Alphabeta Math
RemarkRemark: AI-adaptedProof: Not applicablePipeline-generatedjudge pass (gpt-5.6-terra)
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 prescribed finite jet at zero does not determine the law

Remark

Moments give derivatives of the characteristic function has a one-way hypothesis: a finite absolute moment of order k implies the displayed derivative formulas through order k. It does not assert that differentiability implies that absolute moment exists, or that knowing derivatives at zero recovers the characteristic function away from zero. Taylor reconstruction would require additional hypotheses that the lemma does not provide.

In particular, finite moment data do not determine a law in general. The companion's finite-support construction addresses every prescribed finite number of moments, rather than only a pair of laws with the same mean. This is orientation toward those examples, not a converse theorem or a claim of moment determinacy. No assertion that an arbitrary full moment sequence determines a probability law is made on this page.

Depends on

Used by

Nothing in the library uses this result yet.

Dependency tree · two levels

10 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