hcsn-theory
The HCSN Research Group
Welcome. This is the central research hub for the Holographic Computational Spin-Network (HCSN).
We are developing a unified framework that derives quantum mechanics and general relativity from first principles, utilizing discrete computational processes on quantum hypergraphs.
đź“š Core Research
The HCSN Framework (Documentation)
The complete theoretical foundation, including derivations of Einstein’s equations, QFT emergence, and predictions for Lorentz violation.
- Status: Active / Documentation Live
- Key Prediction: Lorentz-violation parameter $\xi \approx 0.097$.
Read the Full Documentation →
đź’» Simulation & Results: Cosmological Expansion Phase
We conducted a large-scale computational evolution of the HCSN hypergraph to test the “Emergent Big Bang” hypothesis. The simulation tracks the growth of a minimal quantum seed into a complex network structure.
Run ID: SIM-2025-ALPHA
Duration: 3000 Computational Steps
Initial State: $V_0 = 6$ (Minimal Seed)
Dynamics: Iterative Rewriting (Wolfram-style updates)
1. Growth Dynamics
The system exhibited a robust expansion phase. Unlike fixed-topology models, this run allowed for vertex creation, simulating the expansion of spacetime volume.
| Metric | Initial ($t=100$) | Final ($t=3000$) | Growth Factor |
|---|---|---|---|
| Volume (Vertices) | 6 | 1,557 | 259x |
| Avg Degree ($\langle k \rangle$) | 2.50 | 9.27 | Stabilized |
| Metric Dimension ($L$) | 4 | 19 | Expanded |
| Acceptance Rate | 4.0% | 51.8% | Phase Transition |
Analysis: The stabilization of the average degree $\langle k \rangle \approx 9.2$ is a critical result. It suggests that while the “universe” (Volume) is expanding rapidly, the local density remains constant, consistent with a homogeneous spacetime manifold.
2. Visual Data Analysis
(Below are the visualization outputs from the simulation run)
Figure 1: Network Topology Growth
Visualizing the hypergraph structure at $t=1500$. Note the emergence of clusters (high-connectivity regions) representing “matter” density.
Fig 1. Hypergraph snapshot showing emergent clusters.
Figure 2: Tracks of 3000 Steps
Fig 2. Evolution of Time. Note the stabilization after $t=1000$.
Figure 3: Dimensionality Stabilization
The plot below tracks the average degree $\langle k \rangle$ over time. The plateau indicates the emergence of stable physical laws.
Figure 4: Phase Transition
The system underwent a transition at $t \approx 400$, marking the onset of the “inflationary” epoch.
3. Key Observations
- Phase Transition: At $t \approx 400$, the system underwent a transition from low acceptance (4%) to high acceptance (>50%), marking the onset of the “inflationary” epoch.
- Dimensional Emergence: The graph diameter ($L$) grew linearly with time, while volume ($V$) grew polynomially, consistent with a finite-dimensional emergent space.
- Order Parameter ($\Omega$): The order parameter $\Omega$ rose to $\approx 0.71$, indicating strong causal coherence in the final state.
Upcoming: Python Simulation Data
We are currently running Python simulations to model hypergraph evolution and verify the emergence of spacetime intervals.
- Expected Output: Visualizations of graph connectivity and causal growth.
- Status: Processing…
Contact & Code
- GitHub Repository: HCSN-Theory
- Lead Researcher: The HCSN Research Group (ORCID)
đź“ť Citation
Please cite this project as: HCSN-Theory, @hcsn. (2025). The Holographic Computational Spin-Network (HCSN): Theory & Simulation (Version 1.0.0) [Computer software]. https://github.com/hcsn-theory/HCSN-Theory