ExampleConstruction: AI-generatedVerification: AI-generatedPipeline-generatedverified 2026-10-15 (gpt-6-luna, gpt-6.1-sol, and delegated Codex review/repair agents; see completed run evidence)

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.

A symbolic 600 K and 300 K engine bound

Physical scope

A hypothetical two-ideal-bath engine calculation using the preceding conditional theorem; it reports no measured engine or empirical efficiency.

Example

Consider a hypothetical ideal-reservoir engine cycle with $T_{h} = 600 K$ and $T_{c} = 300 K$ , with all the assumptions of Ideal-bath heat-engine efficiency bound. Its efficiency is at most $1 / 2$ . This is a model calculation, not an observed performance.

Facts & Assumptions

Given: $T_{h} = 600 K$ , $T_{c} = 300 K$ , and an admitted heat-engine cycle in the ideal-bath scope of the preceding theorem.

[F1]

Ideal-bath heat-engine efficiency bound: $η \leq 1 - T_{c} / T_{h}$ ; equality requires zero total entropy change.

[F2]

SI quantities and unit conventions: thermodynamic temperature is measured in kelvins, so the ratio of two temperatures is dimensionless.

Verification

1.1givenF2algebra

The stipulated ratio is $T_{c} / T_{h} = 300 / 600 = 1 / 2$ .

2.1F1step 1.1algebra∎

Apply [F1] to obtain $η \leq 1 - 1 / 2 = 1 / 2$ . Equality is available only under the theorem's entropy-neutral condition; no experimental result is being reported.

A symbolic 600 K and 300 K engine bound

Example

Facts & Assumptions

Verification

Depends on

Dependency tree · 2 levels

Sources