DefinitionDefinition: Literature-sourcedProof: Not applicablePipeline-generatedjudge pass (gpt-5.6-terra)audited 2026-09-06

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.

Language padding

Definition

For $A \subseteq {0, 1}^{*}$ and a total function $p : N \to N$ , define ${pad}_{p} (A) = {x # 1^{p (∣ x ∣) - ∣ x ∣ - 1} : x \in A, p (∣ x ∣) > ∣ x ∣} .$ All malformed strings, and strings with a wrong unary-pad length, are outside the padded language. The exponent is a nonnegative integer precisely on the displayed branch $p (∣ x ∣) > ∣ x ∣$ , and the delimiter makes decoding canonical.

Used by

Padding transfers time bounds Lemma

Dependency tree · 0 levels

Nothing. This result depends on no other item in the library.

Sources

Sebastiaan Terwijn, Complexity Theory, Exercise 3.5.2(a) (standard reference, not scraped)