Alphabeta MathHow 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.
Classifying closed, open, and isolated system boundaries
Illustrative boundary classifications in the macroscopic thermodynamic model; the setups below are idealized examples, not reported measurements.
Example
As defined in Thermodynamic systems and permitted exchanges, choose the gas inside a sealed cylinder with a conducting wall and movable piston as the system. If the outer boundary allows energy transfer but no matter transfer, it is closed. Choose instead a vessel whose outlet allows water vapour to cross the boundary; it is open because that named matter species crosses. An ideal rigid, impermeable, thermally insulating enclosure with no other external energy channel is isolated. These classifications depend on the selected boundary and stipulated channels; they do not claim that a real apparatus is perfectly sealed or insulated.