A Computational Physics Framework for Stochastic Projective Gravity & Topological Phase Verification.
willowLab is a specialized research engine designed to ingest raw quantum simulation data (Floquet systems, Kitaev chains) and rigorously validate them against high-order theoretical theorems.
It serves as the bridge between raw eigen-data and "Nobel-ready" falsification, automating the detection of:
- Spectral-Entanglement Duality (Theorem B.1)
- Exceptional Points & Residue Landscapes (Theorem B.2)
- Cosmic Ratchet & Dark Energy Thresholds (SPG / CR-5)
- Nested Wilson Loops & Higher-Form Topology (Theorem B.3)
Whether you are analyzing a local .npz scan or a massive HDF5 cluster, willowLab normalizes the geometry into a unified schema for immediate topological cartography.
The core of the lab. It computes Step-1 invariants instantly upon data ingestion:
-
Cancellation-Safe Resolvents: Accurate traces even near
$| \lambda | \approx 1$ . -
$\eta$ -Lock Detection: Identifies protected topological windows via mod-2 Chern parity. - Duality Checks: Correlates spectral temperature with entanglement thermodynamics.
Turn abstract matrices into navigable maps.
-
Black Hole Potentials: Visualizes gravitational potential
$\Phi(\lambda)$ derived from residue superposition. - Saddle Detection: Automatically flags mountain pass geometries in the phase space.
-
Wind Fields: Computes phase winding
$\nabla \arg \text{Tr}(I-U)^{-1}$ to isolate topological charges.
A production-grade falsification runner that tests your data against physical reality:
-
CR-5 Protocol: Checks for FRW-Radar acceleration thresholds (
$AP' < -1/3$ ). -
Pantheon+ Compliance: Ensures operational curvature
$|\Omega_{op}| < 0.02$ . - 32-Cell Classification: Categorizes Floquet unitary operators into robust bit-packed geometric cells.
The pipeline is designed for robustness—from "Zip to Truth."
willowLab/
├── configs/ # YAML orchestration for validation runs
├── demos/ # Visualization scripts (Cartography, Potentials)
├── willowlab/
│ ├── ingest/ # "Zip-to-Willow" normalization pipeline
│ ├── geometry.py # Non-Abelian Wilson loops & Residue Atlas
│ ├── spg.py # Stochastic Projective Gravity (CR-5/CR-4)
│ ├── trinity.py # Step-1 Invariant computer
│ ├── cartography.py # Scalar fields & Pole detection
│ └── tests/ # Nobel Validation Suites (T_Nobel)
└── README.md
🚀 Quick Start
Installation
Clone the repository and install the Conda environment (Python 3.11 recommended).
git clone [https://github.com/Tnsr-Q/willowLab.git](https://github.com/Tnsr-Q/willowLab.git)
cd willowLab
conda env create -f environment.yml
conda activate willowlab
Running a Nobel Validation
To run the full suite of theorems against a dataset:
# Run the CLI with the "nobel_validation" command
python -m willowlab.cli nobel_validation "reports/my_submission_report.json"
Generating Cartography Maps
Visualize the "Black Hole Potential" and residue landscape of your system:
from willowlab.cartography import poles_and_residues_on_grid, black_hole_potential
import numpy as np
import matplotlib.pyplot as plt
# 1. Load your Unitary Grid
Ugrid = np.load("data/floquet_scan.npz")["Ugrid"]
# 2. Extract Residues (Poles)
atlas = poles_and_residues_on_grid(Ugrid)
# 3. Compute Gravitational Potential
Phi = black_hole_potential(atlas["residue_score"])
# 4. Visualize
plt.imshow(Phi, origin="lower", cmap="magma")
plt.title("Gravitational Potential $\Phi(\lambda)$")
plt.show()
🧬 The Science
Stochastic Projective Gravity (SPG)
willowLab implements the CR-5 criteria, mapping the velocity of the order parameter \xi to the FRW equation of state:
$$ AP' = \tanh\left( \frac{\kappa \cdot \dot{\xi}}{\gamma} \right) $$
A valid geometry must exhibit a "Dark Energy" crossing (AP' < -1/3) at the topological transition point JT^* \approx 1.0.
Higher-Form Topology (T^{14})
For advanced protection, the t14.py module computes invariants over nested 7-torus loops:
$$ c_{14} = \frac{1}{(2\pi)^7} \text{Tr} \left( \bigotimes_{i=1}^7 W_i \right) $$
🤝 Contributing
We welcome contributions to the Residue Atlas and Ingest Sniffers.
* Fork the repo.
* Create your feature branch (git checkout -b feature/AmazingPhysics).
* Commit your changes.
* Open a Pull Request.
📄 License
Distributed under the MIT License. See LICENSE for more information.
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<sub>Built by Tnsr-Q for the advancement of Geometric AI and Quantum Simulation.</sub>
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