Roadmap
Progress to date and future directions
Foundation & Simulation
Axioms, rewrite rules, initial simulation validation.
Phase Transitions & Corrections
Discovery of Ω phase structure. Corrected earlier Ω-carrier claims.
Particle Interactions & Dynamics
Formalized threshold-gated interaction ($chi_c=0.14$), topological force law ($k=182.1$), and back-scattering bias ($71.5^circ$).
Dimensional Selection & Scaling
Large-scale structure, dimension stabilization, continuum limits.
Emergent Structures
Gauge symmetry, conservation laws, possible connections to external frameworks.
Completed Milestones
Phases 1–10: Foundation
- ✓ Discrete event axioms
- ✓ Causal consistency preservation
- ✓ Rewrite rule implementation
- ✓ Ω order parameter definition
- ✓ Initial defect observation
Phase 11: Phase Transitions
- ✓ Ω phase diagram discovery
- ✓ Critical transition at Ω ≈ 1.1
- ✓ Corrected Ω-carrier misconception
- ✓ ξ transport capacity mapping
Phases 12–16: Particles & Dynamics
- ✓ Worldline definition & persistence
- ✓ Particle criteria (empirical & maturity threshold)
- ✓ Momentum & mass operationalization
- ✓ Topological Force Law ($k=182.1, \chi_c=0.14$)
- ✓ Back-scattering bias ($71.5^\circ$)
Documentation Consolidation
- ✓ 5 canonical documents created
- ✓ 20+ earlier drafts archived
- ✓ Concepts deduplicated
- ✓ Claims graded by empirical status
Current Focus (Phase 17+)
Dimensional Selection & Large-Scale Scaling
The primary focus is understanding how:
- Dimension emerges: Preliminary evidence suggests finite effective dimension (≈3–5), but the mechanism remains unexplained.
- Scaling limits: Can continuous effective field theories be derived from discrete rewrites?
- Universality: Are results robust across different rule sets?
- Long-time behavior: Beyond 10⁵ rewrites, computational cost rises sharply. Asymptotic analysis needed.
Future Directions
Structural Classification
Are there discrete classes of defects? Can we identify conserved properties that classify worldlines into families?
Symmetry Emergence
Can rewrite redundancy classes yield nontrivial symmetry-group structures? Is gauge invariance emergent?
Continuum Limits
Can effective field theories be derived rigorously from coarse-grained Ω dynamics? What are the emergent Lagrangians?
Cosmology & Initial Conditions
How do we specify initial conditions on the hypergraph? What does "early universe" mean in a discrete causal framework?
Quantum Behavior
The theory is already probabilistic. Does this naturally give rise to quantum statistics without postulating Born rule?
External Correspondence
If large-scale limits emerge, do they resemble known physics? This remains deeply speculative.
Contribute
HCSN Theory is exploratory research. We welcome:
- Feedback on theory and interpretation
- Simulation implementations in other languages
- Dimension measurement and scaling analysis
- Connections to other research areas