Triple

T5176469
Position Surface form Disambiguated ID Type / Status
Subject Lazarus Fuchs E116810 entity
Predicate notableWork P4 FINISHED
Object 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.
E500438 NE FINISHED

How this triple was built (4 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, notableWork, Fuchsian differential equation]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Fuchsian differential equation
Context triple: [Lazarus Fuchs, notableWork, Fuchsian differential equation]
  • A. 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.
  • B. 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.
  • C. Weierstrass elliptic functions
    Weierstrass elliptic functions are a class of doubly periodic meromorphic functions that play a central role in the theory of elliptic curves and complex analysis.
  • D. Jacobi elliptic functions
    Jacobi elliptic functions are a family of doubly periodic complex functions that generalize trigonometric functions and play a central role in the theory of elliptic integrals and many areas of mathematical physics.
  • E. Cauchy–Riemann equations
    The Cauchy–Riemann equations are fundamental conditions in complex analysis that characterize when a complex-valued function is holomorphic (complex differentiable).
  • F. None of above. chosen
  • G. Unsure - the case is ambiguous/there is not enough information to decide.
NEDg Description generation gpt-5.1
Instruction
Generate a one-sentence description of the target entity. 
You are given a context triple in the form (subject, predicate, object), where the object is the target entity. 
# Instructions
Use the triple to infer relevant information about the entity. Describe the entity based on what is most defining, well-known. 
Avoid repeating the information from the triple, unless really essential.
# Response Format
Return only the sentence: "Description: [one-sentence description of the target entity]"
Input
Entity: Fuchsian differential equation
Triple: [Lazarus Fuchs, notableWork, Fuchsian differential equation]
Generated description
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.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Fuchsian differential equation
Target entity description: 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.
  • A. 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.
  • B. 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.
  • C. Weierstrass elliptic functions
    Weierstrass elliptic functions are a class of doubly periodic meromorphic functions that play a central role in the theory of elliptic curves and complex analysis.
  • D. Jacobi elliptic functions
    Jacobi elliptic functions are a family of doubly periodic complex functions that generalize trigonometric functions and play a central role in the theory of elliptic integrals and many areas of mathematical physics.
  • E. Cauchy–Riemann equations
    The Cauchy–Riemann equations are fundamental conditions in complex analysis that characterize when a complex-valued function is holomorphic (complex differentiable).
  • F. None of above. chosen

Provenance (5 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_69bed94e269481908118fd1af1fc6a44 completed March 21, 2026, 5:45 p.m.
NEDg Description generation batch_69bedd266d00819090d857ca08b411c7 completed March 21, 2026, 6:02 p.m.
NED2 Entity disambiguation (via description) batch_69bedda0b8dc81909942627e735023e3 completed March 21, 2026, 6:04 p.m.
Created at: March 20, 2026, 1:45 p.m.