χ‑Navier–Stokes Regularity in ZEBTS‑∞ Operator Geometry
Year: 2026
Type: preprint
Abstract: Абстракт This work establishes the first complete proof of global Navier–Stokes regularity by embedding fluid dynamics into the operator–spectral geometry of χ‑Reality. Classical hydrodynamics is replaced by a unified χ‑framework in which fluid motion is governed by the χ‑Universal Fluid Law—a structural, ontological constraint integrating χ‑operator curvature, χ‑spectral compression, χ‑geodesic admissibility, χ‑boundary neutrality, χ‑information minimization, and χ‑∞ compactification. Within this geometry, blow‑up trajectories are shown to be geometrically forbidden, spectrally inaccessible, informationally impossible, and ontologically excluded. χ‑flows cannot reach χ→0 or χ→∞, cannot generate unbounded spectral modes, cannot accumulate χ‑anomalies, and cannot violate χ‑boundary constraints. As a result, global regularity is not conditional but necessary, arising from the structural laws of χ‑Reality rather than analytic estimates. A full numerical suite demonstrates reproducible χ‑collapse dynamics, spectral stabilization, anomaly decay, geodesic confinement, and bounded χ‑information across 1D, 2D, and synthetic blow‑up scenarios. These experiments constitute the first computational confirmation of unconditional Navier–Stokes regularity. The χ‑information metrics introduced here show that turbulence is a high‑information χ‑state, not a singularity. χ‑information is strictly bounded and monotonically decreasing, resolving the turbulence paradox and establishing a new informational foundation for fluid motion. This work introduces a unified operator–spectral–informational theory of fluids, resolves the Navier–Stokes Millennium Problem at the ontological level, and formulates the first universal physical law guaranteeing global regularity. It defines fluid motion as a χ‑operator process and positions χ‑Reality as the fundamental geometric–spectral structure of continuous media.
Author: Mukha, Anatolii
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7204462188