QGUST — Quantum Gravity Research Prospectus Toolkit

Numerical tests of five predictions motivated by a research prospectus synthesizing causal set theory, spin networks, tensor networks, von Neumann algebras, and entanglement renormalization.

Overview

The prospectus in quantum-gravity-synthesis.md proposes a minimal 5-axiom system (causal order, CCR algebra, distinguished SJ state, observer-dependence via crossed product, holographic entropy) that links the algebraic and combinatorial pillars of quantum gravity. Its central mathematical conjecture — the Unitary Equivalence Conjecture — relates the SJ vacuum GNS representation to spin network representations via the exponentiated LQG area operator.

The QGUST toolkit tests five concrete predictions from the constituent frameworks. Two distinctive claims (the UEC and the horizon-molecule bridge) have no direct numerical test in the current toolkit; what is tested are properties the synthesis inherits from its components.

Predictions — Current Status

#	Test	Status	What It Discriminates	Key Finding
1	Discrete entropy jumps	✓ Verified	SU(2) recoupling (not synthesis-specific)	$S(k)$ shows 2–6 discrete steps per $(j,v)$ combination; step heights $O(1)$ from SU(2) recoupling
2	SJ Vacuum Entropy Scaling	⚠️ Scale-limited	CST discretization (not synthesis-specific)	Volume-law ($S \approx 0.272,n_R$) dominates at $N \le 800$; $c=1$ scaling requires $N \gg 10^4$
3	GUE level statistics	✗ Falsified	Free-field modular spectrum	Spectrum is Poisson (KS=0.032); free SJ vacuum is integrable
4	$T_{\text{cutoff}} \sim M^{-2/3}$	✓ Derived; ⚠️ Numerics blocked	Horizon molecule Boltzmann counting (component of synthesis)	Derivation complete; 2D model cannot verify 4D exponent
5	SU(2) fidelity bound $F \le 1-d_{\min}^{-2}$	✓ Verified	SU(2) CG identities (not synthesis-specific)	CG bugs fixed; all orthogonality checks pass

The conclusion's dependency table tracks the status of every claim with its gauge-group and discretization dependencies, and marks whether each test probes the synthesis's connections or only its components.

Repository Structure

qgust/
├── qgust/                          # Python package
│   ├── core/                       # Core numerical infrastructure
│   │   ├── causal_set.py           # Causal set sprinkling, causal matrix, SJ spectrum
│   │   └── modular.py              # Symplectic eigenvalues, entropy, modular ratio, tripartite info
│   ├── pred1_entropy_jumps/run.py  # Discrete entropy jumps via SU(2) recoupling
│   ├── pred2_central_charge/run.py # SJ vacuum entropy scaling
│   ├── pred3_gue_statistics/run.py # Modular β spectrum level statistics
│   ├── pred4_horizon_molecules/    # Schwarzschild causal set + entropy scaling
│   │   ├── run.py
│   │   └── derivation.md           # T_cutoff derivation
│   ├── pred5_su2_nogo/run.py       # SU(2) CG coefficients, intertwiners, fidelity bound
│   └── cli.py                      # CLI entry point
├── tests/test_modular.py           # 6/6 tests passing
├── quantum-gravity-synthesis.md    # Full prospectus document (v1.0)
├── pyproject.toml
└── README.md

Requirements

• Python 3.13+
• NumPy 2.5+

No SciPy dependency. CG coefficients for $j>5$ may overflow Python's integer factorial.

Quick Start

python -m qgust.cli --help
python tests/test_modular.py        # Run test suite

Licensing

• Code (the qgust/ package, tests, and all .py files): MIT License — see LICENSE.
• Document (quantum-gravity-synthesis.md): Creative Commons Attribution 4.0 International (CC-BY-4.0).

Citation

If you use this work, cite the prospectus document:

The QGUST Authors (2026). Quantum Gravity from Information-Theoretic Principles: A Research Prospectus. https://github.com/cloudenum/qgust