"The universe may not be described by computation — it may be computation."

HCSN is a framework for emergent physics built from the ground up — starting with nothing but discrete events and directed causal relations, and asking what universe falls out.

📄 Read the Paper → 📺 Watch the Overview → 🔬 Explore the Simulation Repo (Rust) → 🔬 Legacy Simulation Repo →

HCSN (Hierarchical Causal Structure Networks) is a theoretical framework that proposes the universe is fundamentally a causal computation — not a differential manifold, not a Hilbert space, not a lattice.

Starting assumptions (the complete list):

• Discrete events (vertices)
• Directed causal relations (hyperedges)
• Local probabilistic rewrite rules
• No background spacetime, metric, or symmetry

What emerges from these assumptions:

This is not a reinterpretation of existing physics.
It is a theory of why theories work.

1. No circular reasoning
We do not assume the structures we are trying to explain. No manifolds, no wavefunctions, no predefined symmetries.

2. Empirical grounding
Every claim beyond the axioms requires an operational definition, a measurement protocol, and reproducible simulation evidence.

3. Falsifiability
The theory fails if no universal signal speed emerges, no persistent structures form, or universality is absent across rule variations.

4. One definition per concept
Each term (defect, worldline, particle, momentum, mass, interaction) is defined exactly once in the canonical documents.

hcsn-theory/
│
├── docs/                                              # 📚 Canonical theory (read sequentially)
│   ├── 01_axioms_and_methodology.md                  # Minimal axioms + methodology (4.6 KB)
│   ├── 02_defects_worldlines_and_particles.md        # Emergent objects + identity (6.9 KB)
│   ├── 03_emergent_dynamics_momentum_and_interaction.md  # Motion, mass, interaction (8.0 KB)
│   ├── 04_geometry_dimension_uncertainty_and_limits.md   # Geometry + open problems (9.1 KB)
│   ├── 05_emergence_of_particles.md                      # Mechanics of matter condensation [NEW]
│   └── archive/                                       # 17 superseded / historical drafts
│
├── website/                                           # 🌐 Next.js 14 research website
│   ├── app/                                           # 6 pages (home, about, docs, figures, roadmap, contact)
│   ├── components/                                    # 5 reusable React components
│   ├── config/site.ts                                 # All site content — update here
│   └── types/                                         # TypeScript interfaces
│
├── figures/                                           # 📊 Simulation visualizations
├── MANIFESTO.md                                       # Project motivation & philosophy
├── WORKSPACE_STATUS.md                                # Full project status
└── README.md

⚠️ This repository contains no simulation code.
All numerical experiments are conducted in the high-performance hcsn-rust engine, which replaced the legacy hcsn-sim prototype in Phase 10.

The entire HCSN theory is documented in exactly five files, designed to be read in order:

Defines the five core axioms:

• Axiom 0: Discrete relational substrate (hypergraph)
• Axiom 1: Causal consistency (irreflexivity + transitivity → DAG)
• Axiom 2: Local rewrite dynamics (bounded, finite, causal)
• Axiom 3: Local finiteness (finite past/future → emergent signal speed)
• Axiom 4: Hierarchical closure tension (the regulatory principle)
• Axiom 5: Defect permissibility (localized closure violations allowed)

Sets methodological discipline: observation → definition → derived result → conjecture.

Defines the first emergent objects:

• Defect: A localized event where Ω changes discontinuously (|ΔΩ| > ε)
• Worldline: An equivalence class of persistent defect events (identity via overlap continuity)
• Proto-object: A persistent ξ-cluster with measurable identity
• Particle: A proto-object satisfying all four operationally-defined criteria (persistence, momentum coherence, inertial stability, structural coupling)
• Mass: Emergent defect inertia — m ~ 1/Var(p)

Defines how objects move and interact without space:

• Momentum: Statistical persistence of rewrite imbalance
• Interaction: Rewrite competition for the Ω-modulated rewrite pool
• Interaction strength: F_AB = |Φ_A − Φ_B| / τ_coexist
• Interaction graph distance: Rewrite overlap, not spatial proximity
• Conservation: Statistical only — emerges from closure tension, not symmetry axioms

Documents the large-scale structure and known boundaries:

• Phase diagram of Ω regimes (subcritical / critical / supercritical)
• Effective dimension: D_eff(r) = d log N(r) / d log r
• Lifetime–momentum variance relation: Var(p) ∝ τ⁻¹
• Geometry reconstruction attempts (causal distance, interaction-graph distance, spatial slices)
• Explicit open problems and falsification criteria

Formalizes the transition from stochastic noise to persistent structure:

• The Three Pillars: Suppression, Coherence-Gated Growth, and Boundary Tension
• Nucleation Threshold: The maturity point $\tau_c \approx 600 - 1000$ steps
• Scale-Free Scaling: Power-law lifetimes (critical range $\alpha \approx 1.7 - 2.0$)
• Kinematics: Interaction phenomenology (Threshold-gated interaction $\chi > 0.14$, deflection $71.5^\circ$)

1. What mechanism selects effective dimension asymptotically?
2. Can rewrite redundancy classes produce nontrivial symmetry-group structure?
3. Are there discrete defect species with a classification?
4. Can exclusion-like statistics emerge from worldline topology?
5. Can exact invariance principles emerge in a continuum limit?
6. Can Ω dynamics reproduce effective field balance laws under coarse-graining?

A companion research website is included in website/, built with:

• Next.js 14 (App Router, TypeScript, SSG)
• Tailwind CSS 3.3 (responsive, mobile-first)
• 6 pages: Home, About, Docs, Figures, Roadmap, Contact
• Centralized content: All text lives in website/config/site.ts

Run locally:

cd website
npm install
npm run dev
# Visit http://localhost:3000

If you use HCSN in your research, please cite:

Saif Mukhtar. HCSN: A Hierarchical Causal Structure Network Framework for Emergent Physics. ResearchHub, 2026.
DOI: 10.55277/researchhub.fvahxvpt.1

@article{mukhtar2026hcsn,
  author = {Saif Mukhtar},
  title  = {HCSN: A Hierarchical Causal Structure Network Framework for Emergent Physics},
  year   = {2026},
  doi    = {10.55277/researchhub.fvahxvpt.1},
  url    = {https://doi.org/10.55277/researchhub.fvahxvpt.1}
}

This is a theory in formation, not a finished model.

It documents what has been observed in simulation, what has been derived from axioms, and what remains open or speculative. Claims are graded by empirical support. Speculation is explicitly labeled.

See MANIFESTO.md for the full motivation.

This project is licensed under the MIT License.

For collaboration or questions: github.com/hcsn-theory