Experiment A3: XY XYZ Quantum Graph Simulation - FatherTimeSDKP/CEN- GitHub Wiki

🧪 Experiment A3: XY/XYZ Quantum Graph Simulation

Objective:
To model and visualize quantum node behavior across 2D (XY) and 3D (XYZ) graph spaces using SD&N topology rules and QCC compression gradients. This experiment investigates how entangled graph nodes evolve, mutate, and compress under causal flow.

📌 Theoretical Background

🔷 SD&N (Shape–Dimension–Number) Integration:

  • Shape (S): Node or edge form (e.g. knot type, loop state, polygonality)
  • Dimension (D): Planar (2D) vs. volumetric (3D) structure context
  • Number (N): Quantized count of nodes/edges; entangled node pairs have N=±1

🔶 QCC (Quantum Causal Compression) Overlay:

QCC is applied to reduce the dimensional entropy of a system by:

  • Compressing nodes with causal redundancy
  • Mapping macro-patterns onto micro structures
  • Minimizing the "causal curvature" across graphs

🧭 Simulation Parameters

Parameter Description
L Grid length (X or Y dimension)
Z Depth level for 3D mapping
k_shape Shape mutation constant
γ_causal Causal compression coefficient (QCC)
Θ Knot topology encoding (SD&N basis)
σ_entropy Entropic bias per node

🕸️ 2D XY Quantum Graph

  • Nodes are laid out in a Cartesian XY grid
  • Edges represent quantum interaction paths
  • Each node stores a local SD&N vector
  • Compression rule:
    [ ΔN_i = -γ_causal \cdot \nabla C(N_i) ] Where ( \nabla C(N_i) ) is the local causal flow gradient

Visualization:

O─O─O │ │ │ O─O─O │ │ │ O─O─O Each O holds a shape index Θ and entanglement value ε.

🧩 3D XYZ Quantum Graph

  • Nodes extend into the Z-dimension
  • Additional edge complexity and knot-type bifurcation possible
  • Higher-order shape interactions simulated (e.g., tetrahedral fusion)

Compression + Mutation Equation:

[ Θ' = Θ + k_{shape} \cdot f(σ, N, D) ] [ N' = N - γ_{causal} \cdot ΔK ]

Where ΔK is a topological difference from the previous iteration.

🔄 Dynamic Evolution Model

Simulation runs in discrete time steps ( t ) with updates:

  • Recalculate causal gradient
  • Apply QCC compression
  • Apply SD&N mutations
  • Output lattice snapshots at each step

🧪 Outcomes Expected

  • Identify patterns of node collapse under high QCC pressure
  • Observe shape bifurcation events (torus ↔ trefoil ↔ unknot)
  • Explore possible stable lattices (quantum memory encoding)
  • Apply results to QCC–KC kernel predictions (see: A2)

🔗 Related Frameworks

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