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 missing treatment falls outside the complete-block assignment space
Example
There are three treatments and one block, but only two units receive treatments and . This is not a complete block: the assignment omits , so it is not an element of the RCBD assignment space.
Verification
Given: A block with treatments whose observed assignments are and only.
[F1] In an RCBD assignment, each block receives every treatment exactly once; equivalently its unit-to-treatment map is a permutation (Randomized complete-block design).
The image of this block's assignment is , which omits , so the map is not onto and is not a permutation.
Every assignment in the RCBD sample space is a permutation, while this assignment is not; therefore this block is incomplete and outside that sample space.
Depends on
Used by
Nothing in the library uses this result yet.
Dependency tree · two levels
4 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
- Gary W. Oehlert, A First Course in Design and Analysis of Experiments, Chapter 13 §§13.1–13.2 (standard reference, not scraped)