DefinitionDefinition: 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.

Exact sign predicate for a real 2x2 characteristic discriminant

Definition

For a real matrix $B = (\begin{array}{cc} a & b \\ c & d \end{array})$ , define its characteristic-polynomial discriminant by $Δ (B) = (a + d)^{2} - 4 (a d - b c)$ . Define $discSign (B)$ to be $- 1$ , $0$ , or $1$ according as the exact real number $Δ (B)$ is negative, zero, or positive. This is an exact mathematical predicate on the stored real entries, not an operation in the operationwise floating-point model. A computed procedure may report a sign only when its control predicate establishes this exact value; otherwise it reports undecided.

Used by

Dependency tree · 0 levels

Nothing. This result depends on no other item in the library.

Sources

James Demmel, Math 221 Lecture 16: the implicit Q theorem (standard reference, not scraped)
David Bindel, CS 6210 Matrix Computations, Hessenberg QR iteration (standard reference, not scraped)