CAA-X V2.1: Cognitive Physicalism

Abstract

V2.1 is a significant revision of V2 (Cognitive Physicalism), incorporating theoretical refinements, expanded mathematical formalization, and critical responses to feedback received since the original release. It preserves the core thesis of V2 — the rigorous isomorphism between cognitive dynamics and physical field theories — while strengthening the mathematical foundations and clarifying the philosophical position. What Is New in V2.1 1. Expanded Field-Theoretic Formalization- Complete Lagrangian formulation of the predictive tension field Φ(x,t), with explicit derivation of the Euler-Lagrange equations governing cognitive state evolution.- New section on Noether's theorem in cognitive space: proof that conservation laws (energy, momentum analogues) emerge from symmetries of the cognitive Lagrangian.- Extension to non-Abelian gauge fields: modeling intention-interference effects through Yang-Mills-type cognitive field equations. 2. Refined Cognitive Curvature Tensor- Correction of the Riemann tensor definition in V2: the original formulation conflated the Levi-Civita connection with a generic affine connection. V2.1 introduces the cognitive Levi-Civita connection derived from the cognitive metric tensor g_ij = ∂²F/∂x_i∂x_j (Hessian of free energy).- New theorem: Cognitive Singularity Theorem — high-intention regions (λ → 1) induce curvature singularities analogous to black hole horizons, where standard cognitive dynamics breaks down and quantum-cognitive effects become relevant. 3. Thermodynamic Phase Transitions- Expanded analysis of cognitive phases: focused attention (solid), diffuse association (liquid), sleep/dreaming (gas), and critical transitions (phase boundaries).- Introduction of cognitive critical exponents and universality class analysis — showing that attentional phase transitions belong to the Ising universality class under mean-field approximation.- Landau-Ginzburg theory of cognitive symmetry breaking: the λ-order-parameter as an order parameter with explicit free energy expansion. 4. Quantum Cognition Extension- V2's speculative quantum extension is significantly expanded with: - Explicit Hilbert space construction for superposed cognitive states. - Decoherence model based on environmental cognitive noise (inter-agent interference). - Cognitive Bell inequalities: testable bounds on classical vs. quantum cognitive correlations. - Connection to quantum Bayesianism (QBism) as an interpretive framework. 5. Philosophical Clarifications- Explicit response to the "panpsychism" critique: CAA-X-CP is non-reductive physicalism, not panpsychism. Cognitive fields are physical in the same sense that electromagnetic fields are physical — they are organizational patterns of matter/energy, not mystical substances.- New section on the measurement problem in cognitive physics: what constitutes a "cognitive measurement" (decision/commitment event), and how the von Neumann chain terminates in the agent-environment boundary. 6. Mathematical Corrections- V2 Eq. 14 (cognitive geodesic equation): corrected sign error in the Christoffel symbol term.- V2 Eq. 23 (free energy landscape): clarified that the landscape is defined on the cognitive cotangent bundle TM, not the tangent bundle TM.- Added appendix with full tensor index notation and conventions to prevent future ambiguity. Relationship to V2V2.1 supersedes V2 for all citation and reference purposes. The original V2 remains available for historical continuity, but V2.1 contains the corrected and expanded content. Researchers should cite V2.1 when referencing the cognitive physicalism framework. Core Thesis (Preserved from V2)CAA-X-CP establishes a rigorous isomorphism between the CAA-X predictive tension field and classical physical field theories. Cognitive atoms behave as quasi-particles in an information field; intention fields generate curvature in cognitive manifolds analogous to mass-energy in spacetime; the λ-order-parameter functions as a thermodynamic potential governing phase transitions in cognitive state space. Citation & ContextPart of the CAA-X versioned research program. See V0–V2 foundational collection (DOI: 10.5281/zenodo.21835958) for the original trilogy, V3 intention manifesto (DOI: 10.5281/zenodo.21836502), and V4 world models (DOI: 10.5281/zenodo.21836896).