Cross validate

/cross-validate

Format a physics or mathematics claim for cross-model validation.

Use this when Claude has produced a result you want to check against a second AI model (Gemini, ChatGPT, or a fresh Claude 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).

Usage

/cross-validate "the residue of ξ(2s)E(z,s) at s=1/2 is π"
/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: For the completed Eisenstein series E*(z,s) = ξ(2s)E(z,s), where ξ(s) = π^{-s/2} Γ(s/2) ζ(s), the residue at s = 1/2 is 3/π. Check this using the functional equation E*(z,s) = E*(z,1-s) and the pole structure of ξ(s).

Step 2 — List the specific checkpoints. Identify what a second model should verify. Focus on the known Claude 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 Claude session instead

Report which specific step or factor differs and what the most likely source of the discrepancy is.

Free scriptable option

The Gemini CLI can be called from the terminal:

gemini -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.