Part II: Conditional Reconstruction of the Riemann Hypothesis via Inverse Categorical Isomorphism and Spectral Repulsion
Year: 2026
Type: preprint
Abstract: This paper is the second part of our research program. Building upon our previous work (Tan, 2026) [1], which established the conditional reduction skeleton from the Connes-Consani-Moscovici (CCM) 2025 spectral triple framework and explicitly isolated the open interfaces (Assumption I: limit identification; Assumption J: zero non-degeneracy), this paper proposes a novel topological and variational strategy to resolve these two remaining interfaces. We explicitly inherit the research boundary established in Part I: we do not attempt to solve the analytical gaps (Gap #1 and Gap #2). Instead, assuming spectral convergence, we introduce the "Inverse Domain Mapping" to reconstruct the limit identification process via categorical isomorphism, and the "Zero-sum Game Repulsion" mechanism to rigorously prevent the degeneracy of zeros. By combining these two mechanisms, the "Critical Squeezing Theorem" is derived, demonstrating that without assuming any zero lies on Re(s) = 1/2, the topological constraints and energy repulsion inevitably squeeze the zero distribution onto the critical line.
Author: Tan, Bowen
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7225647438
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