Alphabeta Math
ExampleConstruction: AI-adaptedVerification: AI-adaptedSession-authored (Fable 5 assisted)precheck passaudited 2026-08-02
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.

Complex sine is unbounded on the imaginary axis

Example

For real tt, sin⁡(it)=isinh⁡t\sin(it)=i\sinh t, so complex sine is unbounded on the imaginary axis. The conventions and prerequisite facts used below are recorded in The exponential formulas, real restrictions, and trigonometric-hyperbolic dictionary over C\mathbb C, The exponential tends to +∞+\infty at +∞+\infty and to 00 at −∞-\infty.

Facts & Assumptions

Given: A real parameter tt.

Verification

1.1

The dictionary gives sin⁡(it)=isinh⁡t\sin(it)=i\sinh t.

given
2.1

Since sinh⁡t=(et−e−t)/2\sinh t=(e^t-e^{-t})/2 is unbounded as t→∞t\to\infty, so is its modulus.

given∎

Depends on

Used by

Nothing in the library uses this result yet.

Dependency tree · next 3 levels

Direct dependencies and their dependencies through the next three levels: 49 results over 10 levels. An arrow runs from a result to what uses it, and this result sits at the bottom with a heavier outline. Click the chart to enlarge it.

Sources