Alphabeta MathHow 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 Latin square need not be orthogonal to an identical copy of itself
Statement refuted
Any two Latin squares of the same order are orthogonal.
Facts & Assumptions
Given: The addition table of , used twice.
Orthogonality means that every ordered pair of symbols occurs exactly once (Orthogonal Latin squares and complete families of them).
Counterexample
The addition table of is a Latin square, so using it twice gives two Latin squares of the same order.
In the paired array, every cell has the form because the same Latin square is used twice. So the ordered pair never appears, and [L1] shows that the two squares are not orthogonal.
Depends on
Used by
Nothing in the library uses this result yet.
Dependency tree · one level
2 results within one dependency step 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
- Jonathan Davidson, Latin Squares (standard reference, not scraped)