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Example

Seven, checked by hand

7 can only be divided evenly by 1 and 7 — a prime, verified directly.
Formally: 7 is primenumber theoryGentledepth 3 in the graph

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)
  1. Integers form a commutative ring (axiom)
  2. Divisibility (definition)
  3. Prime number (definition)
  4. 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.

sha256:08639b0dcf3631499d7f8add98ac751e49602774117bce7c7669fc053fe768f5

Nothing yet — this is a frontier result.

Nothing depends on it yet, so its failure would be contained.

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