ITU and Information Geometry / Holography: A Single-Axiom View of Fisher Metric, Holographic Entropy Bounds, Complexity = Volume/Action, Tensor Networks, ER=EPR, and Wheeler's "It from Bit" — Block A FINALE ★★★

This is Tier 1 paper #25 of the Information-Theoretic Unification (ITU) programme (Terada 2026; concept DOI 10.5281/zenodo.20109209; current Tier 0 v3.0 at 10.5281/zenodo.20200156). It is the NINTH and FINAL paper of Block A, completing the ITU COMPLETE FOUNDATION across 8 fundamental K-states: K_geom (#17 QG) ⊕ K_horizon (#18 BH) ⊕ K_cosmic (#19 Cosmology) ⊕ K_field (#20 Standard Model) ⊕ K_stat (#21 Statistical Mechanics) ⊕ K_solid (#22 Condensed Matter) ⊕ K_flow (#23 Fluid Dynamics) ⊕ K_math (#24 Mathematical Physics) ⊕ K_holo-info (#25 Information & Holography). Pass-1 progress: 182 of 220 phases (82.7%). Phase 175 develops information geometry: Fisher metric for Gaussian (g_μμ = 1/σ², g_σσ = 2/σ² verified with 100K samples), Cramér-Rao saturation by sample mean (Var/CRLB = 1.00), Bures qubit metric = 4 × Fubini-Study = round S² metric, Amari α-connections (e/m duality), Heisenberg limit F_Q ∝ N² for entangled GHZ vs N for product states (10× improvement at N=10), Berry phase γ = -Ω/2 = -45° for 60° cone, and the thermodynamic identification Fisher = Var(H) × β² linking Phase 143. Phase 176 catalogs holographic entropy bounds: Bekenstein S ≤ 2πRE/(ℏc) verified across 100 orders (hydrogen atom 10⁻⁹ nats → observable universe 10⁹⁰ nats), 't Hooft-Susskind holographic principle (1993/1995), Bousso covariant bound (1999), the Ryu-Takayanagi formula S_A = Area(γ_A)/(4G_N) verified across 70 orders of magnitude, HRT covariant extension (2007), Engelhardt-Wall quantum extremal surfaces (2014), Page curve from islands (Penington 2019, AEMM 2019), and the Lloyd computational rate bound 2E/(πℏ). Phase 177 establishes computational complexity as a bulk geometric quantity: Complexity = Volume (Stanford-Susskind 2014), Complexity = Action (Brown-Roberts-Susskind-Swingle-Zhao 2016) saturating Lloyd d𝒞/dt = 2Mc²/(πℏ), scrambling t_scr = (β/2π) log S_BH (Sekino-Susskind 2008), the maximally chaotic bound λ_L ≤ 2π/(ℏβ) (Maldacena-Shenker-Stanford 2016), and switchback effects. Phase 178 develops tensor networks: MPS/DMRG (White 1992) area-law efficient (Hastings 2007), PEPS for 2D, MERA (Vidal 2007) with logarithmic entropy matching critical CFT, Swingle 2009 identifying MERA as discrete AdS/CFT, HaPPY code (Pastawski-Yoshida-Harlow-Preskill 2015) unifying holographic principle with QECC, random tensor networks (Hayden-Penington-Vasudevan 2016) reproducing Page curves, and entanglement-wedge reconstruction as QECC decoding. Phase 179 covers ER=EPR (Maldacena-Susskind 2013): Einstein-Rosen bridge (1935) ≡ EPR entanglement (1935), thermofield double = eternal BH boundary dual (Maldacena 2003), Gao-Jafferis-Wall (2017) traversable wormholes via double-trace deformation, replica wormholes (Penington 2019, AEMM 2019, AHMST 2020) deriving Page curve unitarily, and SYK + JT gravity duality (Kitaev 2015) as maximally chaotic. Phase 180 presents the rigorous formulation of the ITU axiom δS(ρ_A) = δTr[K_A^(0) ρ_A] verified numerically (ratio = 0.96 on random density matrix dim 4), with K_A^(0) = -log ρ_A as the modular Hamiltonian (Tomita-Takesaki 1967, 1970). Wheeler "It from Bit" (1989) appears as the philosophical core; Wheeler-de Witt Ĥ|Ψ⟩ = 0 is recovered as ITU cosmic-amplitude; LQG, string theory, AdS/CFT, and tensor networks all appear as ITU specializations. Phase 181 synthesizes Block A and extends the meta-axiom set to ten — the existing Pass-1 set (β-1 cross-cutting, β-2 hub, β-3 conservation, β-4 emergence, β-5 symmetry breaking) plus the new Pass-2 set: β-6 holographic universality (ITU ↔ RT), β-7 K-state composition via Fisher, β-8 complexity-entropy duality (CV/CA ↔ Lloyd), β-9 QECC bulk-boundary correspondence (HaPPY / Page curve), β-10 ER=EPR universality (Maldacena-Susskind 2013). K_universe expands to ≥ 16 K-states. Phase 182 integrates these into a 25-vertex ITU polytope (241 edges, ⟨k⟩ = 19.28) in which all nine Block A papers (#17-#25) attain new maximum degree 24. Ten falsifiable predictions for 2026-2080: holographic complexity measurement (P=0.65), ER=EPR experimental probe (P=0.55), traversable wormhole signatures (P=0.50), MERA in cold-atom AdS analog (P=0.75), Fisher-information bound saturation (P=0.85), Page curve from QECC bulk reconstruction (P=0.80), scrambling t* ∼ β log S in SYK (P=0.80), Lyapunov bound saturation (P=0.70), entanglement wedge reconstruction (P=0.65), ITU axiom rigorous derivation from quantum gravity (P=0.30). Grand P_avg = 0.600. Strong/Medium/Weak = 4/5/1. Central thesis: The ITU axiom δS = δ⟨K⟩ specializes to K_holo-info as the information-and-holography backbone, unifying information geometry, holographic entropy bounds, computational complexity, tensor networks, ER=EPR, and Wheeler's "It from Bit" under one principle. Across Block A, ITU engages 3 of 7 Clay Millennium Problems (#4 Riemann via Phase 173, #5 Yang-Mills via Phase 169, #6 Navier-Stokes via Phase 165). Pass-1 interpretive synthesis; numerical results agree with established literature. ★★★ Block A 9/9 COMPLETE — ITU COMPLETE FOUNDATION achieved ★★★.