About the work
We do **not** claim to solve the Clay Millennium Problem on the 3D Navier–Stokes equations. Instead, we introduce a physically motivated extension coupling the NSE with a spectral coherence field \(\Psi(t)\) derived from vacuum geometry (\(\zeta'(1/2)\)) and Calabi–Yau compactification, yielding a universal frequency \(f_0 = 141.7001\) Hz.
Using **dual-limit scaling** (\(\epsilon = \lambda f_0^{-\alpha}\), \(A = a f_0\), \(\alpha > 1\)), we prove that a persistent geometric misalignment \(\delta^* = a^2 c_0^2 / (4\pi^2) > 0\) emerges, independent of \(f_0\). This defect induces **self-regulating damping** in the vorticity evolution.
We establish **global smoothness** in the extended system via two independent routes:
1. **Dyadic Riccati with scale-dependent dissipation** (viscous dominance beyond Kolmogorov scale),
2. **Entropy-Lyapunov control** using \(\Phi(X) = \log \log(1+X^2)\) and Osgood-type integrability.
The Beale–Kato–Majda criterion is satisfied uniformly. Seven **falsifiable protocols** (DNS, turbulent tank, EEG, LIGO, Casimir, double-slit, Calabi–Yau check) are proposed to test the predicted 141.7 Hz resonance.
While outside the classical conjecture, this work offers a **physically grounded, mathematically closed, and experimentally testable resolution** to singularity formation in 3D fluid dynamics, suggesting that quantum vacuum structure enforces macroscopic regularity.
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Title A Quantum-Coherent Regularization of 3D Navier–Stokes: Global Smoothness via Spectral Vacuum Coupling and Entropy-Lyapunov Control
We do **not** claim to solve the Clay Millennium Problem on the 3D Navier–Stokes equations. Instead, we introduce a physically motivated extension coupling the NSE with a spectral coherence field \(\Psi(t)\) derived from vacuum geometry (\(\zeta'(1/2)\)) and Calabi–Yau compactification, yielding a universal frequency \(f_0 = 141.7001\) Hz.
Using **dual-limit scaling** (\(\epsilon = \lambda f_0^{-\alpha}\), \(A = a f_0\), \(\alpha > 1\)), we prove that a persistent geometric misalignment \(\delta^* = a^2 c_0^2 / (4\pi^2) > 0\) emerges, independent of \(f_0\). This defect induces **self-regulating damping** in the vorticity evolution.
We establish **global smoothness** in the extended system via two independent routes:
1. **Dyadic Riccati with scale-dependent dissipation** (viscous dominance beyond Kolmogorov scale),
2. **Entropy-Lyapunov control** using \(\Phi(X) = \log \log(1+X^2)\) and Osgood-type integrability.
The Beale–Kato–Majda criterion is satisfied uniformly. Seven **falsifiable protocols** (DNS, turbulent tank, EEG, LIGO, Casimir, double-slit, Calabi–Yau check) are proposed to test the predicted 141.7 Hz resonance.
While outside the classical conjecture, this work offers a **physically grounded, mathematically closed, and experimentally testable resolution** to singularity formation in 3D fluid dynamics, suggesting that quantum vacuum structure enforces macroscopic regularity.
Work type Unclassified
Tags a quantum-coherent regularization of 3d navier–st
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Identifier 2510303540540
Entry date Oct 30, 2025, 10:48 PM UTC
License Creative Commons Attribution-ShareAlike 4.0
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Author 100.00 %. Holder JOSE MANUEL MOTA BURRUEZO. Date Oct 30, 2025.
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