Historical Euler Compression, Critical Haar Energy, and Event-Rich Crossing Obstructions: A Referee-Audited Candidate Route to the Riemann Hypothesis
Year: 2026
Type: preprint
Abstract: We present a self-contained reconstruction and adversarial audit of a real-variable candidate route to the Riemann hypothesis based on the weighted von Mangoldt deficit, finite Euler adjunction, and a critically normalized Haar energy. The main contribution is a separation of unconditional arithmetic information from the nontrivial estimate needed for a proof. Finite Möbius projection and its Dirichlet inverse give an exact historical convolution identity; the full collection of prime updates contributing to a physical crossing episode is thereby reconstructed without asserting artificial cross-prime orthogonality. A corrected distributional event–bridge identity identifies a normalization error in the predecessor construction. We show that the full square-root prime-update energy and the unprojected critical Möbius energy obey equivalent subexponential targets, each equivalent to the Riemann hypothesis; these targets cannot therefore be invoked as elementary transfer estimates. A geometric split identity reveals a nonnegative fragmentation defect that must be retained. Independently, an elementary event-count argument bounds the total critical charge and every disjointly refined Haar energy of completed positive episodes containing at most a square-root-order number of prime-power events. On the critical microscopic time mesh, all omitted Haar detail energy is polynomial, while the remaining projected energy is again an equivalent Riemann-hypothesis criterion. The candidate is thus reduced to a uniform, one-sided estimate for event-rich completed episodes and an unfinished positive terminal episode, or to a genuinely new directed arithmetic estimate that implies this bound. We formulate this precise missing theorem, describe its dependencies, and provide reproducible finite tests.
Author: Arneth, Borros
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7224079540