DefinitionDefinition: AI-adaptedProof: Not applicableaudited 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.

The standard flat function

Definition

Define $β : R \to R$ by $β (t) : = {\begin{cases} \exp (- 1 / t), & t > 0, \\ 0, & t \leq 0. \end{cases}$ This is the standard flat function.

Remarks

$β (t) > 0$ for every $t > 0$ .
The only nontrivial point in later arguments is the junction at $t = 0$ .

Depends on

The real exponential function and the number $e$ by a power series

Dependency tree · 2 levels

Sources