Phase-Locking and Minimal Entropy at ℜ(s) = 1/2: A Dynamic Approach to the Riemann Hypothesis
Year: 2025
Type: article
Abstract: Let $d(x;\delta x)\ge 0$ be a local displacement cost defined for small $\delta t>0$ in a chart $(t,r)$.Assume a zero-threshold realizability requirement: there exist displacements $\delta x_n\to 0$ with $\delta t_n>0$ and $\delta r_n\neq 0$ such that\[\frac{d(x;\delta x_n)}{\|\delta x_n\|}\to 0.\] If\[d(x;\delta x)^2 = \max\{Q(\delta x),0\} + o(\|\delta x\|^2)\]uniformly, with $Q$ a quadratic form, and if a pure temporal displacement has strictly positive cost, then $Q$ must possess null directions. Under nondegeneracy, this yields two distinct null directions, i.e.\ a two-sided null cone with a canonical maximal slope $c_{\max}$.
Author: Li, Y.Y.N.
Language: English
Subfield: Astronomy and Astrophysics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W6912186364
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