Triple

T11812507
Position Surface form Disambiguated ID Type / Status
Subject Elwin Bruno Christoffel E280907 entity
Predicate notableWork P4 FINISHED
Object Christoffel–Darboux kernel E947533 NE FINISHED

How this triple was built (2 steps)

Every LLM step that produced this triple, in pipeline order — named-entity classification, the disambiguation choices (the exact options shown, with the pick highlighted), and the generated description. The batch + timestamp of each is in the Provenance table below.

NER Named-entity recognition gpt-5-mini
Instruction
Given a phrase, classify it is english named entity (e.g., persons, organizations, works of art) in Latin script, or not (e.g., literals, dates, URLs, verbose phrases). For disambiguation, the statement where the phrase occurs as object is also given. Please return a JSON object with `phrase` (string, the phrase being analyzed) and `is_ne` (boolean, indicating whether the phrase is a Named Entity).
Input
Phrase: Christoffel–Darboux kernel | Statement: [Elwin Bruno Christoffel, notableWork, Christoffel–Darboux kernel]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Christoffel–Darboux kernel
Context triple: [Elwin Bruno Christoffel, notableWork, Christoffel–Darboux kernel]
  • A. Christoffel–Darboux formula chosen
    The Christoffel–Darboux formula is a key result in the theory of orthogonal polynomials that provides an explicit expression for sums of products of such polynomials, with important applications in approximation theory and mathematical physics.
  • B. Szegő kernel
    The Szegő kernel is a fundamental reproducing kernel in complex analysis and operator theory, associated with Hardy spaces on the boundary of a domain and central to the study of orthogonal polynomials and boundary behavior of analytic functions.
  • C. Dirichlet kernel
    The Dirichlet kernel is a trigonometric polynomial that arises in Fourier series as the summation kernel for partial sums, playing a key role in analyzing convergence properties.
  • D. Borg–Marchenko theorem
    The Borg–Marchenko theorem is a fundamental result in inverse spectral theory that characterizes when a potential in a one-dimensional Schrödinger operator is uniquely determined by its spectral data.
  • E. Poisson kernel
    The Poisson kernel is a fundamental function in harmonic analysis and potential theory used to represent harmonic functions inside a domain from their boundary values, especially in the unit disk and upper half-plane.
  • F. None of above.
  • G. Unsure - the case is ambiguous/there is not enough information to decide.

Provenance (3 batches)

The batch behind each pipeline step, in order, with when it ran. Timestamps are batch-level — stages were processed in waves, so the object chain (NER → NED1 → NEDg → NED2) reads in order, but predicate / elicitation batches can sit in a different wave.

Step Stage Batch ID Status When
creating Elicitation batch_69d6ab26aae88190b2489efcb2a24234 completed April 8, 2026, 7:23 p.m.
NER Named-entity recognition batch_69d8a5cba708819097467bb7aca7fc65 completed April 10, 2026, 7:24 a.m.
NED1 Entity disambiguation (via context triple) batch_69f166f16a908190803cc986ce596aa1 completed April 29, 2026, 2:03 a.m.
Created at: April 8, 2026, 9:42 p.m.