Theory: Main results formally proven, not just stated

What to Check

Propositions, theorems, and lemmas in a theory paper must be formally proven. A result stated without proof, or with a proof that is incomplete or circular, does not constitute an established result. Proofs may appear in the main text or in an appendix, but they must exist and be complete.

How to Check

1. List all labeled results: propositions, theorems, lemmas, corollaries.
2. For each result, verify that a proof is provided — either immediately following the result or in a clearly referenced appendix.
3. Evaluate proof completeness at a high level:
   • Does the proof address all cases the result claims to cover?
   • Are all steps that require justification actually justified, or do steps appear as “it follows that…” without explanation?
   • Does the proof use only assumptions stated in the model and previously established results?
4. Check for results labeled “intuition” or “sketch” — these are not proofs. If the formal proof is deferred (“proof in supplementary appendix”), verify the supplementary appendix is actually provided.

Pass Condition

Every labeled result (proposition, theorem, lemma) has a complete proof in the main text or appendix. No result is established only by intuition, example, or simulation (unless the paper explicitly says the result is a conjecture).

Failure Examples

1. No proof provided: Paper states “Proposition 2: The equilibrium wage is increasing in worker ability.” No proof follows and no appendix reference. Fails.
2. Proof by example: Paper demonstrates a result holds for a specific parameterization and calls it proven. An example demonstrates possibility, not generality. Fails.
3. Circular proof: Proof of Proposition 1 invokes “the result of Proposition 2,” which is stated later. If Proposition 2’s proof also depends on Proposition 1, the argument is circular. Fails.
4. “Sketch” only: Paper provides a “proof sketch” with key steps but defers the full proof to “a technical appendix available from the authors.” The appendix is not attached to the submitted paper. Fails.

Notes

• Computational or quantitative theory papers that characterize equilibria numerically should clearly state which results are analytical (proven) and which are established by simulation. Simulation-based results are not proofs — they are quantitative illustrations.
• Corollaries that follow directly from propositions by substitution or inspection can have shortened proofs, but must state what they follow from.