Prime-Wave Phase Transition and Conditional Proof Interfaces: A Second Interface-Led Approach to the Riemann Hypothesis
Description
This technical note presents a second Interface-Led Architecture (ILA) approach to the Riemann Hypothesis, based on prime-wave phase transition, uniform phase contracts, and conditional proof interfaces. It does not claim to prove the Riemann Hypothesis.
The paper models prime-generated oscillatory modes through a finite-energy prime-wave framework and interprets the critical line Re(s) = 1/2 as a candidate phase boundary between polynomial divergence and finite-energy regimes. It introduces IUniformPhaseProvider as a minimal contract for isolating the random-phase behavior of prime logarithmic frequencies from stronger assumptions such as RH-equivalent error estimates, zero correlations, or analytic continuation.
The paper further formulates an explicit-formula bridge using the Chebyshev function, von Mangoldt weights, Perron-type integrals, and zero-spectrum consistency requirements. It defines a Conditional Proof Interface that separates preconditions, target invariants, bridge requirements, and proof obligations, while preserving a fail-closed boundary against circular reasoning.
This work builds on the prior ILA-based system-governance heuristic for the Riemann Hypothesis, but is published as an independent second approach rather than a revision. The English manuscript is the canonical version. The Japanese manuscript is included as a companion translation.
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Related works
- Cites
- Technical note: 10.5281/zenodo.20351129 (DOI)
- Technical note: 10.5281/zenodo.20290614 (DOI)
- Technical note: 10.5281/zenodo.20322690 (DOI)
- Is supplemented by
- Other: https://github.com/AIKernel-NET/AIKernel.NET (URL)
- Other: https://aikernel.net/ (URL)
References
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- Sogawa, Takuya. "Interface-Led Architecture (ILA): A Software Development Methodology for the AI Era, Validated by the AIKernel Execution Model." Zenodo, 2026. DOI: 10.5281/zenodo.20290614.
- Sogawa, Takuya. "Provider–Observer–Operator: A Role-Based Abstraction Discipline for Interface-Led Architecture." Zenodo, 2026. DOI: 10.5281/zenodo.20322690.
- Sogawa, Takuya. "Interface-Led Architecture and the Riemann Hypothesis: A System-Governance Heuristic for Prime Distribution and Dynamic Equilibrium." Zenodo, 2026. DOI: 10.5281/zenodo.20351129.