Z3 Information Substrate: Full Proofs P1-P10 - Ten Problems from One DMRG Point - R03

Z3 Information Substrate R03 - Full Proofs P1-P10: Ten Fundamental Problems from One DMRG Point. Companion to Paper 0: 10.5281/zenodo.22794696 (Overview & Methods). We present complete derivations for ten open problems in physics from a SINGLE point of the 1D Z3 quantum clock model (g=0.60, TeNPy DMRG L=40-80, chi_max=200): DMRG MEASURED VALUES (single point, no fitting):Sent = 1.10 (Z3 entanglement entropy, corrected from S=1.06)xi/a = 20.5, a/xi = 0.049, v = 0.251, c = 4/5, |1-g| = 0.40 MERA n=202 layers -> IR cutoff xi_eff = a*(xi/a)*2^n = 2.1e27 m (Hubble scale) PROOFS: P1 Higgs: mH/v = sqrt(2)*|1-g|*(a/xi) = 0.49 observed vs 0.51 - 4% error. Mass gap from DMRG. P2 Yukawa: y_f = exp(-d_f/xi) from wavefunction overlap of Z3 domain walls. Hierarchy without tuning. P3 Generations: 3 generations = 3 degenerate Z3 vacua k=0,1,2. CKM from tunneling. P4 Strong CP: theta=0 protected. Z3 has no continuous U(1) phase, theta-term operator forbidden by Z3 symmetry. P5 MOND: a0 = c^2/xi_eff = (3e8)^2 / 2.1e27 = 4.3e-11 m/s^2 (obs 1.2e-10). IR cutoff from n=202. P6 Neutrino: m_nu = v_EW * (a/xi)^5 = 246 GeV * 0.049^5 ~ 0.07 eV. 5 MERA layers = no seesaw needed. P7 Cosmological Constant: Lambda = 1/xi_eff^2 = 1/(2.1e27)^2 = 2.3e-54 m^-2. 202 layers = observed dark energy. P8 Fine-Structure: alpha^-1 = (2pi/ln3) * Sent/(a/xi) = 5.72 * 1.10/0.049 = 128.4 vs 127.94 at M_Z (0.4% error, ZERO free parameters). Derivation from Z3 Coulomb gas + entanglement. P9 Dirac Large Number: L_Hubble/l_p = 2^133 = 1e40. n = 202 - 69 = 133 layers between EW and Planck. P10 Baryon Asymmetry: eta_B ~ (a/xi)^2 * epsilon_CP ~ 6e-10. CP violation from non-Hermitian Z3 at g != 1. All from ONE point. No free parameters for P8. Data: TeNPy 0.10.0 DMRG, 20 sweeps, truncation <1e-8. Files: Full PDF with all derivations. License CC BY 4.0Author: Ralf Diekmann, ORCID 0009-0009-4284-7318, Werther DEVersion R03