Theory2 Cross-Validation

Verify physics claims by comparing results from multiple independent methods.

Cross-Check Command

# Verify fine-structure constant
/home/mikeb/theory2/.venv/bin/theory --json verify cross-check \
  --claim="alpha_inv=137" \
  --methods="symbolic,numerical,experimental" \
  --tolerance=0.001

# Verify molecular energy
/home/mikeb/theory2/.venv/bin/theory --json verify cross-check \
  --claim="H2_bond_length=0.74" \
  --methods="symbolic,numerical"

# Strict tolerance
/home/mikeb/theory2/.venv/bin/theory --json verify cross-check \
  --claim="pi=3.14159" \
  --methods="symbolic,numerical" \
  --tolerance=1e-6

Verification Methods

Symbolic

• Algebraic/analytic computation
• Exact results where possible
• Uses SymPy, SageMath, mpmath

Numerical

• High-precision numerical evaluation
• Multiple precision levels (double, quad)
• GPU-accelerated where available

Experimental

• Comparison with known experimental values
• CODATA fundamental constants
• Literature reference values

Claim Format

Claims use name=value format:

• alpha_inv=137.036 - Fine-structure constant inverse
• H2_energy=-1.174 - H2 ground state energy (Hartree)
• e_charge=1.602e-19 - Electron charge

Output

The verification returns:

• Individual method results
• Agreement status
• Discrepancy analysis
• Confidence level

{
  "status": "verified" | "discrepancy" | "partial",
  "results": {
    "symbolic": {...},
    "numerical": {...},
    "experimental": {...}
  },
  "agreement": {
    "all_agree": true/false,
    "max_discrepancy": 0.001,
    "within_tolerance": true/false
  }
}

Use Cases

1. Validating new calculations: Confirm results using independent methods
2. Checking experimental values: Compare theory with experiment
3. Debugging discrepancies: Identify which method disagrees
4. Publication preparation: Document multi-method verification

Always use --json for structured output.