How to read a claim that carries a status badge

This archive labels its claims, and a label you cannot interpret is worse than none, because it invites trust on decoration alone. This post is the reader’s manual: what each badge licenses you to believe, what it forbids, and what questions each one should trigger. Six badges, six short entries.

Theorem

A theorem here means: proved from stated premises, with the proof recomputed by an independent pass. You may treat the result as true given the premises, and you should read the premises, because they carry the scope. What the badge does not mean: that the result is relevant, or that its premises describe our universe. The anomaly-cancellation theorem is exactly true of exactly the stated category, and says nothing about whether that category is physical. When you see a theorem, ask: are the premises the kind of thing reality provides, or the kind of thing a framework assumes?

Benchmark

A benchmark is computed, reproducible, and not derived. The mass gap at 10 to the 12 GeV is the canonical case: the functional-renormalisation-group computation has a definite output, but the input structure has not been independently verified, so the number is only as good as its machinery. Licensed: consistency checks, cross-references, illustration. Forbidden: load-bearing use in a derivation. When you see a benchmark, ask: what would it cost to derive this, and has anyone started?

Conjecture

A conjecture states a testable belief with its falsification route named. The modular fixed point is the live case: a specific complex number, with a specific bulk computation that would confirm or destroy it. Licensed: motivating work, experimental design. Forbidden: citing it as support for anything. When you see a conjecture, ask: what experiment or computation kills this, and when is it scheduled?

Preregistration

A document that binds the programme’s future behaviour: named routes, fixed pipelines, numeric decision rules, and written loss conditions. It makes no claims, which makes it the only badge that cannot be false. Ask instead: is the rule set complete, and would I accept the outcome if it went against the programme?

Retracted

A claim that failed audit, kept public with its failure mode documented. The badge is a warning about the specific result and a map of the error’s species. Licensed: learning. Forbidden: citing the number, in either direction. The corpses are load-bearing for the method, not for the physics.

Proxy

A number standing in for something not yet computed: the code-distance suppression is the case study, a legitimate illustration of scaling that was treated as physics for two paper generations. Licensed: intuition, order-of-magnitude discussion. Forbidden: predictions. When you see a proxy, ask: what is it standing in for, and how far away is the real computation? The badge exists because the gap between an illustration and a result is where trust goes to die, and naming the gap is cheaper than rediscovering it.

The next post runs the method on signals whose answers are already known: cold tests.