DefinitionDefinition: Literature-sourcedProof: Not applicablejudge pass (gpt-5.6-terra)audited 2026-09-07

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.

Effective Hausdorff dimension

Definition

For $s \geq 0$ , an effective $s$ -gale is a lower-semicomputable function $d : {0, 1}^{*} \to R_{\geq 0}$ satisfying $d (σ) = 2^{- s} (d (σ 0) + d (σ 1))$ for every binary string $σ$ ; it succeeds on $X$ when $\sup_{n} d (X ↾ n) = \infty$ . The effective dimension $\dim (X)$ is the infimum of $s$ for which some effective $s$ -gale succeeds on $X$ . Equivalently it is characterized by effective covers made from the cylinders of Effectively open sets in Cantor space.

Depends on

Effectively open sets in Cantor space

Used by

Effective dimension is the liminf prefix-complexity rate Theorem

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

Franklin and Porter, §4.5 (standard reference, not scraped)