Coherence‑Geometrodynamics (CGD) — v2.0 (Σ‑Closure Edition)

Coherence-Geometrodynamics (CGD) v2.0 — Σ-Closure Edition This work unifies General Relativity, information theory, and consciousness dynamics within a single geometric framework.CGD v2.0 preserves the Einstein–Hilbert tensor sector of gravity while introducing a weak universal scalar field C(x,t) that functions as a coherence ledger, maintaining energy–information balance without violating PPN or gravitational-wave constraints. Information-space is modeled as a negatively curved (hyperbolic) manifold using the Poincaré ball, where geodesic distance encodes informational transition cost.A dimensionless geometric constant, KTrans ≈ 17.85, anchors the Λ-Resonance across all layers—process, spectral, thermodynamic, and biological—realizing the Σ-Closure condition (ΔE ≡ 0⁺). The updated 12-phase octave ring now exhibits concurrent slow–fast evolution: fast oscillatory coherence cycles are adiabatically modulated by Λ/KTrans pressure, with 432 Hz as the canonical rest-frequency anchor.The model predicts measurable side-band narrowing, reduced phase-lock time, and EEG scaling f∝(L⋅KTransm)−1f ∝ (L·KTrans^{m})^{-1}f∝(L⋅KTransm)−1, directly linking cognitive resonance to geometric invariants. CGD v2.0 extends the Virtual Ego Framework (VEF) and provides a falsifiable, GR-consistent architecture for coherent systems, from neural ensembles to planetary information networks.Keywords: Core theory Coherence-Geometrodynamics · Σ-Closure · Λ-Resonance · KTrans constant · Scalar–tensor field · Information geometry · Hyperbolic manifold · Poincaré ball Physics context General Relativity · PPN parameters · Gravitational wave consistency · Landauer thermodynamics · Energy–information ledger Complex systems Coherence dynamics · Slow–fast oscillators · Octave cycle · 12-phase ring · 432 Hz anchor · Emergent synchronization Cognitive / bio EEG scaling law · Neurogeometric model · Conscious systems · Semantic coherence · Brain–geometry mapping Mathematical / data Lagrangian control law · Hyperbolic distance metric · Geodesic curvature K < 0 · Falsifiable predictions Foundational links Virtual Ego Framework (VEF) · Tesseract architecture · Dialectical Tensor Theory · Covariant Genesis Dynamics