Triple

T5176473
Position Surface form Disambiguated ID Type / Status
Subject Lazarus Fuchs E116810 entity
Predicate notableConcept P201 FINISHED
Object 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.
E500440 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 singularity | Statement: [Lazarus Fuchs, notableConcept, Fuchsian singularity]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Fuchsian singularity
Context triple: [Lazarus Fuchs, notableConcept, Fuchsian singularity]
  • A. Cauchy horizon
    A Cauchy horizon is a lightlike boundary in certain spacetime solutions of general relativity, such as rotating black holes, beyond which the deterministic evolution from initial data breaks down.
  • B. Cauchy–Riemann equations
    The Cauchy–Riemann equations are fundamental conditions in complex analysis that characterize when a complex-valued function is holomorphic (complex differentiable).
  • C. Picard theorem
    Picard theorem is a fundamental result in complex analysis stating that entire non-constant functions take on all possible complex values, with at most one exception.
  • D. Weierstrass preparation theorem
    The Weierstrass preparation theorem is a fundamental result in complex analysis and analytic geometry that locally expresses analytic functions near a zero as a product of a polynomial and a unit, enabling a power-series analogue of factorization.
  • E. Riemann–Hurwitz formula
    The Riemann–Hurwitz formula is a fundamental result in algebraic geometry and complex analysis that relates the genera of two Riemann surfaces connected by a branched covering map, accounting for the ramification data.
  • 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 singularity
Triple: [Lazarus Fuchs, notableConcept, Fuchsian singularity]
Generated description
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.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Fuchsian singularity
Target entity description: 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.
  • A. Cauchy horizon
    A Cauchy horizon is a lightlike boundary in certain spacetime solutions of general relativity, such as rotating black holes, beyond which the deterministic evolution from initial data breaks down.
  • B. Cauchy–Riemann equations
    The Cauchy–Riemann equations are fundamental conditions in complex analysis that characterize when a complex-valued function is holomorphic (complex differentiable).
  • C. Picard theorem
    Picard theorem is a fundamental result in complex analysis stating that entire non-constant functions take on all possible complex values, with at most one exception.
  • D. Weierstrass preparation theorem
    The Weierstrass preparation theorem is a fundamental result in complex analysis and analytic geometry that locally expresses analytic functions near a zero as a product of a polynomial and a unit, enabling a power-series analogue of factorization.
  • E. Riemann–Hurwitz formula
    The Riemann–Hurwitz formula is a fundamental result in algebraic geometry and complex analysis that relates the genera of two Riemann surfaces connected by a branched covering map, accounting for the ramification data.
  • 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.