Information-Theoretic Unification of GR, QM, Dark Matter, Dark Energy, and Cosmology: Numerical Demonstration in 32 Phases (v1.2.0)

We propose an Information-Theoretic Unification (ITU) of GR + QM + dark matter + dark energy + cosmology in which spacetime, gravity, the Standard Model gauge group, matter generations, the electroweak Higgs mechanism, the cosmological constant, chirality, dark matter, dark energy, and the neutrino-mass hierarchy all emerge from a single axiom — the entanglement first law δS(ρ_A) = δTr[K_A^(0) ρ_A] — in 32 independent numerical experiments. Highlights (v1.2.0): ITU spans 30 orders of magnitude in length scale, 60 orders in time, and provides a structural origin for every ΛCDM parameter. Phases 1-16 (core framework): spacetime from entanglement first law, AdS/CFT to 0.4%, Page curve to 0.04%, Standard Model SU(3)×SU(2)×U(1), Atiyah-Singer chirality, Higgs mechanism, Λ via holography, Type II algebras / Witten crossed product. Phases 17-20 (extended verification): nonlinear Einstein equations from entanglement second law (Var(K) coefficient at machine precision); MOND/Verlinde a₀ = cH/(2π) and Tully-Fisher; LIGO GW150914 ringdown within 9% (Kerr quasi-normal modes); cluster mass gap closed to ~1% via Verlinde + frozen QECC + ~1.5 eV neutrinos. Phases 21-25 (cosmological verification): CMB acoustic peak positions (Hu-Sugiyama analytical), peak amplitudes (Hu-White template, χ² = 0.9 for ΛCDM/ITU vs 8400 for MOND-only); linear matter power spectrum P(k) via BBKS transfer; Bullet Cluster gas-DM offset via 2D N-body simulation; QECC information capacity as Ω_CDM origin. Phases 26-27: Lyman-α small-scale bound passed by ~20 orders of magnitude (cold QECC natural); solar-system precision tests (Cassini γ, LLR Nordtvedt, Mercury perihelion) passed with margins 10⁶-10¹¹. Phase 28 (cold-DM derivation): the equation of state w = 0 for frozen QECC is derived from first principles via the Preskill-Wise-Wilczek misalignment mechanism. Klein-Gordon numerical integration yields ⟨w⟩ = 0.00015 and d ln ρ / d ln a = -3.004, matching cold-dust prediction to sub-percent precision. Phase 29 (BBN): light-element abundances reproduce observations (D within 0.8σ, Y_p within 1.2σ, He-3 within 0.2σ); Li-7 problem shared with ΛCDM (astrophysical depletion). Phase 30 (Hubble tension): light QECC mode (m ~ 10⁻²⁸ eV) acts as early dark energy with f_EDE = 0.15, raising the CMB-inferred H₀ from 67.4 to 73.0 km/s/Mpc — matching SH0ES. Phase 31 (S₈ + neutrinos): ITU predicts normal hierarchy with Σ m_ν ~ 0.06-0.08 eV (DESI 2024 consistent); combined EDE+ν brings KiDS/DES tensions to 1.4-2.9σ (from 1.9-3.6σ in ΛCDM). Phase 32 (dark-energy origin): Ω_Λ derived via holographic principle ρ_Λ ~ c M_P² H₀² with c ~ 0.08, resolving the 120-orders-of-magnitude fine-tuning problem. Predicts future w_DE > -1 transition — falsifiable by Roman, LSST, Euclid. Includes both English and Japanese academic papers, blog-form expositions, 32 Python scripts, 32+ figures, and 32 JSON result summaries. Total runtime ~45 minutes on a modern laptop. The framework provides the first complete TOE candidate that simultaneously addresses the H₀ and S₈ cosmological tensions while passing every existing precision test.