Triple

T13660566
Position Surface form Disambiguated ID Type / Status
Subject Picard–Vessiot theory E326982 entity
Predicate isPartOf P10 FINISHED
Object differential Galois theory E326982 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: differential Galois theory | Statement: [Picard–Vessiot theory, isPartOf, differential Galois theory]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: differential Galois theory
Context triple: [Picard–Vessiot theory, isPartOf, differential Galois theory]
  • A. differential Galois group
    A differential Galois group is the group of differential field automorphisms of a Picard–Vessiot extension that captures the algebraic symmetries of solutions to a linear differential equation.
  • B. Picard–Vessiot theory chosen
    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. Galois theory
    Galois theory is a branch of abstract algebra that studies field extensions and polynomial equations through the structure of their associated symmetry groups.
  • D. theory of D-modules
    The theory of D-modules is a branch of algebraic analysis and algebraic geometry that studies modules over rings of differential operators, providing a powerful framework for understanding systems of linear differential equations and their geometric and representation-theoretic properties.
  • E. 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.
  • 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_69d8076d8270819092afc2f0e9c359a8 completed April 9, 2026, 8:09 p.m.
NER Named-entity recognition batch_69dbc620df208190afaccf3ddd10aa60 completed April 12, 2026, 4:19 p.m.
NED1 Entity disambiguation (via context triple) batch_69f794395618819094a7f0ffcf5d3fb6 completed May 3, 2026, 6:30 p.m.
Created at: April 9, 2026, 9:52 p.m.