kathedraki EDEN-II: Structural Derivation of Standard Model Parameters from the Planck Scale via Exceptional Lie Algebras — Corpus Checkpoint V125

Corpus checkpoint of the kathedraki EDEN-II research programme at version V125 (17 June 2026), establishing the state of the work prior to editorial review of the integral session transcripts. kathedraki EDEN-II aims to derive Standard Model parameters from a single dimensional input — the Planck energy E_P — via a cascade of exceptional Lie algebras E8 ⊃ F4 ⊃ G2 acting on the FCC lattice geometry embedded in the imaginary octonions Im(O) = R^7. The framework produces closed-form expressions for all 12 fermion masses, the electroweak scale, the Higgs coupling, the Weinberg angle, and the atmospheric mixing angle sin²(θ23) = 4/7, with zero free parameters and mean relative error 0.29% on fermion masses. This document records signed results, open gates, falsifiable predictions with experimental deadlines (DUNE 2027, Euclid/CMB-S4, HL-LHC/FCC-ee), and the categorical structure underlying the derivations. It also includes an empirical observation on editorial styles in LLM-assisted research. This work is derived from and built upon The EDEN Method (DOI: 10.5281/zenodo.20523324). The full session record is under editorial review and will be published separately.