RemarkRemark: Literature-sourcedProof: Not suppliedPipeline-generatedaudited 2026-09-06‡ sources checked 2026-09-06‡ not proved here

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.

‡ Recorded, not proved here. This statement is included so the library can refer to it honestly, with a citation to the literature. It is not proved anywhere in this library: the track that would prove it has not been developed here yet.

Cauchy–Kovalevskaya for a noncharacteristic analytic Cauchy problem

For an analytic $m$ th-order PDE posed on an analytic hypersurface and locally solved for the $m$ th derivative in a noncharacteristic normal direction, analytic data prescribing the normal derivatives through order $m - 1$ determine a unique local analytic solution. The existence and uniqueness are within the analytic class and are local. This is a recorded external theorem, not a smooth-data theorem and not a result proved or used by this page.

Used by

The proof boundary of Cauchy–Kovalevskaya Remark

Dependency tree · 0 levels

Nothing. This result depends on no other item in the library.

Sources

Part III: Analysis of Partial Differential Equations, Theorem 2.22 (standard reference, not scraped)