Triple

T5176472
Position Surface form Disambiguated ID Type / Status
Subject Lazarus Fuchs E116810 entity
Predicate notableConcept P201 FINISHED
Object Fuchsian differential equation E500438 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: Fuchsian differential equation | Statement: [Lazarus Fuchs, notableConcept, Fuchsian differential equation]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Fuchsian differential equation
Context triple: [Lazarus Fuchs, notableConcept, Fuchsian differential equation]
  • A. Fuchsian differential equation chosen
    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. Fuchsian singularity
    A Fuchsian singularity is a type of regular singular point of a linear differential equation in the complex plane, characterized by well-controlled (typically polynomially bounded) behavior of solutions near the singularity.
  • 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. Picard–Vessiot theory
    Picard–Vessiot theory is a branch of differential Galois theory that studies linear differential equations via the symmetries of their solution fields, analogous to classical Galois theory for polynomial equations.
  • E. Fuchsian group
    A Fuchsian group is a discrete group of isometries of the hyperbolic plane, fundamental in the study of Riemann surfaces, modular forms, and hyperbolic geometry.
  • 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_69bd446140f08190becb93c61158f27f completed March 20, 2026, 12:58 p.m.
NER Named-entity recognition batch_69bd797349008190b87ad9d0d3eb667f completed March 20, 2026, 4:44 p.m.
NED1 Entity disambiguation (via context triple) batch_69bee07a6620819089e2b3fcb322a47e completed March 21, 2026, 6:16 p.m.
Created at: March 20, 2026, 1:45 p.m.