This release introduces an entanglement module for the Two-Energy Theory (TDE) as a theoretical proposal consistent with the octahedral lattice geometry used in earlier TDE spectroscopy releases. Summary of Key Results: We assume (P1) a shared address in the shadow field ψc for an entangled pair, and (P2) single-shot measurements as linear projections. Under these postulates, the correlation function is explicitly bilinear: E (a, b) = aᵀ M b Imposing full octahedral invariance (Oh) on the spin-sector and applying Schur’s lemma yields M ∝ I. With singlet anticorrelation normalization E (a, a) = −1, this uniquely fixes: M = −I ⇒ E (a, b) = −a·b = −cos (θ) Therefore, the standard quantum Tsirelson bound emerges automatically: |SCHSH| = 2√2 Furthermore, via the double group Oh*, the module reproduces the canonical GHZ/Mermin deterministic contradictions and multipartite violations (4 vs 2 for tri-partite states). Context & Internal Consistency: The same octahedral lattice postulate underlies the TDE mass-sector releases (e. g. , predicting 527 hadronic states with ≈0. 077% mean relative error reported in v16. 9), while this module addresses the correlation structure rather than masses. Optional Falsifiable Extension (Sidereal Time): If Oh is interpreted as a physical discrete micro-geometry, a small cubic-harmonic correction may induce a sidereal modulation of CHSH statistics: E (a, b) = −a·b + ε H4 (a, b) This provides a direct experimental route to bound ε by monitoring correlations over a 24-hour sidereal cycle. Replication Package: The ZIP includes LaTeX sources, generated figures, and Python scripts reproducing: Oh constraint SVD (nullspace dim = 1) M = −I and |S| = 2√2 verification GHZ/Mermin values (deterministic violation) Example leakage scan (sidereal time dependence)
Michał Karol Surowiecki (Mon,) studied this question.