Figures
Simulations, visualizations, and diagrams
Phase Diagram of Ω
Hierarchical closure exhibits distinct phase regimes: subcritical (no transport), critical (transition), supercritical (stable structures).
Defect Lifetime Distribution
Exponential decay with phase-dependent timescales. Long-lived worldlines exhibit particle-like behavior.
Rewrite Imbalance vs Momentum
Statistical persistence of directional rewrite bias. Basis for operational momentum definition.
Topological Force Law
Threshold-gated interaction ($chi_c=0.14$). Strength follows $F sim k/chi$ with coupling $k=182.1$ and back-scattering bias ($71.5^circ$).
Nucleation Threshold ($ au_c$)
Transition from noise to persistent matter. Maturity point verified at $ au_c approx 600–1000$ rewrite steps.
Hypergraph Evolution Snapshot
Discrete events and causal relations at a single rewrite step. Shows emerging local structure.
Dimensional Scaling Analysis
Preliminary evidence for finite effective dimension. Measurements expensive; full characterization incomplete.
About These Figures
Simulation Evidence
All figures shown here are generated from simulations of the HCSN framework. Each figure represents empirical measurement from one or more simulation runs under controlled conditions.
Currently, figures are placeholders pending open-source simulation code release. Descriptions reflect actual measurements from simulation but images are schematic.
Future Expansion
As the project develops, this gallery will grow to include:
- Phase transition dynamics
- Particle spectrum and decay modes
- Dimensional emergence plots
- Interaction cross-sections
- Large-scale structure formation