ExampleConstruction: AI-adaptedVerification: 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.

Pressure-volume and force-distance units

Physical scope

Unit arithmetic for the SI quantities used in the thermodynamic framework; the example does not assert a pressure-volume work law.

Example

The SI units make both a pressure-volume product and a force-distance product have units of energy. In particular, one pascal times one cubic metre is one joule, and one newton times one metre is one joule.

Facts & Assumptions

Given: The SI unit relations specified for this framework.

[F1]

SI quantities and unit conventions: $1 P a = 1 J m^{- 3}$ , $1 N = 1 k g m s^{- 2}$ , and $1 J = 1 k g m^{2} s^{- 2}$ .

Verification

1.1F1algebra

Multiplying the pascal unit by the cubic-metre unit gives $(J m^{- 3}) m^{3} = J$ .

2.1F1algebra∎

Multiplying the newton unit by the metre unit gives $(k g m s^{- 2}) m = k g m^{2} s^{- 2} = J$ .

Pressure-volume and force-distance units

Example

Facts & Assumptions

Verification

Depends on

Dependency tree · 1 level

Sources