DefinitionDefinition: Literature-sourcedProof: Not applicableaudited 2026-08-13

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.

Sum-free subsets of the integers

Definition

A set $B \subseteq Z$ is sum-free when there are no $x, y, z \in B$ with $x + y = z$ . The two summands are allowed to be equal.

Depends on

The integers as equivalence classes of pairs of naturals

Used by

Every nonempty finite set of n nonzero integers has a sum-free subset of size greater than n/3 Theorem

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

Y. Zhao, MIT 18.218 Probabilistic Method in Combinatorics, Section 6.1 (standard reference, not scraped)
M. Bucic, Probabilistic Method, Section 2.3 (standard reference, not scraped)