A Universal Information-Geometric Operator for Particle Couplings and Cosmological Structure

This paper revises the RTLI partition operator G[\lambda_i,\lambda_j;n] as a diagnostic tool on the conserved binary partition manifold a+b=1, interpreted through the three-face framework: Fisher, Poincaré, and compound. The operator is reframed as a face-weighted integral of coupling capacity between two states, where the Thales altitude h=\sqrt{ab} provides the coherence amplitude, the spectral suppression factor weights proximity to the self-dual resonance, and the empirical band factor projects the result onto one of the three metric faces. In this revision, the operator is no longer presented as a zero-free-parameter derivation of Standard Model constants, but as a structured geometric diagnostic whose functional form is fixed by partition geometry while its numerical outputs depend on measured inputs from galactic dynamics and cosmology. The paper explicitly introduces epistemic tiering to separate exact algebraic content, empirical inputs, and broader interpretive claims. The note also connects the operator to the broader partition program developed in subsequent work, including the three-face metric dictionary, the Gudermannian bridge, and the Pythagorean mean identity \mathrm{QM}^2+\mathrm{GM}^2=1/2. Within this reframed setting, the paper reports several structural coincidences between operator outputs and known physical parameters, including approximate values for the fine-structure constant, weak mixing angle, Higgs quartic coupling, and selected CKM and PMNS hierarchy elements. These matches are presented as suggestive structural observations rather than proofs of geometric determination. The paper’s main contribution is therefore not a derivation of Standard Model constants, but a careful reinterpretation of the partition operator as the quantitative completion of the three-face dictionary: a tool that integrates coupling capacity across the manifold and projects it into sector-dependent numerical outputs. The paper concludes with falsifiable predictions for neutrino masses, leptonic CP phase, and cosmological evolution, while clearly stating the framework’s present limitations.