The Emergent Spacetime Quantum-Entanglement Theory (ESQET): E8 Root Systems, Octonionic Invariants, and Exact Discrete Geometries — Corrected Edition

Corrected edition (2026-11-02) of the ESQET architecture whitepaper, superseding the uncorrected draft of the same title circulated the same day. ESQET is a developing research framework, not established or independently validated physics; every claim carries a status tag — [EXACT] (proved in exact integer/rational/algebraic arithmetic, re-run on two machines), [MODEL] (output of an explicitly labelled toy model), or [HYPOTHESIS] (the author's field hypothesis with falsifiable predictions). The paper sets out the exact chain from the Cayley–Dickson octonions through the Hurwitz units and binary tetrahedral group (element-order census {1:1, 2:1, 3:8, 4:6, 6:8}) to the F4 root system (reflection closure 2304/2304, Cartan determinant 1, Weyl group order 1152, Coxeter data Φ12 with exponents [1,5,7,11]) and the D4⊕D4 pair-sum projection of the 240 E8 roots (census 24/192/24 over 49 distinct points, projected support identified as the F4 root system, spherical 7-design with an exact degree-8 failure witness of 18, exact graph spectra kept operator-separated). The IBM ibm_marrakesh hardware run is reported with full statistics including its deviation (χ² = 497241/8192, Aer control consistent), attributed to the device. Corrections in this edition: the 3.3096 spectral value restored to the 48-node F4 root graph it belongs to; the E8-to-4D route stated as the verified D4⊕D4 pair-sum projection (the H4 identification is retracted); permineralization figures tagged [MODEL] throughout; a Wulff anisotropy ratio withdrawn as a grid artifact; and a new §8 collects every quantitative prediction with its empirical status — including the dark-sector point at f = 1, which is already EXCLUDED by observation and is kept in the record as such, the λ₀ chain stated as conditional on the framework's postulates, and the field predictions P1–P5 with the P3 ceiling at 5.7279327045218342947825977741260981723533945274567 µm. Related record: the E8 shell-circuit audit underlying §4 is deposited separately (DOI 10.5281/zenodo.23911368).