Triple

T7871867
Position Surface form Disambiguated ID Type / Status
Subject Jacobi operator E182754 entity
Predicate relatedTo P37 FINISHED
Object Sturm–Liouville theory E697758 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: Sturm–Liouville theory | Statement: [Jacobi operator, relatedTo, Sturm–Liouville theory]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Sturm–Liouville theory
Context triple: [Jacobi operator, relatedTo, Sturm–Liouville theory]
  • A. Sturm–Liouville problem chosen
    The Sturm–Liouville problem is a class of second-order linear differential equations with boundary conditions that yield real eigenvalues and orthogonal eigenfunctions forming a basis for function expansions in mathematical physics and engineering.
  • B. Gelfand–Levitan theory
    Gelfand–Levitan theory is a foundational framework in inverse spectral theory that reconstructs differential operators or potentials from their spectral data using integral equations.
  • C. Methods of Mathematical Physics
    Methods of Mathematical Physics is a classic two-volume textbook by Richard Courant and David Hilbert that rigorously develops the mathematical foundations and techniques used in theoretical physics.
  • D. Green's functions
    Green's functions are mathematical tools used in physics and engineering to solve inhomogeneous differential equations and describe the propagation of fields or particles in space and time.
  • E. Orthogonal Polynomials
    Orthogonal Polynomials is a classic mathematical monograph by Gábor Szegő that systematically develops the theory and applications of orthogonal polynomial systems in analysis and approximation theory.
  • 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_69ca82894d9081908a832bfce71a4714 completed March 30, 2026, 2:02 p.m.
NER Named-entity recognition batch_69cb39a5950481908399211c5dfe2569 completed March 31, 2026, 3:04 a.m.
NED1 Entity disambiguation (via context triple) batch_69cbdf844f24819091cb8757d29a4a3f completed March 31, 2026, 2:51 p.m.
Created at: March 30, 2026, 4:56 p.m.