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.

Conforming P1 edge mesh on an anchored metric graph

Definition

Assume E≠∅. For each edge e, choose a finite partition 0=xe,0<xe,1<⋯<xe,Ne=ℓe, where Ne≥1, and let Th be the union of the resulting interval cells Ke,j=[xe,j−1,xe,j]. Set h=max⁡e,j(xe,j−xe,j−1). The conforming P1 edge space is Vh={w∈VD: we is affine on every Ke,j}. Thus internal nodal values are single-valued along each edge, while the original-vertex matching and zero-anchor conditions are inherited from VD. The maximum step h is positive and finite because the mesh has finitely many cells of positive length.

Depends on

Used by

Dependency tree · two levels

6 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