Triple

T179447
Position Surface form Disambiguated ID Type / Status
Subject Janet–Cartan theorem E3651 entity
Predicate relatedTo P37 FINISHED
Object Cartan–Janet system of partial differential equations E3651 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: Cartan–Janet system of partial differential equations | Statement: [Janet–Cartan theorem, relatedTo, Cartan–Janet system of partial differential equations]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Cartan–Janet system of partial differential equations
Context triple: [Janet–Cartan theorem, relatedTo, Cartan–Janet system of partial differential equations]
  • A. Janet–Cartan theorem chosen
    The Janet–Cartan theorem is a fundamental result in differential geometry stating that any real-analytic Riemannian manifold can be locally isometrically embedded into a Euclidean space of sufficiently high dimension.
  • B. Nash embedding theorem
    The Nash embedding theorem is a fundamental result in differential geometry that shows any Riemannian manifold can be isometrically embedded into some Euclidean space, thereby realizing abstract curved spaces as concrete subsets of standard Euclidean space.
  • C. Riemannian manifolds
    Riemannian manifolds are smooth manifolds equipped with an inner product on each tangent space that allows one to measure lengths, angles, and curvature in a curved geometric setting.
  • D. Feynman–Kac formula
    The Feynman–Kac formula is a fundamental result connecting solutions of certain partial differential equations with expectations over stochastic processes, forming a bridge between quantum mechanics, probability theory, and mathematical finance.
  • E. Dyson’s transform in number theory
    Dyson’s transform in number theory is a combinatorial technique introduced by Freeman Dyson to manipulate and relate integer partitions, particularly in the study of partition identities and congruences.
  • 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_69a25374990081909766d30c79a18e0e completed Feb. 28, 2026, 2:31 a.m.
NER Named-entity recognition batch_69a25900709c8190a65e778936be5dd5 completed Feb. 28, 2026, 2:54 a.m.
NED1 Entity disambiguation (via context triple) batch_69a2f0b4f1708190b766e1d9b43038ed completed Feb. 28, 2026, 1:42 p.m.
Created at: Feb. 28, 2026, 2:39 a.m.