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.
Joule's 1850 paddle-wheel report
A source-based example of a historical calorimetry report and its apparatus-specific work-heat estimate; it is not a modern remeasurement or a proof of a universal law.
Example
Joule's 1850 report describes falling lead weights driving a paddle wheel in a sealed copper vessel of water. The water apparatus has rotating brass arms working between stationary vanes; a boxwood interruption reduces heat conduction along the shaft. The report describes thermometer calibration and resting trials arranged to estimate heat exchanged with the surroundings, alongside the friction trials. These are source-reported apparatus and procedure details, not measurements made for this library.
The water-series tabulation reports a nominal mechanical equivalent of 772.692 in the paper's historical convention: foot-pounds of falling-weight work compared with the heat needed to raise one pound of water by one Fahrenheit degree. The concluding proposition rounds that figure to 772 foot-pounds for raising one pound of water, weighed in vacuo and taken between 55°F and 60°F, by 1°F. Joule states that vibration and sound may make the estimate slightly high. This item adds no modern uncertainty interval or statistical inference. The historical result is empirical evidence from a particular apparatus and correction chain; it does not deductively establish the adopted first-law postulate for all systems.
Dependency tree · 0 levels
Nothing. This result depends on no other item in the library.