Alphabeta MathDefinitionDefinition: Literature-sourcedProof: Not applicablePipeline-generatedjudge pass (gpt-6-luna)
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.
Extended-real indicator of a set
Definition
For any set , its extended-real indicator is
Depends on
Used by
- Projected stochastic-gradient update Definition
- Proximal-gradient mapping and projected-gradient mapping Definition
- Diagonal AdaGrad subproblem has a unique minimizer Lemma
- The convex normal-cone operator is maximal monotone and its resolvent is projection Lemma
- The proximal map of an indicator is Euclidean projection Lemma
- Projected SGD converges almost surely on a strongly convex objective Theorem
Dependency tree · two levels
10 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
- Neal Parikh and Stephen Boyd, Proximal Algorithms, §2.4.2 (standard reference, not scraped)