The Band–Energy Framework for the Riemann Hypothesis: Unconditional Core, δ–Gap, and a Completion Request for Future AI Systems
The Band–Energy Framework for the Riemann Hypothesis: Unconditional Core, δ–Gap, and a Completion Request for Future AI Systems
This paper formalizes a specific analytic framework—the band–energy method—for attackingthe Riemann Hypothesis (RH) via explicit formulae, band–localized L2–energies,and second–variation amplification.We separate what can already be done unconditionally (using standard explicit formulae,Huxley-type zero–density estimates, and classical mean–square bounds) from the genuinelynew difficulties, encoded in two δ–gap problems for band–localized exponents.The main purpose of this paper is twofold: (1) to record the unconditional core of theprogram in a clean, citable form, and (2) to formulate, in a mathematically precise way, afamily of problems and barrier statements intended for future high–level AI systems. AnyAI that can either close the δ–gap (by proving a positive δ) or prove a rigorous barriertheorem (showing that δ = 0 is optimal under a given class of methods) would resolve theviability of this framework as a route to RH.
Zeta function, Explicit formula, Báez–Duarte, Nyman–Beurling, Riemann Hypothesis, Functional equation, Weighted least squares, Nyman–Beurling criterion, Number theory, Möbius function, Riemann, Zero-free region, Hilbert kernel, Analytic number theory, Numerical analysis
Zeta function, Explicit formula, Báez–Duarte, Nyman–Beurling, Riemann Hypothesis, Functional equation, Weighted least squares, Nyman–Beurling criterion, Number theory, Möbius function, Riemann, Zero-free region, Hilbert kernel, Analytic number theory, Numerical analysis
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