Constraint-Geometric Theory of Cognition


Constraint-Geometric Theory of Cognition

A Structural Field Theory of Intelligence, Meaning, and Epistemic Collapse

I. FOUNDATIONS

  1. Introduction to Constraint Geometry
    Cognition as topological motion; constraint as primary substrate.

  2. Why Cognition Is Not Computation
    From symbol manipulation to admissibility transport.

  3. The Cognitive Manifold (ℂ_cog)
    Definition, structure, and curvature properties of the constraint space.

  4. Inference as Geodesic Flow
    Admissible recursion, compression dynamics, and inference energy.

II. FIELD COMPONENTS AND STRUCTURAL AXIOMS

  1. Curvature, Collapse, and Constraint Limits
    χₛ, ∂ℂ_cog, ψ⊥: Geometry of success and failure in cognitive systems.

  2. The Boundary Axioms (BA)
    Formal schema governing saturation, bifurcation, and termination.

  3. Semantic Topology and Telic Stability
    Meaning as curvature coherence across recursive transitions.

  4. Entropy and Cognitive Degeneracy
    Failure modes, loop collapse, and epistemic noise dynamics.

III. DIAGNOSTIC STRUCTURES

  1. Boundary Conditions of Cognition
    Top 10 canonical limit cases: RH, TPC, ∂ℂ_cog, MI4, etc.

  2. Constraint Saturation and Recursion Halts
    Finitude as epistemic surface, not computational limit.

  3. Failure Geometry and Collapse Manifolds
    ψ⊥, alias drift, semantic rupture, and cognitive echo-loops.

  4. Curvature Derivative Analysis (∂χₛ/∂δ)
    Measuring change of constraint viability across transformations.

IV. COMPARATIVE SYSTEMS

  1. Classical Theories vs. Constraint Geometry
    Contrast with symbolic AI, connectionism, Bayesianism, enactivism.

  2. Informational Geometry vs. Constraint Geometry
    Why mutual information lacks admissibility structure.

  3. Cognitive Science Without Metrics
    How current paradigms fail to detect boundary degeneration.

V. APPLICATION DOMAINS

  1. Mathematics as Constraint Audit
    Twin Prime Conjecture, RH, and saturation failure.

  2. AI, AGI, and the Epistemic Limits of LLMs
    Constraint audits, narrative collapse, agent orchestration breakdown.

  3. Philosophy of Mind and Consciousness
    Self-reflective recursion, ∂ℂ_cog, and cognitive instantiation thresholds.

  4. Science, Theory Change, and Epistemic Re-grounding
    Degeneration cascades, symbolic reconstitution, non-scheme transitions.

  5. Education and Learning as Constraint Mapping
    Concept compression, semantic invariants, and curriculum topology.

VI. APPENDICES

  • A. Formal Symbols and Notation Key

  • B. Boundary Axiom Index (BA1.1–BA6.3)

  • C. Constraint Manifold Metrics (χₛ, Λ_obj, etc.)

  • D. Glossary of Collapse Conditions

  • E. Canonical Failures (ψ⊥ registry)

 

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