ADR-040: Advice on how to prove a theorem is out of scope; advice on how to find out whether a technique worked is not

Context

The import behind #139 struck six recommendations as “not filed — advice on proof technique, not on training”. Three of them:

• use the bounded-Lipschitz metric and Neunzert-style empirical-measure coupling
• check whether the N-particle Gibbs measure satisfies a log-Sobolev inequality uniformly in N
• work in a rigged Hilbert space and analytically continue the resolvent

The cut was made by one filer, in the course of doing something else, and #139 is right that it wants deciding in writing — because the vocabulary does not obviously exclude it. analysis-and-evaluation is blurbed as “how to find out whether something worked… theory, interpretability and debugging belong here too”. Theory belongs there. A proof is theory. Nothing in the tag list says no.

DP-009 is the reason this cannot be left as a shrug. A claim the categories cannot express is evidence about the categories until someone shows otherwise, and the cheap reading — “out of scope” — is self-confirming, because declining the documents leaves the vocabulary looking complete. Six documents declined for the same missing category would be a missing category.

Decision

Advice whose reader is constructing a proof is out of scope. Advice whose reader is finding out whether a technique worked is in scope, and is what analysis-and-evaluation is for.

The test is the one ADR-026 already uses, applied to the audience rather than the domain: who does the sentence tell what to do?

• “Measure the gradient noise scale instead of sweeping batch size” — the reader is running a training job. In scope. It is SOTA-198.
• “Check whether the N-particle Gibbs measure satisfies a log-Sobolev inequality uniformly in N” — the reader is writing the convergence section of a paper. Out of scope.

Both are about theory. Only one is addressed to somebody training a model, and ADR-026 scopes this record by the kind of claim, which is a claim about what the reader does next.

The paper stays, the reading stays, the recommendation stays struck in place. This decides nothing about admitting mean-field or particle-system papers as LIT documents; THEORY-009 is a wide two-layer network’s gradient flow and is filed, correctly. What is out of scope is one kind of sentence inside such a paper, and the ## Recommendations section of the note keeps it with a strikethrough and the reason, which is how the cut stays auditable.

Why this is not the vocabulary being short a category

Applying DP-009’s own two tests:

Would you decline this claim if it arrived with excellent evidence and a familiar author? Yes — and this is the test that settles it. A beautifully evidenced result that the bounded-Lipschitz metric is the right one for coupling empirical measures is still not something a reader of this anthology does. The objection was never about the strength of the work.

Are the claims already in the record on this subject filed coherently? Yes. Twelve THEORY documents, all of them accounts of why a technique behaves as it does, none of them about how to establish such an account. The subject exists in the corpus with one consistent shape, and proof technique is not scattered across four ill-fitting categories — it is absent, which under DP-009 is the state that needs explaining, and this is the explanation.

What this does not decide

It does not narrow analysis-and-evaluation. Debugging, interpretability, evaluation methodology and the accounts in THEORY all stay exactly where they are. This removes one class the blurb could be read as admitting, and the blurb is not changed, because the boundary is about audience and a topic tag cannot express that.

It does not say a proof technique can never become in scope. If a particular argument became the standard way practitioners verify a training claim — the way a scaling-law fit did — the sentence would then be addressed to a practitioner and would pass the test. The decision is about what the sentence does, not about which field it came from.

It does not decide the reverse case: a training recommendation that only exists inside a theory paper. Those are in scope on this test and always were; #139’s six are not that.

Alternatives considered

• Admit them under analysis-and-evaluation. The tag’s blurb allows it on a literal reading. Rejected because it would make the registry hold advice two different professions act on, and a reader filtering to that tag for “how do I tell whether my run worked” would get resolvent continuation.
• Add a proof-technique topic. This is the DP-009-shaped move and it fails its own first test: the category would be added so that a decision would not have to be, which is exactly what DP-008’s corollary forbids.
• Leave it undecided and cut case by case. The status quo, and what #139 filed the objection against. The cost is a filer re-deriving the same judgement at every mean-field paper, with nothing pointing at the last time it was made.