Triple

T7419987
Position Surface form Disambiguated ID Type / Status
Subject Cauchy–Kovalevskaya theorem E171220 entity
Predicate isAnalogOf P3882 FINISHED
Object Picard–Lindelöf theorem for ordinary differential equations E22820 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: Picard–Lindelöf theorem for ordinary differential equations | Statement: [Cauchy–Kovalevskaya theorem, isAnalogOf, Picard–Lindelöf theorem for ordinary differential equations]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Picard–Lindelöf theorem for ordinary differential equations
Context triple: [Cauchy–Kovalevskaya theorem, isAnalogOf, Picard–Lindelöf theorem for ordinary differential equations]
  • A. Peano existence theorem
    The Peano existence theorem is a fundamental result in the theory of ordinary differential equations that guarantees the existence (but not necessarily uniqueness) of solutions under mild continuity conditions on the right-hand side.
  • B. local existence and uniqueness theorem chosen
    The local existence and uniqueness theorem is a fundamental result in differential equations that guarantees, under suitable conditions, a single solution passing through a given initial point, valid in some neighborhood of that point.
  • C. 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.
  • D. Carathéodory existence theorem
    The Carathéodory existence theorem is a result in the theory of ordinary differential equations that guarantees the existence (and sometimes uniqueness) of solutions under weaker regularity conditions on the right-hand side than those required by classical theorems like Picard–Lindelöf.
  • E. Bendixson–Dulac criterion
    The Bendixson–Dulac criterion is a result in the qualitative theory of planar dynamical systems that provides conditions under which a system has no periodic orbits in a given region.
  • 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_69c68a625d048190af70eb8b63bec5a0 completed March 27, 2026, 1:47 p.m.
NER Named-entity recognition batch_69c6f2ea61248190886e8e55b42ba5f1 completed March 27, 2026, 9:13 p.m.
NED1 Entity disambiguation (via context triple) batch_69c81ef7fc808190a564ab4d9d97ab37 completed March 28, 2026, 6:33 p.m.
Created at: March 27, 2026, 3:11 p.m.