Alphabeta Math
ExampleConstruction: AI-generatedVerification: AI-generatedprecheck passverified 2026-09-24 (gpt-6-sol)
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.

The functional equation shows that ζ(−2)=0 through the sine factor

Example

Assume countable choice.

ζ(−2)=0.

Facts & Assumptions

Given: Countable choice and the trivial-zero theorem.

[L1]

For every integer m≥1, ζ(−2m)=0 (The only zeros of zeta on the nonpositive real axis are the negative even integers, and every other zero lies in the open critical strip).

Verification

technique · direct
1.1L1given

Apply [L1] with m=1. Then ζ(−2)=0.

2.1step 1.1algebra∎

This is exactly the first trivial zero.

Depends on

Used by

Nothing in the library uses this result yet.

Dependency tree · two levels

13 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