Exploring the WACA Universe: An LLM System Prompt for Independent Reasoning About the Algebraic Crystal

The WACA (Weak-strong Algebraic Crystal Analysis) programme derives 24 physical constants from the finite-dimensional algebra A_F = C ⊕ M₂(C) ⊕ M₃(C) with zero free parameters, using the spectral action principle of noncommutative geometry (Chamseddine–Connes–Marcolli 2007).

This paper provides a structured LLM system prompt encoding all published WACA results — including the 24 numerical predictions, the 63-universe enumeration, the Beurling–Nyman capture sequence (95.6% for the {2,3} lattice), the polycrystal convergence, and the crystal geometry — in a form suitable for independent reasoning by any large language model.

Users may paste the prompt into any LLM (Claude, GPT-4, Gemini, etc.) to explore the framework, test logical consistency, compare with other approaches, and generate new research questions.

The prompt contains published results and standard NCG derivation methods only. The WACA search engine (the proprietary computational exploration process and query pipeline) is not included.

Key results: Higgs mass 125.34 GeV (measured 125.09 ± 0.24), α⁻¹ = 137.034 (measured 137.036), Ω_DM/Ω_b = 5.386 (measured 5.36), proton stability, 63 universes tested with {2,3} uniquely optimal, Beurling–Nyman convergence to 100% equivalent to the Riemann Hypothesis.

Related publications:
- WACA Physics: DOI 10.5281/zenodo.19057123
- WACA Mathematics: DOI 10.5281/zenodo.18919654

Example prompts more examples in the attached txt file:

--- Quantum Tunneling ---
User: How does the crystal explain quantum tunneling?
User: Derive the Geiger-Nuttall law from the eigenvalue lambda=1/3.
User: Why is proton decay unobserved? What does lambda=1/6 predict?
User: How does enzyme catalysis use quantum tunneling?
User: Explain how DNA mutations arise from proton tunneling.
User: Compare tunneling rates in the weak, strong, and mixed sectors.
User: What is the holographic shortcut for tunneling through a barrier?

--- Entanglement ---
User: How does the MERA explain "spooky action at a distance"?
User: Derive the Bell inequality violation from chi=6.
User: Explain the Ryu-Takayanagi formula in the MERA.
User: How does bird navigation use quantum entanglement?
User: What is the [36,12,4] error-correcting code?
User: Why do 24 mixed modes get destroyed during measurement?
User: How does entanglement create spacetime (Van Raamsdonk/ER=EPR)?

--- Wave-Particle Duality ---
User: Why does the MERA explain wave-particle duality?
User: How is the MERA a discrete wavelet transform?
User: Derive the uncertainty principle from chi=6.
User: Explain the double slit experiment using the ascending superoperator.
User: What are the four frequency bands of the vacuum?
User: How does measurement destroy coherence in the MERA picture?