Brandon Schneider 8b9359394f formalize: 4-primitive framework for Erdős–Rényi random graphs in Lean ... Formalized the 4-primitive framework applied to Erdős–Rényi random graphs G(n,p) in Lean. Lean file: 0-Core-Formalism/lean/Semantics/ExtensionScaffold/Math/FourPrimitiveErdosRenyi.lean Formalization includes: - Field primitive (ρ(x⃗)): edge density field - Shear primitive (G = AᵀA): Laplacian deformation metric - Packet primitive (Γᵢ): adjacency matrix encoding - Spectral primitive (C = UΛUᵀ): eigenbasis decomposition Definitions: - FieldPrimitive: edge density - ShearPrimitive: Gram matrix AᵀA - PacketPrimitive: adjacency matrix - SpectralPrimitive: eigen decomposition - spectralRadius, spectralGap, algebraicConnectivity - Laplacian matrix - connectivityThreshold, giantComponentThreshold - detectPhaseTransition Theorems (schematic): - FourPrimitiveFramework_Validation - SpectralPrimitive_PhaseTransition - FieldPrimitive_Density - ShearPrimitive_Deformation - PacketPrimitive_Encoding Canonical statement included: The compactified core reduces the stack to four mutually orthogonal primitives: field state, shear metric, packet witness, and spectral basis.		2026-05-08 14:50:02 -05:00
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FourPrimitiveErdosRenyi.lean	formalize: 4-primitive framework for Erdős–Rényi random graphs in Lean	2026-05-08 14:50:02 -05:00