Triple

T20404892
Position Surface form Disambiguated ID Type / Status
Subject Fuchsian singularity E500440 entity
Predicate relatedConcept P37 FINISHED
Object Frobenius method NE NERFINISHED

How this triple was built (3 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: Frobenius method | Statement: [Fuchsian singularity, relatedConcept, Frobenius method]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Frobenius method
Context triple: [Fuchsian singularity, relatedConcept, Frobenius method]
  • A. Fuchsian differential equation
    A Fuchsian differential equation is a type of linear ordinary differential equation characterized by having only regular singular points, extensively studied in complex analysis and the theory of special functions.
  • B. Kummer's differential equation
    Kummer's differential equation is a second-order linear ordinary differential equation whose solutions are the confluent hypergeometric functions, playing a central role in special function theory and mathematical physics.
  • C. Cauchy–Euler equation
    The Cauchy–Euler equation is a type of linear ordinary differential equation with variable coefficients that often appears in problems with power-law or scale-invariant behavior.
  • D. Gauss hypergeometric function
    The Gauss hypergeometric function is a special function defined by a power series that generalizes many elementary and higher transcendental functions and plays a central role in mathematical analysis, differential equations, and mathematical physics.
  • E. Sturm–Liouville problem
    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.
  • F. None of above. chosen
  • G. Unsure - the case is ambiguous/there is not enough information to decide.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Frobenius method
Target entity description: The Frobenius method is a technique in differential equations for finding power series solutions near singular points, especially regular (Fuchsian) singularities.
  • A. Fuchsian differential equation
    A Fuchsian differential equation is a type of linear ordinary differential equation characterized by having only regular singular points, extensively studied in complex analysis and the theory of special functions.
  • B. Kummer's differential equation
    Kummer's differential equation is a second-order linear ordinary differential equation whose solutions are the confluent hypergeometric functions, playing a central role in special function theory and mathematical physics.
  • C. Cauchy–Euler equation
    The Cauchy–Euler equation is a type of linear ordinary differential equation with variable coefficients that often appears in problems with power-law or scale-invariant behavior.
  • D. Gauss hypergeometric function
    The Gauss hypergeometric function is a special function defined by a power series that generalizes many elementary and higher transcendental functions and plays a central role in mathematical analysis, differential equations, and mathematical physics.
  • E. Sturm–Liouville problem
    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.
  • F. None of above. chosen

Provenance (2 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_69e0b4a81bec8190b69adfdc1336a015 completed April 16, 2026, 10:06 a.m.
NER Named-entity recognition batch_69e6799161c48190825eca3027d1aa51 completed April 20, 2026, 7:08 p.m.
Created at: April 16, 2026, 11:29 a.m.