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.18904809
- WACA Mathematics: DOI 10.5281/zenodo.18919654