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Research-Stack/0-Core-Formalism
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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
..
core initial: sovereign research stack (consolidated, weightless, and lfs-optimized) 2026-05-04 18:11:36 -05:00
lean formalize: 4-primitive framework for Erdős–Rényi random graphs in Lean 2026-05-08 14:50:02 -05:00
otom collapse: prover orchestration layers, FAMM verilator harness, swarm topological prober, spec sheets, virtual FPGA system tests, merge conflict resolution 2026-05-06 23:42:01 -05:00
rust/ftdi_gimbal initial: sovereign research stack (consolidated, weightless, and lfs-optimized) 2026-05-04 18:11:36 -05:00
README.md initial: sovereign research stack (consolidated, weightless, and lfs-optimized) 2026-05-04 18:11:36 -05:00

README.md

0-Core-Formalism

Purpose: Formal foundations for the entire Research Stack — Lean modules, bind primitive, Triumvirate consensus, core source.

No external dependencies. All other layers depend on this.

Contents (Target)

Source Destination
0-Core-Formalism/lean/Semantics/ 0-Core-Formalism/lean/Semantics/
core/ 0-Core-Formalism/core/

Concepts

  • bind — State → (State → Action) → State
  • TriumvirateClock — ternary consensus (ADD/PAUSE/SUBTRACT)
  • Builder/Judge/Warden — roles mapped to hardware registers
  • OTOM — Ordered Transformation & Orchestration Model

Build

cd "0-Core-Formalism"
lake build