DefinitionDefinition: Literature-sourcedProof: Not applicablePipeline-generatedjudge pass (gpt-5.6-terra)audited 2026-09-14

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.

Suspension and sphere prespectra

For a well-pointed based CGWH space $X$ , its suspension prespectrum is

$(Σ^{\infty} X)_{n} = S^{n} \land X,$

where $S^{n} = (S^{1})^{\land n}$ and $S^{0}$ is the smash unit. Its structure map

$S^{1} \land (S^{n} \land X) ⟶ S^{n + 1} \land X$

is the canonical associativity homeomorphism, with the new $S^{1}$ coordinate placed first. Coherence makes the iterated construction unambiguous.

The sphere prespectrum is

$S = Σ^{\infty} S^{0}, S_{n} = S^{n} .$

These are prespectra. The definition does not assert that an arbitrary suspension prespectrum is an Omega-spectrum.

Depends on