ExampleConstruction: Literature-sourcedVerification: AI-generatedSession-authored (Fable 5 assisted)precheck passaudited 2026-08-27

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.

Every tree is 0-hyperbolic

Example

Every tree is $0$ -hyperbolic.

Facts & Assumptions

Given: A tree $T$ .

[L1]

Cayley trees are $0$ -hyperbolic (Cayley trees are 0-hyperbolic).

Verification

technique · direct

1.1

The proposition [L1] states exactly that every tree is $0$ -hyperbolic.

2.1

Therefore $T$ is a model example of a hyperbolic space with the best possible constant $δ = 0$ .

step 1.1∎

Depends on

Cayley trees are 0-hyperbolic

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

Clara Löh, Geometric Group Theory, Section 6.2.4 (standard reference, not scraped)