Ξ–Twin Star EOS Analysis: Structural Correlations Without Causal Coupling

This record contains the main manuscript and methods supplement for the study: “Ξ–Twin Star EOS Analysis: Structural Correlations Without Causal Coupling” We report a robust structural ordering of neutron-star compactness in the narrow high-mass window 2.00–2.08 M⊙, obtained from a uniform Tolman–Oppenheimer–Volkoff (TOV) pipeline applied to microphysical equations of state (EOS). The central observable is:Q_env = ln[ISE_core50(M_high) / ISE_core50(M_low)], where ISE_core50 is a volume-weighted stress-energy norm over the inner stellar core. Across all tested EOS satisfying observational constraints (M_max ≳ 2.08 M⊙), the ordering Q_env > 0 is preserved on the same connected stable branch. This result is shown to be:- Mechanism-independent within the admissible EOS class- Stable under continuous CSS-parametric deformations (1350+ scenarios)- Only breakable under pathological EOS constructions not realized in CompOSE-grade tables The work explicitly separates:(1) Structural predictions (robust, EOS-independent within domain)(2) Effective parameters (e.g., Γ_damp = 255)(3) Open problems (notably the undeclared energy scale E_ref in the GCFT framework) The accompanying methods supplement provides:- Full TOV pipeline implementation details- CompOSE integration protocol- A1–A4 physical argument for Q_env > 0- Falsifier hierarchy (F0–F3) and hostile EOS scans- Explicit blocking conditions for first-principles derivation of Γ_damp This result constitutes a structural constraint on admissible neutron-star equations of state: any viable microscopic completion must reproduce the observed ordering while satisfying maximum-mass and branch-continuity conditions. No claim is made of a derived underlying field-theoretic mechanism; the GCFT framework is presented strictly as an interpretation layer consistent with the structural result.