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Solving P vs NP

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 P vs NP Class Inclusion Question (P vs NP) Universal Quantifier Over Algorithms Need for Representation-Stable Structure Introduction of Intrinsic Cost Functional Reinterpretation of Time as Path Length Emergence of State Space Geometry Directional Asymmetry (Verification vs Solving) From Isotropic Cost to Anisotropic Metric Adoption of Finsler Structure Definition of Action as Computational Distance Introduction of Global Obstruction (Torsion) Vacuum State as Trivial Configuration Collapse as Energy Minimization Mass Gap as Intrinsic Hardness Phase Boundary Formulation (Polynomial vs Superpolynomial Action) Full Rigid Geometric Engine (RGE) Ontology The path from P vs NP to RGE is not an expansion of the problem. It is the progressive introduction of exactly the structural primitives required to transform: A universal algorithmic exclusion statement into An intrinsic geometric boundary condition. Every step removes ambiguity and adds rigidity. Nothing beyond these primitives is s...
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From Geometry to Spacetime

  From Geometry to Spacetime (Constraint–Transport Foundations of Emergent Lorentzian Structure) PART I — PRE-GEOMETRY 1. Distinction Before Structure Binary separation as primitive Identity vs admissibility Boundary without space Constraint as first invariant 2. Relation Without Embedding Graphs, orders, compositional systems Adjacency without metric Depth vs distance Transport without coordinates 3. Constraint Closure Admissibility predicates Stability under recursion Collapse as spectral contraction Persistence as invariant intersection 4. Transport as Primitive Compositional update rules Bounded accessibility Finite propagation without metric Hyperbolicity as structural condition PART II — TOPOLOGY EMERGES 5. Stable Neighborhoods from Transport Equivalence classes under admissibility Persistent local structure Emergent separation axioms When topology is induced 6. Cost Functionals and Ordering Relaxation cost Minimal admissible paths Path composition Depth → ordering → geometry...
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Semantic Cloud Architectures

Semantic Cloud Architectures Geometry, Constraint, and the Distributed Emergence of Meaning Part I — The Problem of Meaning Without Symbols 1. The Collapse of the Symbolic Model Why units don’t encode meaning Mixed selectivity and distributed failure of localization The end of modular cognition From representation to geometry 2. What Is a Semantic Cloud? High-dimensional distributed state Meaning as position and trajectory Projection as readout Attractors and regime stability Necessary and sufficient conditions for SCA 3. Constraint as the Organizing Principle Recoverability over optimization Reuse of degrees of freedom Interference minimization Why geometry scales and symbols do not Part II — The Evolution of Semantic Cloud Architectures 4. Pre-Neural Clouds: Chemical and Metabolic Control Gradient sensing in bacteria Osmotic regulation Homeostasis as geometric stabilization 3-billion-year lineage of non-representational control 5. Gastric and Enteric Systems ENS as autonomous cloud M...
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