Experiment A5: Quantum Shape Mutation in SD&N - FatherTimeSDKP/CEN- GitHub Wiki

🧪 Experiment A5: Quantum Shape Mutation in SD&N

Objective:
To simulate and analyze how discrete quantum shape mutations (as encoded in the SD&N model) impact mass and energy behavior in particle systems, and how these topological shifts might influence entanglement, coherence, and stability.

🧬 Background: SD&N Topological Encoding

The SD&N model encodes particles using:

  • S (Shape): A topological invariant (e.g. trefoil knot = 3, figure-eight = 4)
  • D (Dimension): Spatial embedding dimension (3D default; 4D for QCC-extended)
  • N (Number): Quantum count or class identifier

These are mapped into the SDKP mass engine: [ M = \gamma \cdot (N \cdot S) + \beta \cdot S + \alpha \cdot N ]

In this experiment, we focus on mutations in S — small topological transitions that mimic changes in knot class or torsion.

🔄 Shape Mutation Model

Base Encoding Table

Shape Code S-value
Unknot (circle) U 1
Trefoil Knot T 3
Figure-eight F8 4
Cinquefoil Knot C5 5
Double loop D 6

Mutation Transition Graph

[ U \leftrightarrow T \leftrightarrow F8 \leftrightarrow C5 \leftrightarrow D ]

Each transition corresponds to a shape energy delta, ΔS, affecting mass as:

[ \Delta M = \gamma \cdot N \cdot \Delta S + \beta \cdot \Delta S ]

📊 Simulation Steps

  1. Choose a fixed N value (e.g., electron class = 1)
  2. Assign base S shape (e.g., T = 3)
  3. Simulate one-step mutation to next topology (e.g., F8 = 4)
  4. Compute:
    • ΔS = 1
    • (\Delta M = \gamma \cdot N \cdot \Delta S + \beta \cdot \Delta S)
  5. Repeat for full mutation cycle
  6. Plot mass vs. S evolution over mutation series

💡 Purpose

  • Observe mass inflation or suppression across topological mutation
  • Detect nonlinearities where mutation introduces dimensional instabilities
  • Compare results with known phenomena (e.g., neutrino oscillation, muon decay)

🔬 Future Expansion

  • Introduce D-variation: crossing from 3D to 4D embedding
  • Apply mutations inside QCC causal field — simulate decoherence
  • Develop entropy model:
    [ \mathcal{S}_{\text{topo}} \sim \log(\text{Knot Complexity}) ]

🔗 Related Frameworks