TMD: The Riemann Boundary of Computability (Version 2.0)

Version 2.0 is a major mathematical revision of the original work. The core structure of the paper remains unchanged: the triadic update operator is defined, its spectral properties are analyzed, and the computability boundary is introduced as the point where the operator loses convergence. This version clarifies the mathematical status of the proposed connection between the computability boundary and the critical line of the Riemann zeta function. The Riemann link is now presented as a heuristic structural analogy, not as a proven equivalence. A new section discusses the open problem of constructing a spectral determinant for the triadic operator and its potential relation to ζ(s). All claims are now formulated in a mathematically rigorous and conservative way. The computability boundary itself — defined by the spectral radius condition ∣λ∣=1 — remains the central result of the work.

Authors

Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-05-30
DOI
https://doi.org/10.5281/zenodo.20457376
Primary Topic
Computability, Logic, AI Algorithms
Type
preprint
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preprint

TMD: The Riemann Boundary of Computability (Version 2.0)

Aleš Kováč
Zenodo (CERN European Organization for Nuclear Research)
Computability, Logic, AI Algorithms
preprint

TMD: The Riemann Boundary of Computability (Version 2.0)

Aleš Kováč
preprint en

Abstract

Version 2.0 is a major mathematical revision of the original work. The core structure of the paper remains unchanged: the triadic update operator is defined, its spectral properties are analyzed, and the computability boundary is introduced as the point where the operator loses convergence. This version clarifies the mathematical status of the proposed connection between the computability boundary and the critical line of the Riemann zeta function. The Riemann link is now presented as a heuristic structural analogy, not as a proven equivalence. A new section discusses the open problem of constructing a spectral determinant for the triadic operator and its potential relation to ζ(s). All claims are now formulated in a mathematically rigorous and conservative way. The computability boundary itself — defined by the spectral radius condition ∣λ∣=1 — remains the central result of the work.

Zenodo (CERN European Organization for Nuclear Research)
Reduced inequalities
Computability, Logic, AI Algorithms
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