ITU and Black Holes: A Single-Axiom View of Schwarzschild-Kerr Solutions, Bekenstein-Hawking Entropy, the Page Curve, Information Paradox Resolutions, AdS/CFT BHs, Primordial BHs, and the 2026-2050 Observational Roadmap

We apply the Information-Theoretic Unification (ITU) framework (Terada 2026, concept DOI 10.5281/zenodo.20109209; current latest Tier 0 v3.0 at 10.5281/zenodo.20200156) to black holes. This is Tier 1 paper #18, the second paper of Block A (Physics/Math deepening) and the specialization of Tier 1 #17 Quantum Gravity (DOI 10.5281/zenodo.20230667) to the BH horizon. The ITU polytope reaches 18 vertices with Tier 1 #18 attaining degree 17 (new maximum). Pass-1 progress: 126 of 220 phases (57.3 %). Phase 119 establishes classical BH solutions. Schwarzschild radius r_s = 2 G M / c^2 spans 2.95 km (1 M_sun) to 1303 AU (TON 618). Kerr outer/inner horizons r_pm vs spin a* (extremal r_+ = r_- = r_s/2). ISCO (Bardeen-Press-Teukolsky 1972): 6 r_g Schwarzschild, 1 r_g extremal prograde, 9 r_g extremal retrograde. Penrose process max 29.29% (Christodoulou-Ruffini 1971). No-hair theorem (M, J, Q). Phase 120 covers BH thermodynamics. S_BH = A/(4 l_P^2) spans 1.05e+79 (10 M_sun) to 4.43e+96 nats (M87*). Hawking T_H = hbar c^3 / (8 pi G M k_B) spans 6.17e-09 K to 9.49e-18 K (all colder than CMB). Negative heat capacity. Evaporation t_evap ~ M^3 = 2.10e+67 yr for solar mass. First law dM c^2 = T_H dS verified to mean rel diff 8.43e-04. Phase 121 presents rigorous Page curve. Page (1993) formula matches log approximation within 0.01 at d_total = 64. BH evaporation M(t) = M_0(1-t/t_evap)^{1/3}; Page time t_Page = 0.643 t_evap. Pure-state mutual info I(R:B) max = 0.997; S(R|B) negative confirms quantum entanglement. QECC interpretation: BH stores 10^{77}-10^{98} logical qubits (Page-Yang 1998, HaPPY tensor 2015). Phase 122 unifies 7 information-paradox resolution proposals under ITU axiom dS = d<K>: Fuzzball (Mathur 2005), Soft hair (HPS 2016), Maldacena-Maoz (2004), Complementarity (Susskind 1993), Holography of information (LPRS 2020), Island formula (Penington 2019), ER=EPR (Maldacena-Susskind 2013). Phase 123 covers AdS/CFT BHs. AdS-Schwarzschild T_min at r_h^min = sqrt((d-2)/d) L_AdS. Hawking-Page (1983) phase transition T_HP = (d-1)/(2 pi L_AdS) = 0.4775. Bekenstein bound S <= 2 pi k_B R E / (hbar c) saturated by Schwarzschild BH (ratio = 1.0). Holographic complexity (Susskind 2014): dC/dt = 2 E / (pi hbar) Lloyd-bound saturation; 1.08e+82 ops/s for 10 M_sun. Phase 124 develops Maxwell demon + Q-BH simulation. Landauer bound 1.79e-2 eV/bit at 300 K, 5.97e-7 eV/bit at 0.01 K. BH = ultimate Maxwell demon: DeltaE/bit minimized for massive BHs (3.68e-12 eV/bit for 1 M_sun). Hawking radiation mutual info I(R_i:R_j) spikes after Page time. Petz map (1986) fidelity sharp at t_Page (Hayden-Preskill 2007). SYK / JT gravity tractable on 100-1000 qubit QPUs (IBM Eagle 127, Condor 1121, Atom Computing 1180). ITU triangle: Quantum Computing <-> BH <-> ITU axiom. Phase 125 covers primordial BHs and observational statistics. PBH formation M ~ c^3 t / G spans 10^{-38} M_sun (Planck) to 10^{17} M_sun (recombination). Asteroid mass window 10^17-10^22 g remains open for 100% DM. Scrambling time t_scr = (beta/2 pi) log S_BH (MSS 2016): 3.5e-3 s for 1 M_sun, 0.90 yr for M87*. GWTC-3/-4: BBH mass distribution alpha = 2.5, peak 30-50 M_sun, pair-instability gap 45-80 M_sun. Merger rate 17-39 /Gpc^3/yr constrains f_PBH < ~10% in stellar mass range. Phase 126 integrates under K_horizon (K_geom restricted to BH horizon). 18-vertex polytope: 93 edges, avg degree 10.33. Tier 1 #18 couples strongly to #17 QG (1.00, parent), #1 QC (0.85, QECC), #10 Energy (0.85); medium to #11 Climate (0.50), #14 Communications (0.70). Average coupling 0.382. Tier 1 #17 (general K_geom) and #18 (BH specialization) form symmetric pair phase-by-phase. Ten falsifiable predictions for 2026-2050: EHT M87* 5 uas 2030 P=0.90, GWTC-5 300+ BBH 2030 P=0.85, Sgr A* Kerr <1% 2035 P=0.75, LISA IMBH 2038 P=0.70, pair-instability gap 2032 P=0.65, PBH asteroid window 2038 P=0.55, Q-computer BH sim 2032 P=0.70, BMV gravitational entanglement 2032 P=0.65, Hawking-Page CFT 2040 P=0.40, SMBH origin 2045 P=0.45. Grand P_avg = 0.660. Strong/Medium = 7/3. Central thesis: ITU axiom delta S = delta <K> specializes naturally to K_horizon at BH horizons, unifying classical BHs, thermodynamics, Hawking radiation, Page curve, information-paradox resolutions, AdS/CFT, complexity, quantum-computer BH simulations, and PBH cosmology under one principle. EHT 5 uas (2030) and GWTC-5 (LIGO O5) provide strongest near-term tests; Q-computer BH simulation (2032) and BMV gravitational entanglement (2032) open direct quantum tests. Pass-2 (Phase 222) will derive ITU-specific BH predictions. Honest framing: Pass-1 interpretive paper. Numerical results agree with established literature. No new physical predictions; contribution is the unified ITU axiom narrative under K_horizon and the symmetric pairing with Tier 1 #17 QG. Includes 8 theory documents (theory_phase119-126.md), 8 Python numerical experiments, 8 figures (PNG), 8 JSON summaries. Total runtime ~12 seconds.