Assumptions, Results & Proof Architecture (jet-identification-strategy)

When to trigger

• You have a candidate theorem and need to make its assumptions and proof referee-proof
• A referee may ask "is assumption X necessary?" or "does this hold in the general case?"
• You are choosing between a clean special case and a more general but opaque statement

Why this replaces a causal "identification strategy"

JET is theory-first: there is no data design to identify. The credibility of a JET paper rests on assumptions that are explicit and minimal, results stated precisely, and proofs an expert can check — refereed single-blind by at least two reviewers who will verify each step.

The theory checklist

Assumptions

• [ ] Every assumption is stated formally (domain, regularity: continuity, convexity, single-crossing,

finiteness) before it is used

• [ ] Each assumption is load-bearing — for each one, you can name the step that fails without it
• [ ] No silent assumption smuggled into a proof (a common referee catch)
• [ ] Necessity is addressed: a counterexample shows what breaks if a key assumption is dropped

Results

• [ ] The main result is a clean theorem/proposition/characterization, numbered and self-contained
• [ ] Genericity, existence, uniqueness, and comparative statics are separated into distinct statements
• [ ] The statement says exactly what is proved — no informal "essentially" claims beyond the proof

Proof exposition

• [ ] Proof architecture is visible: lemmas in dependency order, a one-paragraph roadmap for long proofs
• [ ] Key step (fixed point, duality, induction, envelope/revelation argument) is named and motivated
• [ ] Long/technical proofs moved to an appendix (thm-restate to restate); body keeps the idea
• [ ] Notation is consistent end-to-end (referees abandon proofs they cannot parse)

Generality vs. tractability

• [ ] The chosen level of generality is defended: a transparent special case can beat an unverifiable

general one; a general result is worth it only if the proof remains checkable

• [ ] Any restriction (finite types, two players) is flagged as a scope limit, not hidden

Assumption-set architecture (three tiers)

JET papers separate three tiers of premises; label them so referees see which is which:

• Maintained structure — the model itself (agents, type spaces, action sets, timing). Lives in

the model section as prose and definitions, not as numbered assumptions.

• Economic assumptions — single-crossing, private values, independence, ambiguity attitudes,

substitutability. Numbered A1, A2, …; each carries economic content and each earns a necessity discussion.

• Technical regularity — compactness, continuity, measurability. Numbered last; defensible as

standard, but still say which proof step uses each one.

Referee heuristic: the first thing checked is whether the theorem statement quantifies over exactly the numbered assumptions — nothing more, nothing less. A theorem invoking "the assumptions of Section 2" without numbers invites a hostile read.

Proof-spine scaffold

Theorem 1 (statement quantified over A1–A3 only)
 ├─ Lemma 1: existence of the auxiliary object      [uses A1, A3 (compactness)]
 ├─ Lemma 2: monotonicity / single-crossing step    [uses A2]
 │    └─ Claim 2.1: boundary case                   [where A2 binds → necessity candidate]
 ├─ Main argument: fixed point / duality / induction (named in one body sentence)
 └─ Appendix B: full proofs of Lemmas 1–2; the body keeps the roadmap paragraph + key step
Example 1 (tightness): drop A2, hold everything else fixed → conclusion fails; cite it
right after Theorem 1, not in a footnote.

Writing the tightness discussion JET-style

• Place the counterexample immediately after the theorem as a numbered Example, with one

sentence saying which assumption it targets.

• Make it minimal: change exactly one assumption and keep the rest of the environment fixed,

so the referee attributes the failure to the right premise.

• If no counterexample is available, state openly that necessity is an open question — JET

referees respect a flagged open problem more than silence.

Micro-vignette (decision theory)

A representation theorem for ambiguity-averse preferences: A1 (weak order, continuity) is regularity; A2 (certainty independence) is the economic axiom. The proof's separation argument fails exactly when A2 is weakened to independence on constants only; Example 1 exhibits a maxmin preference violating the conclusion under the weakening. One page settles A2's tier, load-bearing step, and necessity — the page both referees read first.

Anti-patterns

• A "general" theorem whose proof silently needs finiteness or continuity
• Assumptions introduced inside a proof rather than stated up front
• A monolithic 6-page proof with no roadmap or lemma decomposition
• Claiming necessity of an assumption without a counterexample

Output format

【Theorem】<precise statement>
【Assumptions】[A1 used at step __ | A2 used at __ | necessity of Ak: counterexample/general]
【Proof spine】lemmas in order → key argument named → appendix offload
【Generality call】special-case-clean | general-but-checkable | (reject) general-unverifiable
【Next】jet-contribution-framing / jet-tables-figures (schematic) / jet-rebuttal