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Planck-Scale Physical Regularization of Navier-Stokes Blow-up: V_min = L_P^3 and Effective Viscosity nu_eff(l)=nu_0(1+(L_P/l)^alpha) as Continuum Limit Cutoff to OpenAI Finite-Time Construction Cases C/D - Not a Clay Proof - Historical Concept Oct 2025 - Honest Bilingual v3.0 - Authors Miguel Angel Percudani & Jorge Ivan Diaz
2026-09-10

NEW REPOSITORY v3.0 - HONEST BILINGUAL - 11 Sep 2026 - Authors Miguel Angel Percudani ORCID 0009-0007-1748-3212 & Jorge Ivan Diaz co-author - Status NOT a Clay Millennium formal proof. Historical Clarification: v1.0 26 Oct 2025 GitHub https://github.com/miguelpercu/The_UAT_Physical_Guarantee_of_Navier_Stokes_Regularity + 6 Feb 2026 Zenodo DOI 10.5281/zenodo.18509390 (Concept DOI 10.5281/zenodo.18509389) contained 5-page PDF + Python script proposing Planck energy density rho_max prevents infinite velocities. That v1 is kept as HISTORICAL CONCEPT, not formal development, explicitly stated in original PDF as not formal proof. This new repository withdraws any claim of priority over OpenAI Theorem 1.1 Sep 8 2026. OpenAI Sep 8 2026 (166 pages, 1000 Euler agents 50h + 10000 NS agents 11h, 130B tokens, Lean 17h): Theorem 1.1 exists smooth compact force f and smooth u,p on R3 x [0,1) with sup ||u||_L2 finite but limsup ||u||_Linf = inf at t->1. Scaling tau=1-t, lr~tau^{1/2}, lz~tau^{1/2-h} h<0.01, Vol~tau^{3/2-h}->0, |u|~tau^{-1/2-h}->inf, E_core~tau^{1/2-3h}->0 finite because volume collapses faster. Angular Reynolds Re_theta~tau^{-h}->inf, radial Re_r=O(1). Pulses on auxiliary torus T2 zero mean but non-zero flux <wr w_theta> cancel singular background Prop 7.5, 9.5, residual flat O(q^N), localization X_chi, force f=R(u,p) smooth compact. This work does NOT dispute mathematical construction. Proposes physical regularization preventing realization in nature. Correction: v1 code v_max^2 = 2*rho_max/rho_fluid =1.015e47 m/s missing c^2. Corrected v3 v_max = sqrt(2*rho_max*c^2/rho_fluid)=9.66e56 m/s finite. Velocity bound alone does NOT imply smoothness Cinf. Regularity requires Beale-Kato-Majda integral of vorticity. Formalization: nu_eff(l)=nu_0*(1+(L_P/l)^alpha) alpha>0, optional R_geom factor 0.279182: nu_eff(l)=nu_0*(1+(R_geom*L_P/l)^alpha). When l=lr~tau^{1/2} -> L_P, nu_eff->inf, dissipation diverges, prevents blow-up. This links V_min=L_P^3=4.22e-105 m3 to BKM criterion. When Vol_phys < V_min, physical volume cannot shrink, E_core_phys=0.5 rho|v|^2 V_min ->inf violating rho_max c^2 bound. Contradiction => physical cutoff stops mathematical blow-up. R_geom 8 coils dephased: R_geom=0.279182 residual of 8 axes dephased at DeltaTheta=43.515 deg, heuristic geometric filter NOT first principles, 2*R_geom=0.558364 projection mass observable/pure resonance, cycle truncated at 348.12 deg leaving epsilon=11.88 deg=3.3 percent deficit arrow-of-time, k_early=0.967, kappa_crit=1e-78. Included per discretion as cutoff analogue to V_min. Needs formal derivation. Document 8-COILS-DEPHASED-R_geom.txt explains. Honest reframing: Map = pure continuous forced NS -> can blow-up mathematically (OpenAI Cases C/D). Territory = physical NS with V_min and nu_eff -> cannot blow-up physically (UAT). Both can be true on different objects. Forced vs unforced distinct: OpenAI proves Case D forced breakdown, Case A/B unforced smoothness remains open. Files in this new repository (14 files): - MAIN_PAPER_HONESTO_EN.pdf / ES.pdf - Full honest paper with nu_eff, BKM, dimensional correction - Addenda_v9_4_Honesta_EN.pdf / ES.pdf - Detailed tau vs V_min with Figure_Tau_Vmin.png - Figure_Tau_Vmin.png - Log-log plot lr, lz, Vol vs tau and E_core vs cutoff - limitacion_del_caos_CORREGIDO.py / codigo_python_CORREGIDO.txt - Corrected script with c^2 and nu_eff - README_EN.md / ES.md - Bilingual overview - HISTORICAL_NOTE.md - Clarifies v1 as historical concept - CHANGELOG_HONESTO.md - Timeline Oct 2025 -> Sep 2026 with honest corrections - 8-COILS-DEPHASED-R_geom.txt - Value R_geom=0.279182 heuristic - BIBLIOGRAPHY.bib - References - TITULO_Y_DESCRIPCION_ZENODO.txt - This file Related DOIs: UAT 10.5281/zenodo.17729221, UPC 10.5281/zenodo.18210808, Antifrequency/R_geom 10.5281/zenodo.22678424, Historical v1 10.5281/zenodo.18509390, GitHub https://github.com/miguelpercu/The_UAT_Physical_Guarantee_of_Navier_Stokes_Regularity, ORCID 0009-0007-1748-3212 License CC BY 4.0 - Intended venue Foundations of Physics / PhilSci Archive, not Clay submission.

Ссылка для цитирования:

Percudani M. A. 2026. Planck-Scale Physical Regularization of Navier-Stokes Blow-up: V_min = L_P^3 and Effective Viscosity nu_eff(l)=nu_0(1+(L_P/l)^alpha) as Continuum Limit Cutoff to OpenAI Finite-Time Construction Cases C/D - Not a Clay Proof - Historical Concept Oct 2025 - Honest Bilingual v3.0 - Authors Miguel Angel Percudani & Jorge Ivan Diaz. PREPRINTS.RU. https://doi.org/10.24108/preprints-3116343

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