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 rₛ = 2 G M / c² spans 2. 95 km (1 Mₛun) to 1303 AU (TON 618). Kerr outer/inner horizons rₚm vs spin a* (extremal r_+ = r_- = rₛ/2). ISCO (Bardeen-Press-Teukolsky 1972): 6 rg Schwarzschild, 1 rg extremal prograde, 9 rg extremal retrograde. Penrose process max 29. 29% (Christodoulou-Ruffini 1971). No-hair theorem (M, J, Q). Phase 120 covers BH thermodynamics. SBH = A/ (4 lP²) spans 1. 05e+79 (10 Mₛun) to 4. 43e+96 nats (M87*). Hawking TH = hbar c³ / (8 pi G M kB) spans 6. 17e-09 K to 9. 49e-18 K (all colder than CMB). Negative heat capacity. Evaporation tₑvap ~ M³ = 2. 10e+67 yr for solar mass. First law dM c² = TH 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 dₜotal = 64. BH evaporation M (t) = M₀ (1-t/tₑvap) ^1/3; Page time tPage = 0. 643 tₑvap. 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: 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 Tₘin at rₕᵐin = sqrt ( (d-2) /d) LAdS. Hawking-Page (1983) phase transition THP = (d-1) / (2 pi LAdS) = 0. 4775. Bekenstein bound S BH ITU axiom. Phase 125 covers primordial BHs and observational statistics. PBH formation M ~ c³ t / G spans 10^-38 Mₛun (Planck) to 10^17 Mₛun (recombination). Asteroid mass window 10¹7-10²2 g remains open for 100% DM. Scrambling time tₛcr = (beta/2 pi) log SBH (MSS 2016): 3. 5e-3 s for 1 Mₛun, 0. 90 yr for M87*. GWTC-3/-4: BBH mass distribution alpha = 2. 5, peak 30-50 Mₛun, pair-instability gap 45-80 Mₛun. Merger rate 17-39 /Gpc³/yr constrains fPBH specializes naturally to Kₕorizon 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 Kₕorizon and the symmetric pairing with Tier 1 #17 QG. Includes 8 theory documents (theoryₚhase119-126. md), 8 Python numerical experiments, 8 figures (PNG), 8 JSON summaries. Total runtime ~12 seconds.