Entanglement–Variational Geometry: A Closed Response Architecture for Geometry, Gravity, Tail Phases, Chirality, Dynamics, and Visibility

This paper presents Version 2 of Entanglement–Variational Geometry (EVG), reformulated as a closed response architecture based on an admissible ordered second-order response form. Its canonical decomposition separates a symmetric readable sector from an antisymmetric oriented response sector, with ordinary Hessian geometry recovered exactly when the antisymmetric sector vanishes. The symmetric sector defines the readable quotient Hilbert geometry and supports the geometric, gravitational, symmetric-tail, dark-sector, and visibility phases. The antisymmetric sector, when representable, gives a skew-adjoint response operator whose scalar diagonal vanishes; its scalar content appears only through compatible projected quadratic response. This structure organizes reversible kernels, chiral profiles, baryon-asymmetry readouts, parity-odd dynamical channels, and Born-type visibility readout. The central aim of the paper is to record geometry, gravity, cosmological tail phases, dark-sector profiles, chirality, gravitational-wave response, and measurement as mutually compatible phase presentations inside one closed EVG architecture, rather than as a one-directional causal chain.