Tier 1 #23: Fluid Dynamics in the Information-Theoretic Unification framework — Navier-Stokes, turbulence, boundary layers, vortices, MHD, astrophysical fluids, and the Clay Millennium Problem

This paper formulates fluid dynamics — viscous flow, turbulence, boundary layers, compressible shocks, vortex dynamics, magnetohydrodynamics (MHD), astrophysical flows, and the Clay Millennium Problem — entirely inside the Information-Theoretic Unification (ITU) framework. Across eight phases (159-166), we (i) establish the Kflow backbone via the Euler and Navier-Stokes equations, Reynolds number scanning bacteria (Re ~ 10⁻⁵) to solar convection (Re ~ 10¹³), Hagen-Poiseuille pipe flow Q ∝ R⁴ verified to slope 4. 000, and Stokes drag matching the Einstein relation of Phase 146; (ii) demonstrate Kolmogorov 1941 turbulence universality with numerical spectrum slope -1. 667 (theory exactly -5/3), Kolmogorov microscale η = (ν³/ε) ^ (1/4) computed across air/water/glycerol/superfluid He, and the She-Leveque (1994) intermittency correction; (iii) recover Prandtl's boundary-layer theory with Blasius f'' (0) = 0. 3321 (Howarth-table 0. 3320) and η₉9 = 4. 925 (theory 5. 0), and the Rankine-Hugoniot normal shock jumps (Ma=2 → p×4. 5, ρ×2. 67, T×1. 69, Ma₂ = 0. 577) ; (iv) prove Kelvin's circulation and Helmholtz's vortex theorems, verify universal Strouhal St ≈ 0. 21 for cylinder Kármán shedding, Rayleigh-Bénard critical Rac = 1708, and Onsager-Feynman quantum-vortex circulation Γ = h/mHe4 = 9. 98×10⁻⁸ m²/s — establishing a topological-quanta family with Phase 153 SC flux Φ₀ = h/ (2e) ; (v) develop MHD covering magnetic Reynolds Rₘ spanning 13 orders, Alfvén speed vA across eight cosmic plasmas (photosphere to magnetar), plasma β classification, Parker solar wind, and ITER tokamak Lawson criterion ratio 1. 85 (Q=10 target) ; (vi) cover astrophysical fluids — Eddington LEdd = 1. 26×10³¹ (M/Mₛun) W, Shakura-Sunyaev α-disk with Kerr efficiency ηₑxtreme = 1 - 1/√3 = 0. 423, M87* and Sgr A* EHT shadows (consistent with Phase 122), Doppler boost δ⁴ for Γ=100 reaching 1. 6×10⁹, Blandford-Znajek mechanism, and Sedov-Taylor blast-wave reproducing Crab Nebula 5. 32 pc at 1000 yr (observed ~5 pc) ; (vii) present the Clay Millennium Navier-Stokes problem (still open after 26 years), the resolved 2D case (Ladyzhenskaya 1969), the Beale-Kato-Majda criterion, Caffarelli-Kohn-Nirenberg singular-set bound, Tao's 2014/2016 averaged-NS blow-up and barrier results, and the Onsager (1949) Hölder 1/3 threshold proved by Isett (2018) — Fourier dual of K41 -5/3 spectrum. Phase 166 integrates into a 23-vertex ITU polytope in which #17-#23 all attain new maximum degree 22 (195 edges, ⟨k⟩ = 16. 96). The construction establishes the EXTENDED MATTER BLOCK Kgeom ⊕ Kcosmic ⊕ Kfield ⊕ Kₛtat ⊕ Kₛolid ⊕ Kflow, expressing physics in six fundamental K-states, and yields 10 falsifiable predictions (Pₐvg = 0. 650; 5 strong, 4 medium, 1 weak) for 2026-2050. Block A paper 7/9, Pass-1 milestone 75. 5% (Phase 166/220). Companion archive contains eight reproducible Python simulations and their figures and JSON summaries. Tier 0 concept DOI: 10. 5281/zenodo. 20109209. Tier 0 v3. 0: 10. 5281/zenodo. 20200156. Block A prior: #17 QG (10. 5281/zenodo. 20230667), #18 BH (10. 5281/zenodo. 20233070), #19 Cosmology (10. 5281/zenodo. 20233952), #20 SM (10. 5281/zenodo. 20234703), #21 Stat Mech (10. 5281/zenodo. 20237082), #22 CM (10. 5281/zenodo. 20249191).