🌀 HCSN — Hierarchical Causal Structure Network (Legacy Implementation)

Caution

🏛️ Legacy / Reference Implementation

This Python-based engine is now LEGACY. Due to Python execution bottlenecks in high-density causal graphs (Phase 10+), core development has migrated to the high-performance hcsn-rust engine.

Note: Features are only backported to this repository if specifically required for cross-validation. For active research and the latest Phase 12 results, please use the Rust Core.

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HCSN explores the hypothesis that the universe is fundamentally computational — built from discrete events and directed causal relations, with no assumed background space, time, or quantum framework.

📺 Watch the overview on YouTube → 📄 Read the paper on ResearchHub →

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✨ Highlights

• 🔁 Local rewrite rules drive the evolution of a causal hypergraph
• 📐 Geometry, time, and dimensionality emerge — they are not assumed
• 🧲 Particles appear as persistent topological defects in the network
• 🔬 Reproducible experiments test emergence of Lorentz invariance, mass, and interaction
• 🎥 Built-in visualizer and Blender importer for 3D cinematic rendering

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📋 Table of Contents

• Overview
• Repository Structure
• Quick Start
• How to Run Experiments
• Diagnostics Explained
• Visualization
• Current Research Focus
• Contributing
• Citation
• License & Contact

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Overview

HCSN proposes a discrete, causal, and computational substrate for physics:

• Events are vertices in a hypergraph; causal relations are directed hyperedges
• Dynamics are local probabilistic rewrite rules — no global clock, no background metric
• Time is the count of irreversible rewrites (rewrite depth)
• Geometry, dimension, and particles emerge from what statistically persists

The long-term goal is to identify the minimal rule set that produces universes consistent with:

• Lorentz invariance (emergent attractor)
• 4D spacetime-like structure
• Holographic scaling of information
• Quantum probabilistic behavior (Born rule from causal ignorance)

The companion theory repository is at hcsn-theory.

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Repository Structure

hcsn-sim/
├── engine/                     # Core simulation engine
│   ├── hypergraph.py           # Vertices, hyperedges, causal ordering
│   ├── rules.py                # Rewrite rules
│   ├── rewrite_engine.py       # Acceptance dynamics and rewrite scheduling
│   ├── observables.py          # Physical diagnostic measurements
│   └── physics_params.py       # Shared physics parameters
│
├── sim-exp/                    # Reproducible experiments
│   ├── run_simulation.py       # Main simulation runner
│   ├── exp_critical_scan.py    # Phase transition scan
│   ├── exp_phase_diagram.py    # Omega phase diagram
│   ├── exp_long_critical_run.py
│   ├── exp_worldline_interactions.py
│   ├── scattering_experiment.py
│   ├── measure/                # Measurement scripts
│   ├── plot/                   # Plotting scripts
│   ├── tests/                  # Test suite
│   └── json/                   # Experiment output data
│
├── multiverse/                 # Multi-variant universe runs (universality tests)
│   ├── baseline/
│   ├── variant_1/ … variant_4/
│
├── analysis/                   # Legacy analysis scripts
├── visualizer.html             # Interactive browser-based visualizer
├── visualizer_server.py        # Local server for the visualizer
├── blender_importer.py         # Import cinematic frames into Blender
├── export_cinematic.py         # Export simulation to cinematic frame format
├── export_csv.py               # Export simulation data to CSV
├── cinematic_frames.json       # Pre-exported cinematic data
├── hcsn_sample.csv             # Sample simulation output
├── simulation.log              # Latest simulation log
└── requirements.txt            # Python dependencies

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Quick Start

Requirements

• Python 3.10 or later
• Dependencies: pytest, websockets, asyncio

pip install -r requirements.txt

Clone and run:

git clone https://github.com/hcsn-theory/hcsn-sim.git
cd hcsn-sim
python3 sim-exp/run_simulation.py

This runs a toy universe and prints diagnostics periodically.

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How to Run Experiments

The sim-exp/ directory contains all reproducible experiments:

Script	Purpose
run_simulation.py	Main simulation runner
exp_critical_scan.py	Scan Ω values to locate phase transition
exp_phase_diagram.py	Map defect rate across Ω regimes
exp_long_critical_run.py	Extended run at critical Ω
exp_worldline_interactions.py	Two-particle interaction experiment
scattering_experiment.py	Scattering geometry test

Key printed diagnostics (periodic):

• average coordination ⟨k⟩
• causal depth (L)
• interaction concentration (Φ)
• closure density (Ψ)
• hierarchical stability (Ω)

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Diagnostics Explained

Symbol	Name	Meaning	Target Range
⟨k⟩	Avg coordination	Controls effective dimensionality	≈ 7.5–8.5 for spacetime-like geometry
L	Causal depth	Maximum causal chain length — emergent time	Grows with rewrites
Φ	Interaction concentration	Hub dominance (lower = more uniform)	Small Φ preferred
Ψ	Closure density	Redundancy in causal closure	Non-zero = error correction
Ω	Hierarchical closure	RG-like stability across scales	> 1.0 for persistent structure

Phase interpretation:

Ω Regime	Behavior
Ω < 1.0 (subcritical)	Transient defects, no stable transport
Ω ≈ 1.08–1.18 (critical)	Phase transition, marginal stability
Ω > 1.2 (supercritical)	Persistent worldlines, stable emergent structure

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Visualization

HCSN includes a browser-based visualizer and a Blender pipeline for cinematic rendering:

Browser Visualizer:

python3 visualizer_server.py
# Open visualizer.html in your browser

Blender 3D Import:

1. Run export_cinematic.py to generate cinematic_frames.json
2. Import into Blender with blender_importer.py

CSV Export:

python3 export_csv.py

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Current Research Focus

Active directions:

• Prevent metric collapse under coarse-graining
• Implement logarithmic information metrics (holographic scaling tests)
• Enforce holographic bounds dynamically during evolution
• Search for Lorentz-invariant fixed points of the rewrite dynamics
• Derive quantum probabilistic behavior (Born rule) from causal ignorance

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Contributing

We welcome contributions from physicists, mathematicians, and programmers.

Getting started:

1. Fork the repo, create a feature branch
2. Add reproducible experiments under sim-exp/
3. Document new rules, diagnostics, and observed behaviors
4. Open a PR with clear description, expected behavior, and reproducibility notes

Guidelines:

• Seed all RNGs for reproducibility
• New rules or observables belong in engine/
• Keep experiments modular and self-contained

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Citation

If you use HCSN in your research, please cite both the paper and the software:

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

BibTeX:

@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}
}

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License & Contact

Published under the Apache 2.0 licence.

For collaboration or questions, open an issue or contact via GitHub: hcsn-theory

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🏛️ Governance

The HCSN Research Group is maintained by @hcsn.

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

HCSN treats this as a testable hypothesis: build minimal computational rules and examine what emerges.

Enjoy exploring! 🧩