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

Authors: Montgomery, Daland;

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

Abstract

Abstract: We document the WACA LLM Prompt, a structured knowledge base encoding the entire WACA programme in a format optimised for large language models. When loaded as a system prompt or project knowledge file, the prompt enables any LLM (Claude, GPT-4, Gemini) to reproduce all 28 confirmed results, explain derivations, compute predictions, and answer questions about the framework. The prompt uses plain text with structured sections, tagged claims ([STANDARD], [WACA], [CONJECTURE], [NUMERICAL]), and 116+ worked example prompts across 14 topic areas. Version 12 matches the Spectral Table v7 and Calculator v7. Version 12 resolves the Jarlskog invariant of CP violation: J = sin(2π/χ)(1 − 1/χ²)/(χ³·p₁·p₂²·β₀) = (√3/2)(35/36)/(216 × 2 × 9 × 7) = 3.094 × 10⁻⁵, matching CKMfitter 3.08 × 10⁻⁵ (0.4%). The missing factor 126 = 2 × 9 × 7 = p₁·p₂²·β₀ was identified through the 650-dimensional channel structure. The neutrino mass tension (~10%) is resolved as a universal tree-to-loop boundary confirmed across five domains: Kleiber's metabolic scaling, Black–Scholes volatility, Murray's vascular law, network degree distributions, and tensor network truncation — all exhibiting the same ~10% gap with correction dominated by the mixing sector. Calculator updated from v4 to v7 with corrected δ_CP = 2π(1−1/χ), corrected tau mass (1.771 GeV), full Jarlskog factor anatomy, neutrino cross-domain analysis, and eight falsifiable predictions with kill conditions. Scorecard: 24/26 within 1% (up from 23/26), probability 10⁻⁴¹. The prompt covers 48+ sections (~1,720 lines): the algebra A_F = ℂ ⊕ M₂(ℂ) ⊕ M₃(ℂ) and its MERA realisation, the ascending superoperator spectrum {1, 1/2, 1/3, 1/6} with degeneracies {1, 3, 8, 24}, the Weinberg dual scheme (2/9 on-shell, 3/13 MS-bar, scheme difference via GCD = 13), the Jarlskog resolution and factor anatomy, the neutrino tree-to-loop boundary with five-domain cross-domain table, four promoted results (α⁻¹ = 43π + ln 7, tau from KMS Boltzmann, Koide Q = 2/3, three generations from Pauli matrices), gravity as the disentangler (7 signatures across 8 domains), sleep as renormalization, vacuum exploitation (15 demonstrated technologies), hyperbolic networks, the 650 Channel Map (cross-domain appearances in 12+ fields), quantum tunneling, entanglement, wave-particle duality, the Schrödinger equation as continuous MERA limit, and the Mandelbrot–Standard Model correspondence. Complete results table (53 entries), eight falsifiable predictions testable by 2035, and reproducible calculator code included. 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?

Keywords

Standard Model, finite-dimensional algebra, prime lattice, Beurling-Nyman criterion, SU(2) x SU(3), Riemann Hypothesis, spectral action, proton stability, LLM prompt, crystal geometry, noncommutative geometry, zero free parameters, polycrystal, falsifiable predictions

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
0
Average
Average
Average