Triple

T20404799
Position Surface form Disambiguated ID Type / Status
Subject Fuchsian differential equation E500438 entity
Predicate relatedTo P37 FINISHED
Object Picard–Fuchs equation — NE NERFINISHED

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: Picard–Fuchs equation | Statement: [Fuchsian differential equation, relatedTo, Picard–Fuchs equation]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Picard–Fuchs equation
Context triple: [Fuchsian differential equation, relatedTo, Picard–Fuchs 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. Riemann–Hilbert correspondence
    The Riemann–Hilbert correspondence is a fundamental result in mathematics that establishes an equivalence between certain differential equations (or flat connections) on complex manifolds and representations of their fundamental groups, linking analytic and topological data.
  • C. Bernstein–Sato polynomial
    The Bernstein–Sato polynomial is a fundamental object in algebraic analysis and singularity theory that encodes deep information about the behavior of functions and their singularities via differential equations.
  • D. Grothendieck–Ogg–Shafarevich formula
    The Grothendieck–Ogg–Shafarevich formula is a result in arithmetic geometry that relates the Euler characteristic of an ℓ-adic sheaf on a curve over a finite field to local invariants such as conductors and ramification data.
  • E. 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.
  • F. None of above.
  • G. Unsure - the case is ambiguous/there is not enough information to decide.

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.