Triple

T20404822
Position Surface form Disambiguated ID Type / Status
Subject Fuchsian differential equation E500438 entity
Predicate relatedConcept P37 FINISHED
Object Fuchs’ theorem
Fuchs’ theorem is a result in the theory of linear differential equations that characterizes when all singular points of such an equation are regular (i.e., the equation is Fuchsian) based on the behavior of its coefficients.
E1429959 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: Fuchs’ theorem | Statement: [Fuchsian differential equation, relatedConcept, Fuchs’ theorem]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Fuchs’ theorem
Context triple: [Fuchsian differential equation, relatedConcept, Fuchs’ theorem]
  • A. Cauchy–Kovalevskaya theorem
    The Cauchy–Kovalevskaya theorem is a fundamental result in partial differential equations that guarantees the existence and uniqueness of analytic solutions to certain initial value problems under appropriate analyticity conditions.
  • B. Busemann–Feller theorem
    The Busemann–Feller theorem is a result in geometric measure theory that characterizes when a metric space is geodesic by relating distance properties to the existence of shortest paths between points.
  • 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. Mittag-Leffler theorem
    The Mittag-Leffler theorem is a fundamental result in complex analysis that characterizes meromorphic functions by allowing the construction of such functions with prescribed principal parts at given poles.
  • E. Malgrange–Ehrenpreis theorem
    The Malgrange–Ehrenpreis theorem is a fundamental result in the theory of partial differential equations stating that every linear partial differential operator with constant coefficients admits a fundamental solution.
  • 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: Fuchs’ theorem
Triple: [Fuchsian differential equation, relatedConcept, Fuchs’ theorem]
Generated description
Fuchs’ theorem is a result in the theory of linear differential equations that characterizes when all singular points of such an equation are regular (i.e., the equation is Fuchsian) based on the behavior of its coefficients.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Fuchs’ theorem
Target entity description: Fuchs’ theorem is a result in the theory of linear differential equations that characterizes when all singular points of such an equation are regular (i.e., the equation is Fuchsian) based on the behavior of its coefficients.
  • A. Cauchy–Kovalevskaya theorem
    The Cauchy–Kovalevskaya theorem is a fundamental result in partial differential equations that guarantees the existence and uniqueness of analytic solutions to certain initial value problems under appropriate analyticity conditions.
  • B. Busemann–Feller theorem
    The Busemann–Feller theorem is a result in geometric measure theory that characterizes when a metric space is geodesic by relating distance properties to the existence of shortest paths between points.
  • 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. Mittag-Leffler theorem
    The Mittag-Leffler theorem is a fundamental result in complex analysis that characterizes meromorphic functions by allowing the construction of such functions with prescribed principal parts at given poles.
  • E. Malgrange–Ehrenpreis theorem
    The Malgrange–Ehrenpreis theorem is a fundamental result in the theory of partial differential equations stating that every linear partial differential operator with constant coefficients admits a fundamental solution.
  • 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_69e0b4a81bec8190b69adfdc1336a015 completed April 16, 2026, 10:06 a.m.
NER Named-entity recognition batch_69e6799161c48190825eca3027d1aa51 completed April 20, 2026, 7:08 p.m.
NED1 Entity disambiguation (via context triple) batch_6a087b1a1328819094815b69aa19daab completed May 16, 2026, 2:11 p.m.
NEDg Description generation batch_6a088014c30c8190937586dc3f23862e completed May 16, 2026, 2:32 p.m.
NED2 Entity disambiguation (via description) batch_6a08810e37c08190bd7e8b584204064c completed May 16, 2026, 2:37 p.m.
Created at: April 16, 2026, 11:29 a.m.