CorollaryStatement: Literature-sourcedProof: AI-generatedPipeline-generatedprecheck passjudge 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.

L is properly contained in PSPACE

Statement

With $L : = D W O R K S P A C E (⌈ \log_{2} (n + 2) ⌉)$ , $L ⊊ P S P A C E .$

Facts & Assumptions

Given: $f (n) = ⌈ \log_{2} (n + 2) ⌉$ and $g (n) = n$ .

Proof

technique · direct

1.1

The local hierarchy applies to $f, g$ , yielding a language in $D W O R K S P A C E (n) ∖ L$ .

givenconstruct

2.1

The bridge puts that language in $D S P A C E (2 n)$ , hence in PSPACE. Since every $L$ computation is also polynomial all-tapes space, this proves the proper containment.

step 1.1∎

Depends on

Used by

Nothing in the library uses this result yet.

Dependency tree · two levels

7 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

Arora and Barak, Computational Complexity, Definition 4.5 (standard reference, not scraped)