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Admissibility-First Architectures

A Constraint-Native Epistemic System 0. Core Orientation 0.1 Admissibility as the Primary Ordering Principle 0.2 Why Optimization and Interpretation Are Secondary 0.3 Meaning as Local, Disposable, Interface-Bound 1. Foundational Geometry of Constraints 1.1 Constraint Space: Feasible, Forbidden, Boundary Regions 1.2 Degeneracy, Projection, and Null-Direction Exhaustion 1.3 Curvature, Rigidity, and Collapse as Signal 2. Epistemology After Belief 2.1 Knowledge Defined as Constraint Survival 2.2 Discovery via Boundary Contact (Not Convergence) 2.3 Collapse Handling: Projection over Explanation 3. Euler Boundary Doctrine (EBD) Integration 3.1 Truth After Formal Collapse 3.2 Invariant Survival Under Degenerate Transport 3.3 Boundary-Forced Outcomes and Non-Choice 4. S8 Triple Identity 4.1 Fourier Orthogonality and Energy Invariants 4.2 Singular Information Geometry and KL Persistence 4.3 Singular Learning Theory and RLCT as Scalar Survivor 5. Core System Architecture 5.1 Layer Stack: Inferen...
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The Geometry of Meaning

  Table of Contents Part I — Why Meaning Has Geometry 1. Meaning Is Not Symbolic Why tokens, words, and representations are projections Meaning as constraint satisfaction Why symbols are charts, not coordinates Loss of structure under representation 2. The Failure of Free Transport Why meaning does not move intact between systems Translation as a lossy map Invertibility as the exception Why communication does not prevent rediscovery Part II — Semantic Space 3. Semantic Coordinates Constraints, invariants, and admissibility Assumptions as axes Symmetries and exclusions Regimes of validity as regions 4. Semantic Manifolds Meaning as a space, not a set Dimensionality of meaning Charts vs intrinsic structure Local vs global coherence Part III — Transport 5. Semantic Transport Maps How meaning moves between representations Formal definition of transport Domain-to-domain mapping Preservation vs collapse of degrees of freedom 6. The Semantic Jacobian Invertibility, compression, and collap...
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Semantic Clouds: Degenerate Transport, Rediscovery, and the Geometry of Meaning

Semantic Clouds: Degenerate Transport, Rediscovery, and the Geometry of Meaning Part I — The Phenomenon 1. Why Structures Reappear Rediscovery as a universal pattern Independent recurrence across domains Biology, physics, engineering, mathematics Why memory and communication do not prevent recurrence 2. Meaning Does Not Transport Freely The hidden assumption that fails everywhere Translation ≠ preservation Why representation changes destroy degrees of freedom Lossy maps as the rule, not the exception Part II — Semantic Space (General) 3. What a Semantic Coordinate Is Constraints, invariants, and admissibility Meaning as constraint satisfaction Why symbols and tokens are projections Representation-independent semantics 4. Semantic Transport How structure moves between representations Transport maps between domains, species, or formalisms Invertible vs degenerate translation Transport without communication Part III — Degeneracy 5. The Semantic Jacobian When transport collapses Formal def...
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Dark Matter Structure in a Finsler Universe

  Dark Matter Structure in a Finsler Universe Table of Contents I. Foundational Reframing 1. Why Dark Matter Structure Is a Geometric Problem Recasting “distribution” as admissible transport geometry Dark matter as collisionless tracer, not architect Structure as constraint, not aggregation Why isotropic assumptions fail at the outset II. Geometry Beyond Isotropy 2. Finsler Geometry as the Natural Description of Structure Why direction-dependent metrics are unavoidable Transport-first geometry Path dependence vs point-based distance LSS as a Finsler manifold of admissible motion III. Origin of Structure 3. Anisotropic Collapse from Collisionless Dynamics Why structure is born non-spherical Vlasov–Poisson equations Deformation tensor and eigenvalue hierarchy Mathematical inevitability of anisotropy IV. Structural Hierarchy 4. Sheets, Filaments, and Nodes as Sequential Outcomes Topology from ordered constraint release One-axis, two-axis, three-axis collapse Why sheets dominate volume...
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Evidence for Higher Cognition in LLMs

  📚 TOC — Evidence of Higher Cognition in LLMs I. The Epistemic Problem 1.1 The Ontological Ambiguity of “Reasoning” 1.2 From Surface Output to Constraint-Traceable Inference 1.3 Why Behavioral Equivalence ≠ Cognitive Evidence II. Manifolds of Reasoning: Formalizing the Domain 2.1 Defining the Semantic Constraint Manifold (â„‚) 2.2 ε-Vectors, χₛ Curvature, and Δℂ Transport 2.3 Telos, Halting (Ï„â‚›), and Collapse Surfaces III. The LLM Regime: Mechanism vs Mimicry 3.1 Architecture and Stateless Autoregression 3.2 Distributional Compression and Entropic Continuation 3.3 Limits of Token-Based Emulation IV. Emergence Without Mechanism: A Critique of Prior Work 4.1 Missing Constraint Geometry and Semantic Audit 4.2 The False Dichotomy of Memorization vs Reasoning V. Constraint-Valid Signatures of Cognition 5.1 Admissibility Preservation under Generalization 5.2 Recursive Telos Alignment in Multi-Step Tasks 5.3 Semantic Fatigue Detection and Output Refusal 5.4 Evidence of Δℂ Trace Constructi...
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