H.O.U.T. Material Structure Unification: Spectral Closure Law and Two‑Loop Refined CKM/PMNS Parameters

H.O.U.T. Material Structure Unification v43 – Spectral Closure Law & Two‑Loop CKM/PMNS Corrections This document presents the forty‑third version (v43) of the H.O.U.T. Material Structure Unification, achieving complete theoretical closure of the particle physics sector of the H.O.U.T. framework. All 26 Standard Model + neutrino parameters are derived from first principles using the Universal Alphabet $\{\pi,6\}$ and two primitive axioms (3D space + 2‑bit vacuum). No free algebraic parameters are used; all constants are derived, not fitted. Key achievements of v43 1. Law VII (Spectral Closure Law) – The counting $8+12+6 = 26$ is elevated from a geometric corollary to a spectral principle: the 26 parameters are the first 26 eigenmodes of the complex action $\mathcal{Z} = \mathcal{A} + i\mathcal{P}$ on the Keplerian complex manifold $M_\Omega$, with $n \le 3$ modes carrying >80% spectral weight. Higher modes are suppressed by $1/n^2$ and decouple. 2. Two‑loop corrections derived from geometry – An edge‑vertex interference factor $F_{\text{EV}} = \left(\frac{\Omega_8}{V_3}\right)^{\epsilon_{\text{OBE}} P^*/2} \approx 1.01132$ is derived from the complex action structure. It reduces: - $|V_{us}|$ error from 0.86% to 0.26% (3.3× improvement) - $\delta_{\text{CKM}}$ error from 1.10% to 0.018% (60× improvement) 3. Complete group‑theoretic mapping – The automorphism group $O_h$ of the 2‑bit vacuum forces the gauge group $SU(3)\times SU(2)\times U(1)$ and the assignment of the 26 parameters to the 8 vertices, 12 edges, and 6 faces of the Keplerian body $K_\Omega$. 4. All 26 parameters are fully solved – errors <1%, most <0.3%. Detailed tables for gauge couplings, Yukawas, PMNS angles, neutrino masses, and CKM parameters are provided with honest errors. 5. Verification code (Python) – runs all checks to machine precision, including spectral weight truncation, two‑loop factors, and group‑theoretic decompositions. Critical clarifications - The Higgs self‑coupling is assigned to the bulk volume mode of $K_\Omega$ (zero mode of the spectral action), not to a vertex.- The DII threshold $0.6 = 3/5$ remains a phenomenological scale (empirical). - The Ramanujan $\pi/6$ wormhole remains a conjecture.- Explicit RG beta functions for the 26 parameters are not computed here but follow from Law III (Omandac Balance Equation); this is a natural extension, not a structural gap. Companion documents Walnut Report v37 (Laws 0–V, OBE) Boundary Calculus v15.0 (Law VI, complex action, sheet transitions) HOUT Research Status Honest Final Closure – All fundamental parameters <1%, no ad‑hoc fitting factors, 0 partially solved gaps, 1 conjecture (Ramanujan gateway). Author & License - Author: Clarence Omandac (Independent Researcher, Queensland, Australia) - ORCID: 0009‑0001‑8994‑3739 - License: CC BY‑NC‑ND 4.0 - Version Date: 2026‑06‑09