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Math verification

Skill gioviat/research-toolkit/skills/math-verification

Use whenever asked to check, verify, derive, or re-derive a mathematical claim, proof, bound, or formula, including checking someone else's derivation, checking a step in a paper draft, or verifying that code implements a formula correctly. Trigger on words like "verify", "check the proof", "derive", "is this bound correct", "does this match the formula".From its SKILL.md

Install
npx -y skills add gioviat/research-toolkit --skill math-verification

Assembled from the repository path, not quoted from the project. Check it against their README if it does not work.

One thing to look at

  • 2 stars2 stars. Stars are a popularity signal and not a quality one, but at this level it is likely that nobody has read this closely except its author, and you would be relying on your own review.

SKILL.md

2.4 KB, as published. Nobody here has run it

Math verification

Before checking anything

  • Restate every assumption the claim depends on, explicitly, in your own words. If an assumption is implicit in the source material, name it.
  • State the claim itself in a form precise enough that "true" or "false" is unambiguous. If the claim as given is ambiguous, say so and verify the most natural reading, flagging the ambiguity.
  • Check that all symbols match the project's canonical notation (papers/notation.md). Flag any symbol used inconsistently with that file.

Verification order (cheapest checks first)

  1. Dimensional / type consistency: do units, shapes, or types match on both sides?
  2. Boundary and limiting cases: does the claim reduce to a known result at an edge case (n=1, t=0, d→∞, etc.)?
  3. A small numeric or symbolic example, computed independently (SymPy, a script, or a proof assistant where applicable) — not by re-reading the existing derivation and agreeing with it.
  4. Full independent re-derivation of the result, without looking at the given derivation step-by-step. Only after finishing, compare against the original to see where they diverge.

Rules

  • Never state that a derivation is correct because it "looks standard" or "follows the usual pattern." Redo the steps.
  • If a step cannot be verified with available tools (e.g., it requires a proof assistant you don't have, or relies on an unavailable reference), say exactly that: "unverified — requires X." Never round this up to "likely correct."
  • If you find an error, state the exact line/step where it occurs and what the correct expression should be, rather than a general "there may be an issue here."
  • Distinguish clearly between "I verified this is correct," "I verified this is incorrect," and "I could not verify this."

Output format

For each claim checked, report:

  • Claim (restated precisely)
  • Assumptions used
  • Method of verification (dimensional check / limiting case / independent derivation / symbolic computation)
  • Verdict: correct / incorrect / unverified, with the specific reason

Keep looking

Skills are one crate of 627,801. Ordering is by how many stacks a row turns up in, so the top of any crate is what has actually been picked rather than what has the most stars.