TOE — Theory of Everything (RubikConeConduit v10.8)

Flux Flywheels, Gauged Hopf Lattice, and Emergent Reality

A self-consistent Hopf-lattice model in which the periodic table emerges as stable flux-flywheel configurations in a porous vacuum sponge, with observer synchronization explaining current null results while leaving distinctive non-local predictions testable.

Quick Start (One-Click Reproduction)

1. Clone Repository:

git clone https://github.com/kinaar8340/toe.git
cd toe

2. Create Environment:

python -m venv venv
source venv/bin/activate

3. Install Dependencies:

pip install -r requirements.txt

4. Run the Simulation:

# Single-Node (default 30 trials)
python scripts/epoch_bake_sweep.py
python scripts/run_reproduction.py

# Or Run the Module as a Script
python -m scripts.epoch_bake_sweep
python -m scripts.run_reproduction

# Single-Node (custom)
python scripts/epoch_bake_sweep.py --trials 1000 --dense
python scripts/run_reproduction.py --trials 1000 --dense

# Multi-Node (custom)
python scripts/epoch_bake_sweep.py --use-ray --trials 1000 --dense
python scripts/run_reproduction.py --use-ray --trials 1000 --dense

5. Generate Plots:

python scripts/plot_sweep_results.py

6. Tests:

python -m pytest tests/ -q --cov=conduit

7. Python API Example:

from config import load_config
from conduit import RubikConeConduit

cfg = load_config("configs/default.yaml")
model = RubikConeConduit(
    embed_dim=cfg.model.embed_dim,
    twist_rate=cfg.model.twist_rate,
       # ... other params
    )
loss = model.training_step(inputs, optimizer)
recall = model.recall()
print(f"Final recall: {recall:.4f}")

Full File Structure

toe/
├── src/
│   └── conduit.py
├── scripts/
│   ├── run_reproduction.py
│   ├── epoch_bake_sweep.py
│   ├── pde_relaxation.py
│   ├── z_flywheel_map.py
│   └── two_gyro_lattice_demo.py
├── facts/
│   └── public_facts.json
├── outputs/
│   ├── epoch_bake/
│   │   └── epoch_sweep.csv
│   ├── pde_relaxation/
│   │   └── twist_pde_relaxation.png
│   ├── reproduction/
│   │   ├── reproduction_results.csv
│   │   └── stability_islands.png
│   ├── two_gyro_lattice/
│   │   └── two_gyro_full_split_demo_FINAL.mp4
│   └── plots/
│       ├── top10_stability_table.png
│       ├── braiding_phase_histogram.png
│       ├── param_vs_stability_scatter.png
│       └── stability_islands_heatmap.png
├── papers/
│   ├── Aaron's_TOE_Complete.pdf
│   ├── GW_Burste_Threshold.pdf
│   ├── GW_Echo.pdf
│   ├── GW_Echo_Derivation.pdf
│   ├── Lagrangian_Derivation.pdf
│   ├── Observer_Synchronization.pdf
│   └── Relativistic_Completion.pdf
├── pyproject.toml
├── requirements.txt
├── README.md
├── CITATION.cff
└── CONTRIBUTING.md

Latest Reproduction Results (April 17, 2026)

   Conduit created successfully
   Using device: cpu
   Loaded RubikConeConduit v10.8
   Trial 10000 complete | braiding_phase=0.81404

============================================================
 REPRODUCTION RESULTS
============================================================
W_g lock          : 111.4080 ± 0.0000  → LOCKED
Braiding phase    : 0.8140 ± 0.0008  (expected ~0.8141)
Mean active_cubes : 12.01  (stability islands observed)
============================================================

 All outputs saved to: outputs/reproduction/
   • reproduction_results_*.csv
   • stability_islands_*.png

 Reproduction complete! The invariants lock as expected.

Related: Mystery φ-e-π Residual Probes

The companion mystery repo quantifies the near-Pythagorean residual R = φ² + e² − π² ≈ +0.137486 and its dynamical analogs (golden-angle packing ≈ 0.1375; exponential survival e⁻² ≈ 0.1353 at λt = 2).

Dual-role κ (see mystery RESULTS.md):

Symbol	Value	Role
κ_doc	0.85	Documentation / theory (θ_crit, B(κ), Hopf framing)
κ_sim	≈ 0.89	Simulation / production (meta-opt, survival @ λt=2)
κ*	≈ 0.8513	Exact null e/π − R/π²

Production meta-opt uses κ_sim; documented formulas retain κ_doc.

TOE integration:

File	Purpose
src/relaxation_survival.py	λt normalization utilities; PDE + gauged-twist survival probes
src/conduit.py → RubikConeConduit.run_survival_probe()	Conduit invariants at normalized λt = 2
scripts/pde_relaxation.py --normalize-to-lambda-t 2	PDE survival benchmark
scripts/epoch_bake_sweep.py --topology-grid	Topology κ bake grid; braid_feedback_gain default 0.002
scripts/magic_island_sweep.py --topology-grid	Magic-island braid-gain × topology grid

Run from mystery: python scripts/exponential_survival_probe.py (imports toe modules).

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Citation

@misc{kinder2026aarontoe,
  author       = {Kinder, Aaron},
  title        = {Aaron’s Theory of Everything: Flux Flywheels, Gauged Hopf Lattice, and Emergent Reality},
  year         = {2026},
  howpublished = {\url{https://github.com/kinaar8340/toe}},
  note         = {arXiv preprint (pending)}
}

License

MIT License — see LICENSE.

Contacts

Name:   Aaron Kinder
X:      @kinaar8340
Emails: kinaar0@protonmail.com
Date:   April 2026

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Thank you for helping verify the locked invariants!

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