Triple

T5729450
Position Surface form Disambiguated ID Type / Status
Subject Banach fixed-point theorem E126344 entity
Predicate relatedTo P37 FINISHED
Object Schauder fixed-point theorem E121350 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: Schauder fixed-point theorem | Statement: [Banach fixed-point theorem, relatedTo, Schauder fixed-point theorem]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Schauder fixed-point theorem
Context triple: [Banach fixed-point theorem, relatedTo, Schauder fixed-point theorem]
  • A. Schauder fixed-point theorem chosen
    The Schauder fixed-point theorem is a fundamental result in functional analysis that guarantees the existence of fixed points for continuous compact mappings on convex closed subsets of Banach spaces, generalizing the Brouwer fixed-point theorem to infinite-dimensional settings.
  • B. Banach fixed-point theorem
    The Banach fixed-point theorem is a fundamental result in metric space theory that guarantees the existence and uniqueness of a fixed point for any contraction mapping and provides a method for finding it via iterative approximation.
  • C. Glicksberg fixed-point theorem
    The Glicksberg fixed-point theorem is a result in functional analysis that extends Kakutani’s fixed-point theorem to certain infinite-dimensional or compact convex subsets of locally convex topological vector spaces.
  • D. Kakutani fixed-point theorem
    The Kakutani fixed-point theorem is a fundamental result in mathematical analysis and game theory that guarantees the existence of fixed points for certain set-valued (multivalued) functions, underpinning key existence proofs such as Nash equilibria.
  • E. Brouwer fixed-point theorem
    The Brouwer fixed-point theorem is a fundamental result in topology stating that any continuous function from a compact convex set (such as a closed disk) to itself has at least one fixed point.
  • 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_69c07dffe45481909eb617e40c83bd14 completed March 22, 2026, 11:40 p.m.
Created at: March 22, 2026, 3:47 p.m.