Alphabeta Math
ExampleConstruction: AI-generatedVerification: AI-generatedPipeline-generatedprecheck passjudge 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.

A four-row tridiagonal matrix in CSR form

Example

Let T∈M4×4(Q) have diagonal entries 2, entries −1 immediately above and below the diagonal, and all other entries 0. A CSR record for T is

r=(0,2,5,8,10),c=(0,1,0,1,2,1,2,3,2,3),v=(2,−1,−1,2,−1,−1,2,−1,−1,2).

This record stores s=10 entries and has no empty row, duplicate column, or explicit zero.

Facts & Assumptions

Given: The displayed arrays and the zero-based CSR convention.

[L1]

Compressed sparse row matrices with stored-entry semantics: the row pointers delimit each row's stored-index interval, and each stored value contributes to the matrix entry at its row and column index.

[L2]

The rationals form a field: the rational numbers with their standard operations form a field.

Verification

1.1givenL1algebra

The row-pointer array has length 5, starts at 0, ends at 10, and is nondecreasing. Every listed column index lies in {0,1,2,3}, so the data satisfy the CSR invariants for a 4 by 4 matrix.

2.1givenL1L2step 1.1algebra∎

Row 0 uses columns 0,1 with values 2,−1; row 1 uses columns 0,1,2 with values −1,2,−1; row 2 uses columns 1,2,3 with values −1,2,−1; row 3 uses columns 2,3 with values −1,2. These rational sums are the specified entries of T, so the record represents T.

Depends on

Used by

Nothing in the library uses this result yet.

Dependency tree · two levels

9 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