion October 2026 revision and checks

References

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Version history

  1. v1Submitted by Kunal TyagiInitial depositSupersededOct 15, 2026
  2. v2Submitted by Kunal TyagiSubmitted as a new versionCurrentOct 18, 2026