2 Claim types and logical boundaries
On this page · Permalink · Source line 270
A useful theory of proof paths must not turn every recorded object into a proof step. A notebook may contain a theorem, a conjecture, a failed analogy, a numerical experiment, and a historical interpretation on the same page. Their coexistence does not give them the same logical status.
Definition 2.1: Evidence kind
An evidence kind is a declared type attached to a record supporting a claim or justification. The core finite vocabulary used here is
An evidence record also states its source, scope, and whether it certifies the justification to which it is attached.
The word “certifies” is deliberately separate from the evidence label. An exact computation may certify a finite identity while providing only numerical evidence for a general statement. An external result may certify a step only on the domain covered by its hypotheses. The scope field is therefore part of the mathematical object.
Warning 2.2: Evidence types are not one ranking
The evidence kinds do not form a universal total order. A formal proof of a weak statement and an exact computation of a stronger finite instance cannot be compared by one scalar without specifying the task. The ledger retains type and scope instead of replacing them with a single confidence number.
This separation will be used throughout. Candidate edges may remain in the discovery field, but only certified edges enter a proof certificate.