Alphabeta Math
DefinitionDefinition: Literature-sourcedProof: Not applicablePipeline-generatedjudge pass (gpt-6-luna)
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.

Mixed local wave curve for a genuinely nonlinear or linearly degenerate family

Definition

Fix a local characteristic family on a neighborhood where it is either genuinely nonlinear with constant sign di=Dλi ri≠0, or linearly degenerate. For a genuinely nonlinear family define Ψi(σ;u)={Ri(σ;u),σdi>0,Si(σ;u),σdi<0,u,σ=0. where Ri is the local rarefaction curve and Si the local shock curve of Local shock curve by an augmented Rankine–Hugoniot equation. For a linearly degenerate family set Ψi(σ;u)=Ri(σ;u) for either sign; its nonzero-strength wave is the contact of A linearly-degenerate characteristic curve is a contact wave. The parameter σ is local and is restricted so the entire curve stays in the chosen neighborhood.

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