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.
Scope of the continuum heat solution results
Source-backed scope and limitation note for the local rectangular Fourier heat model; it reports no experiment and asserts no universal continuum closure.
Remarks
The existence and relaxation results on this page apply to a fixed rectangle, constant positive and , homogeneous Neumann boundary data, and the specified even-periodic initial profiles. They do not prove existence for rough initial data, arbitrary domains or boundary conditions, state-dependent conductivity, or a microscopic Boltzmann-to-Fourier limit. For the constant-coefficient heat equation of Constant-conductivity heat evolution on an insulated rectangle, the Gaussian-kernel solution gives an immediate nonzero response throughout the rectangle for the compactly supported perturbation in The rectangular Fourier model has instantaneous spatial support ↗. That is a mathematical property of this adopted diffusion model; it is not a measurement or a claim about finite-speed physical signals.