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 240 K and 300 K refrigerator bound

Physical scope

A hypothetical ideal two-bath refrigerator calculation using the preceding conditional theorem; it reports no measured appliance coefficient or work.

Example

Consider a hypothetical refrigerator cycle with cold-bath temperature $T_{c} = 240 K$ , hot-bath temperature $T_{h} = 300 K$ , and $Q_{c} = 1200 J$ extracted per cycle. In the ideal-bath model, its cooling coefficient of performance is at most $4$ , so its work input is at least $300 J$ . No appliance measurement is asserted.

Facts & Assumptions

Given: The stipulated positive temperatures, $Q_{c} = 1200 J$ , and an admitted ideal-bath refrigerator cycle.

[F1]

Ideal-bath refrigerator coefficient-of-performance bound: ${C O P}_{R} = Q_{c} / W_{i n} \leq T_{c} / (T_{h} - T_{c})$ .

[F2]

SI quantities and unit conventions: $T$ is measured in kelvins and $Q_{c}, W_{i n}$ in joules.

Verification

1.1givenF2algebra

The temperature difference is $T_{h} - T_{c} = 60 K > 0$ , so $T_{c} / (T_{h} - T_{c}) = 240 / 60 = 4$ .

2.1givenF1step 1.1algebra∎

By [F1], $Q_{c} / W_{i n} \leq 4$ . Since $W_{i n} > 0$ , this implies $W_{i n} \geq Q_{c} / 4 = 1200 / 4 = 300 J$ .

A symbolic 240 K and 300 K refrigerator bound

Example

Facts & Assumptions

Verification

Depends on

Dependency tree · 2 levels

Sources