Seven, checked by hand
Examples are first-class citizens in Ouroboros: a definition without an instance is just words. Checking that 7's divisors are exactly {1, 7} takes seconds and grounds the abstract definition in something you can verify with your fingers.
A specimen in a natural history museum — one concrete prime, pinned and labeled.
Candidates 2..6: 7/2, 7/3, 7/4, 7/5, 7/6 all leave remainders. Divisors: 1 and 7 only. Prime ✓.
Witnesses like this keep the graph honest at the ground level: every definition demonstrably has instances.
Level 1 The precise statement
7 is prime: its only positive divisors are 1 and 7.
Level 3 What it stands on (1 direct)
- Integers form a commutative ring (axiom)
- Divisibility (definition)
- Prime number (definition)
- 7 is prime (example)
Level 4 The verified record
This page is generated from a machine-checked node. The kernel confirms its dependencies resolve, nothing is circular, and it grounds in axioms (foundation: peano). The content hash below makes tampering evident.
Nothing yet — this is a frontier result.
Nothing depends on it yet, so its failure would be contained.