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.
Bounded-spectrum covariance class
Definition
For and , define For positive semidefinite , the operator norm is its largest eigenvalue, so this is the bounded-spectrum covariance class.
Depends on
Used by
- A bounded covariance class forces a capped lower rate Counterexample
- Matrix depth and covariance estimators Definition
- Single-block sparse covariance class and restricted directions Definition
- A covariance matrix with one correlated block Example
- Dense Gaussian Huber covariance model Example
- A matrix-depth maximizer exists on the bounded covariance classes Lemma
- Clean Gaussian covariance has a capped squared operator lower rate Lemma
- Huber covariance modulus lower bound for unrestricted matrix-valued actions Lemma
- Operator error bound for the Gaussian Huber matrix-depth estimator Lemma
- The Huber covariance contamination modulus has a quadratic lower bound Lemma
- Dense Gaussian Huber covariance: high-probability upper and capped lower bounds Theorem
Dependency tree · two levels
11 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
- Mengjie Chen, Chao Gao and Zhao Ren, Robust Covariance and Scatter Matrix Estimation under Huber's Contamination Model, §3.2 (standard reference, not scraped)