Triple

T5729452
Position Surface form Disambiguated ID Type / Status
Subject Banach fixed-point theorem E126344 entity
Predicate relatedTo P37 FINISHED
Object Picard–Lindelöf theorem 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 | Statement: [Banach fixed-point theorem, relatedTo, Picard–Lindelöf theorem]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Picard–Lindelöf theorem
Context triple: [Banach fixed-point theorem, relatedTo, Picard–Lindelöf theorem]
  • 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. 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. Poincaré–Bendixson theorem
    The Poincaré–Bendixson theorem is a fundamental result in the qualitative theory of dynamical systems that characterizes the possible long-term behaviors of trajectories in two-dimensional continuous flows, ruling out chaotic dynamics in the plane.
  • 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_69c0082f723881908ce8bb13a0c0f8b7 completed March 22, 2026, 3:18 p.m.
NER Named-entity recognition batch_69c025303860819093e51f176babed71 completed March 22, 2026, 5:21 p.m.
NED1 Entity disambiguation (via context triple) batch_69c05a8cca748190b471c842fd2ce218 completed March 22, 2026, 9:09 p.m.
Created at: March 22, 2026, 3:47 p.m.