Alphabeta Math
ExampleConstruction: AI-adaptedVerification: AI-generatedprecheck passaudited 2026-08-30
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 Mittag-Leffler function with double poles at the integers

Example

There exists a meromorphic function on C whose poles are exactly the integers and whose principal part at each integer n is (z−n)−2.

Facts & Assumptions

Given: The discrete set Z and the prescribed principal parts pn(z)=(z−n)−2.

[L1]

Mittag-Leffler on the plane realizes every discrete family of prescribed principal parts (Mittag-Leffler on the complex plane).

Verification

technique · direct
1.1

The set Z is discrete in C, and each pn(z)=(z−n)−2 is a finite negative Laurent polynomial at n.

given
2.1

Applying [L1] to this data yields a meromorphic function f whose principal part at every integer is exactly (z−n)−2. Because that principal part is nonzero and contains only the degree −2 term, each pole has exact order 2.

step 1.1L1algebra∎

Depends on

Used by

Nothing in the library uses this result yet.

Dependency tree · two levels

3 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