Develop and mechanically check a mathematical argument with agents

Why use this

1. A researcher may have a convincing informal argument alongside finite examples and partial formal work, yet still need to know whether all three address the same claim. A successful check can be less informative than it appears if assumptions changed during translation.

2. This job could coordinate distinct forms of scrutiny and keep their scope visible. Separating conjecture, counterexample search, informal reasoning and mechanical records helps the researcher decide what has actually been established and what remains open.

Why an agent / simpler alternative

Useful judgment

Identify missing hypotheses, reconcile objections and check that formal statements match the intended mathematical claim.

Simpler alternative

Use direct human proof review for a short argument with familiar definitions.

Unsuitable when

The workflow treats finite search as a universal proof or accepts verification records without inspecting their scope.

Proposed inputs

1. Name

   Problem statement

   Owner

   Researcher

   Minimum scope

   Precise definitions, hypotheses and desired conclusion

   Quality check

   Separate conjecture from already established results

2. Name

   Argument/verification materials

   Owner

   Research owner

   Minimum scope

   Authorized proof text, search specification and formal sources

   Quality check

   Track versions, assumptions and reported verification boundaries

Access and setup — proposed or unknown

Proposed minimum

1. Begin with a synthetic statement-alignment exercise; no searches, proof execution, installs or paid compute.

Compatibility unknowns

1. Current prover versions, library dependencies, compute needs and exact runtime compatibility are unknown.

External actions requiring approval

1. Large computations, repository publication, external disclosure and infrastructure changes require authorization.

Expected deliverable and review checks

Proposed artifact

Research review packet linking claims, objections, finite-search scope and proposed formal-verification checks.

Critical checks

1. Compare hypotheses and conclusion exactly; inspect trusted assumptions; distinguish public artifacts from new independent reproduction.

Missing output evidence

This overlay adds no new output inspection, execution or validation; consult the referenced canonical source outcome limits.

Failure signals and proposed responses

1. Signal

   The formal theorem omits a crucial hypothesis

   Why it matters

   It may prove a different statement or fail for the wrong reason

   Proposed response

   Reconcile the statement before interpreting verification.

2. Signal

   A bounded search finds no counterexample

   Why it matters

   Absence within the bound is mistaken for proof

   Proposed response

   Report the bound and leave the general claim unresolved.

Effort and cost — unknown

Setup work

1. Fix definitions and evidence/version conventions.

Ongoing review

1. Researcher reviews objections and the interpretation of verification records.

Unknowns

1. Formalization effort, library compatibility, compute demand and costs are unknown.

First check — proposed, unexecuted

Status

proposed_unexecuted

Synthetic fixture

Use the synthetic claim that two even integers have an even sum; pair it with a target accidentally allowing arbitrary integers and a list of even-only examples.

Acceptance checks

1. Identify the dropped hypotheses; separate examples from proof; claim no execution or new verification.

Stop conditions

1. Stop if the intended statement is ambiguous or verification would require unapproved resources.

Limits

1. Preserve the canonical public-artifact status and outcome limit; this overlay performs no independent reproduction.