Alphabeta Math
ExampleConstruction: AI-adaptedVerification: AI-adaptedSession-authored (Fable 5 assisted)precheck passjudge pass (gpt-5.6-terra)audited 2026-08-28
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.

Gershgorin disks for an explicit 3x3 matrix contain the true spectrum

Example

For

A=(210031004),

the Gershgorin disks are

D1={z:∣z−2∣≤1},D2={z:∣z−3∣≤1},D3={4},

and they contain the whole spectrum {2,3,4}.

Facts & Assumptions

Given: The upper-triangular matrix A above.

[L1]

Every eigenvalue lies in some Gershgorin disk (Every eigenvalue lies in some Gershgorin disk).

Verification

technique · direct
1.1

The row sums off the diagonal are 1,1,0, so the displayed three Gershgorin disks are exactly the ones attached to A.

algebra
2.1

Because A is upper triangular, its eigenvalues are the diagonal entries 2,3,4, and each of these lies in the displayed union of disks. This is the concrete containment asserted abstractly by [L1].

L1step 1.1∎

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