theory2-physics_skill

Overview

This skill provides a compact guide to using the Theory2 CLI for mathematical physics workflows: symbolic math, quantum chemistry, PDE solvers, neural operators, theorem proving, and verification. It explains key commands, module selection, and practical workflows for reproducible, cross-validated computation. The content focuses on actionable examples, recommended defaults, and verification patterns for scientific results.

How this skill works

The skill inspects common Theory2 command groups and shows the canonical --json invocation pattern for parseable output. It maps tasks to modules (symbolic, numerical, ml, prove, verify) and provides ready-to-run command templates for Lie algebra calculations, quantum-chemistry runs, PDE/ML training, and automated Lean proofs. It also prescribes verification steps (cross-check, caching policy, and hermeneutic iteration) to ensure reproducibility and scientific validation.

When to use it

• Deriving algebraic identities, Lie algebra properties, or symbolic calculus steps.
• Running molecular energy calculations, basis-set experiments, or quantum-circuit simulations.
• Training or applying Fourier Neural Operators and equivariant E3NN models for PDEs.
• Automated theorem proving and proof search with Lean 4 and RobustLeanProver.
• Cross-validating important numerical or symbolic claims with multiple methods.
• Biosequence operations and protein structure analyses that need scriptable, parseable output.

Best practices

• Always invoke the CLI with --json to get structured, machine-readable output.
• Search prior results before computing to reuse cached proofs and prior runs.
• Cross-validate critical results using symbolic, numerical, and experimental methods.
• Record methods, parameters, environment, and uncertainty for reproducibility.
• Use proof caching for frequent theorem checks and --no-cache to force recomputation when needed.

Example use cases

• Compute α⁻¹ from the E7 Lie algebra and verify with symbolic queries and cross-check.
• Run a DFT energy calculation for H2O, then re-run with CCSD for high-accuracy benchmarking.
• Train an FNO with Tucker factorization to reduce memory footprint for large PDE operators.
• Auto-prove elementary arithmetic or inductive lemmas using RobustLeanProver and save verified proofs.
• Perform sequence translation and compute protein molecular weight as part of an analysis pipeline.