Triple

T16892546
Position Surface form Disambiguated ID Type / Status
Subject Banach–Alaoglu theorem E424210 entity
Predicate relatedTo P37 FINISHED
Object Krein–Milman theorem E506849 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: Krein–Milman theorem | Statement: [Banach–Alaoglu theorem, relatedTo, Krein–Milman theorem]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Krein–Milman theorem
Context triple: [Banach–Alaoglu theorem, relatedTo, Krein–Milman theorem]
  • A. Krein–Milman theorem chosen
    The Krein–Milman theorem is a fundamental result in functional analysis and convex geometry stating that a compact convex set in a locally convex topological vector space is the closed convex hull of its extreme points.
  • B. Banach–Alaoglu theorem
    The Banach–Alaoglu theorem is a fundamental result in functional analysis stating that the closed unit ball in the dual of a normed space is compact in the weak-* topology.
  • C. Hahn–Banach theorem
    The Hahn–Banach theorem is a fundamental result in functional analysis that guarantees the extension of bounded linear functionals from a subspace to the whole space without increasing their norm.
  • D. Banach–Mazur theorem
    The Banach–Mazur theorem is a fundamental result in functional analysis that characterizes separable Banach spaces as isometrically isomorphic to closed subspaces of spaces of continuous functions on compact metric spaces.
  • E. Borel–Lebesgue theorem
    The Borel–Lebesgue theorem is a fundamental result in real analysis and topology that characterizes compact subsets of Euclidean space via the property that every open cover admits a finite subcover.
  • 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_69d889da3e8c8190a2b118f383f0beac completed April 10, 2026, 5:25 a.m.
NER Named-entity recognition batch_69e3bbc5a5308190937ebd05356bd91d completed April 18, 2026, 5:13 p.m.
NED1 Entity disambiguation (via context triple) batch_6a00c7a7fd8481908ef82a13418b1c2d completed May 10, 2026, 6 p.m.
Created at: April 10, 2026, 5:29 a.m.