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.
Limits of the elliptic-parabolic-hyperbolic trichotomy
Remark
The names on this page combine related but differently formulated pointwise notions: ellipticity and strict hyperbolicity are conditions on real scalar second-order principal symbols, whereas the stated parabolic condition is for a space-time operator with a first-order time derivative and a semidefinite spatial quadratic form. These notions do not by themselves give a global taxonomy of equations that change type from point to point, systems with matrix-valued principal symbols, higher-order equations, or fully nonlinear equations whose leading behavior is not a single quadratic form.
Depends on
Used by
Dependency tree · two levels
7 results within two dependency steps of this one, each drawn at its shortest distance from it. An arrow runs from a result to what uses it, so the chart reads left to right and ends at this result, which carries a heavier outline. Every node is a link to that result. Click elsewhere on the chart to enlarge it.
Sources
- Victor Ivrii, Partial Differential Equations (standard reference, not scraped)