antiamerican-postponer432 $cross-validate
Format a physics or mathematics claim for cross-model validation.
Use this when Codex has produced a result you want to check against a second AI model (Claude, Gemini, or a fresh Codex context). Different models fail in different ways on the same physics, so agreement between models is meaningful evidence; disagreement tells you exactly where to look harder.
Inspired by the "hallucination orthogonality" principle and council-mode verification in flonat/claude-research, and the physics-specific failure modes documented by Tim Andersen (How to use Claude to do physics) — documented for Claude, but the same categories (dimensional analysis, formula provenance, plausible-but-wrong arguments) apply to every current model, including the ones behind Codex.
Usage
$cross-validate "the Gaussian integral sqrt(pi) follows from squaring and polar coordinates"
$cross-validate (no argument — validate the last substantial result)
Steps
Step 1 — State the claim precisely. Write the claim as a self-contained statement including:
- The exact formula or result
- All notation and conventions needed to read it (do not assume the other model shares your conventions)
- The domain of validity or the specific input values
Example:
Claim: The Gaussian integral I = ∫_{-∞}^{∞} e^{-x²} dx equals √π. Check this by computing I² = ∫∫ e^{-(x²+y²)} dx dy in polar coordinates, and confirm the radial integral gives π.
Step 2 — List the specific checkpoints. Identify what a second model should verify. Focus on the documented LLM weak spots:
- Dimensional analysis: are all quantities dimensionally consistent?
- Sign conventions: which sign convention is being used and is it applied consistently?
- Formula provenance: is this formula standard? Does it appear (with the same normalisation) in a named reference?
- Special-case check: does the result reduce correctly at a known special value?
- Step that looks too easy: any step summarised as "one computes" or "it follows that" — ask the other model to expand it.
Step 3 — Output the validation prompt. Produce a prompt ready to paste into another model. Format:
I want to verify a specific mathematical claim. Please check it independently —
do not try to agree with me, just derive it yourself from scratch.
[Exact statement from Step 1]
Please check:
1. [Checkpoint from Step 2]
2. [Checkpoint from Step 2]
...
If you reach a different answer, say so and explain where the derivations diverge.
Step 4 — After the user returns with the second model's answer. Compare the two answers:
| Outcome | Interpretation |
|---|---|
| Both agree | High confidence — proceed |
| Disagree on a sign or factor | Check the normalisation convention; one model is using a different definition |
| Disagree on the method | Both might be right via different routes — or one is wrong; trace the discrepancy |
| Second model refuses or is vague | Try a fresh Codex context (codex exec) instead |
Report which specific step or factor differs and what the most likely source of the discrepancy is.
Free scriptable option
The Gemini CLI and Anthropic's Claude Code can both be called from the terminal:
gemini -p "$(cat /tmp/validation_prompt.txt)"
# or, with Claude Code installed:
claude -p "$(cat /tmp/validation_prompt.txt)"
This lets you run the second-model check from the same terminal without switching
context. The cross-validate skill can write the prompt to /tmp/validation_prompt.txt
automatically if you pass --write-prompt.