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.

Computable martingales on binary strings

Definition

A computable martingale is a total computable nonnegative real-valued function $d : {0, 1}^{*} \to R_{\geq 0}$ satisfying $d (σ) = (d (σ 0) + d (σ 1)) / 2$ . For an infinite binary sequence $X \in 2^{ω}$ , it succeeds on $X$ if $\sup_{n} d (X ↾ n) = \infty$ . Binary-string conventions are from Computation alphabets, words, the empty word, and $Σ^{*}$ .

Depends on

Computation alphabets, words, the empty word, and $\Sigma^*$

Used by

Martin-Löf randomness implies computable randomness Theorem

Dependency tree · two levels

4 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, Definition 2.8 (standard reference, not scraped)