Alphabeta Math
ExampleConstruction: Literature-sourcedVerification: AI-generatedprecheck passjudge pass (gpt-5.6-terra)audited 2026-09-05
How statement and proof provenance work

The first chip identifies the source of the statement or construction; the second identifies the source of its local proof or verification.

  • Literature-sourced: the exact statement appears in a cited source; only wording and notation differ.
  • AI-adapted: a semantically identical restatement of literature-sourced material, modulo indexing, notation, and boundary cases adopted by the library.
  • AI-generated: a genuinely novel statement formulated by AI, with no source for the claim itself.

These labels describe origin, not correctness: citations and verification chips remain separate evidence.

A preordered set read as a category enriched in the two-element lattice

Example

Let (P,≤) be a preordered set. Define a 2-valued hom-object by P(x,y)=1 exactly when x≤y and 0 otherwise. Then P is a 2-enriched category.

Facts & Assumptions

Given: A preordered set (P,≤).

[L1]

A 2-enriched category is exactly a preordered set (A category enriched in the two-element lattice is a preordered set).

Verification

technique · direct
1.1

The displayed hom-object assignment is the standard construction used in [L1]. Reflexivity gives the enriched identities and transitivity gives enriched composition.

L1given
2.1

Hence the preorder (P,≤) is an example of a 2-enriched category.

step 1.1∎

Depends on

Used by

Nothing in the library uses this result yet.

Dependency tree · two levels

3 results within two dependency steps of this one, each drawn at its shortest distance from it. An arrow runs from a result to what uses it, so the chart reads left to right and ends at this result, which carries a heavier outline. Every node is a link to that result. Click elsewhere on the chart to enlarge it.

Sources