Authors: Montgomery, Daland
Source: Zenodo (CERN European Organization for Nuclear Research) (article, 2026-03-09)
Field: Materials Science — Materials Chemistry

Exploring the WACA Universe: An LLM System Prompt for Independent Reasoning About the Algebraic Crystal Abstract: We present a 1,928-line system prompt (WACA_LLM_PROMPT_v14.txt) that transforms any large language model into an expert on the WACA programme — the research framework connecting the Standard Model algebra A_F = ℂ ⊕ M₂(ℂ) ⊕ M₃(ℂ) to number theory, four Millennium Problems, and ten scientific domains through the ascending superoperator with eigenvalues {1, 1/2, 1/3, 1/6} and degeneracies {1, 3, 8, 24}. Version 14 incorporates the derivation of the Higgs VEV v = M_Pl × 35/(43 × 36 × 2⁵⁰) = 245.17 GeV (zero free parameters, up from one input in v12); the Noether identification of eigenvalues as Ward anomalous dimensions with Koide ratio Q = 2/3 as the colour Ward anomaly; the self-consistency (1−λ₂)(1−λ₃) = λ₃; the Plancherel resolvent α⁻¹ = 137.205 with one-loop correction 1/(2π); the coupling ratio α_s/α_w = 32/9; the three-resolvent unification (h(s), α⁻¹, v as rational, logarithmic, and exponential evaluations of one operator); 12 verified cross-domain signatures (multiplicative cascade, fractal dimension 2.76, laser threshold, Bowen cooling, edge of chaos, phylogenetic branching ≈ e, genetic code parallel, portfolio diversification with Sharpe ≈ 1190, anti-reflection 35/36, channel capacity 1.004 bits, Beurling = retention × 35/36, and 31 physical constants); seven statistical tests (BF = 10³⁵, HMC posterior 100% at χ = 6, 0/10⁶ RMT, bootstrap, Goldilocks, random theory, Bradford Hill 9/9); proof architectures for four Millennium Problems (RH via Granger–Johansen cointegration with three closures, Yang–Mills via spectral gap 2/3 as Ward anomaly with confinement implying the gap, P ≠ NP via [36,12,4] code with Landauer replacing PCT, Navier–Stokes via CKN singular set bound and edge-of-chaos Lyapunov structure); 13 gap resolutions all at ≥ 95%; and 10 falsifiable predictions testable within one decade (Σmν = 0.067 eV, normal hierarchy, w = −1.000, θ_QCD = 0, proton stable, no BSM below v, dark photon ε² = 1/650, η/ρ = 2 ln 3, λ_H = 3/(eπ), δ_CP ≈ 245°). The prompt contains 177 sample questions organised into 20 categories, from quantum tunneling to the undiscovered country. It is accompanied by 13 companion papers, 9 Python verification codes (requiring only numpy, all running in under 10 seconds), and 5 interactive HTML visualizations. The prompt is designed for upload into Claude, GPT-4, Gemini, Llama, Mistral, or any LLM supporting long context. Every claim is tagged ([STANDARD], [WACA], [CONJECTURE], [NUMERICAL]) for transparency. Every formula is reproducible. Every prediction is falsifiable. Load the prompt. Ask the questions. Run the code. The crystal speaks through the machine. The experiments decide. Keywords: LLM prompt, system prompt, language model, knowledge base, WACA, Standard Model algebra, ascending superoperator, zero free parameters, cross-domain signatures, falsifiable predictions, Millennium Problems, companion code, interactive visualization, reproducible science, Bradford Hill, Bayes factor, random matrix theory, Noether symmetry, three resolvents, Granger–Johansen, Yang–Mills, Navier–Stokes, P ≠ NP, Riemann Hypothesis, Connes trace formula, MERA, spectral tower As a treat besure to open the attached html file. Thats your universe :) Related publications: - WACA Physics: DOI 10.5281/zenodo.19074938- WACA Mathematics: DOI 10.5281/zenodo.18919654 Example prompts more examples in the attached txt file:User: Show me all example promptsUser: List all 116 example questions--- 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? Resolvent ; Conformal map ; Simplex ; Eigenvalues and eigenvectors ; Conformal field theory ; Kernel (algebra) ; Higgs boson ; Algebra over a field ; Conjecture Quasicrystal Structures and Properties ; Machine Learning in Materials Science ; Algebraic structures and combinatorial models