ExampleConstruction: Literature-sourcedVerification: 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.

Converting work-on and work-by conventions

Physical scope

Algebraic conversion between two signed-work conventions for the closed process class of the adopted first-law postulate.

Example

Some sources take work done by the system as positive and write the first law as $Δ U = Q - W_{b y}$ . The present framework takes work done on the system as positive. Setting $W_{b y} [P] : = - W_{o n} [P]$ converts one equation to the other.

Facts & Assumptions

Given: An admitted core closed process record $P \in P_{c l} (s)$ with the equilibrium endpoints and energy exclusions of [F1], and the two declared sign conventions.

[F1]

First-law energy balance for closed process records: For an admitted closed record with the stated energy exclusions in the process-selected chart, $U_{c} (x_{P}^{+}) - U_{c} (x_{P}^{-}) = Q [P] + W_{o n} [P]$ .

[F2]

Thermodynamic process records and transfer conventions: $W_{o n} [P] > 0$ means mechanical work is done on the system.

Verification

1.1givenF2algebra

Define the work-by-positive value by $W_{b y} [P] : = - W_{o n} [P]$ , so $W_{o n} [P] = - W_{b y} [P]$ .

2.1F1step 1.1algebra∎

Substituting the equality from step 1.1 into [F1] gives $U_{c} (x_{P}^{+}) - U_{c} (x_{P}^{-}) = Q [P] - W_{b y} [P]$ .

Depends on

Dependency tree · 2 levels

Sources

Ling, Moebs, and Sanny, University Physics Volume 2, §3.3 First Law of Thermodynamics