Triple

T8640754
Position Surface form Disambiguated ID Type / Status
Subject Frigyes Riesz E204639 entity
Predicate knownFor P22 FINISHED
Object Riesz–Markov–Kakutani representation theorem E621089 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: Riesz–Markov–Kakutani representation theorem | Statement: [Frigyes Riesz, knownFor, Riesz–Markov–Kakutani representation theorem]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Riesz–Markov–Kakutani representation theorem
Context triple: [Frigyes Riesz, knownFor, Riesz–Markov–Kakutani representation theorem]
  • A. Riesz representation theorem chosen
    The Riesz representation theorem is a fundamental result in functional analysis that characterizes continuous linear functionals on Hilbert spaces as inner products with a unique vector in the space.
  • B. Gelfand–Naimark theorem
    The Gelfand–Naimark theorem is a foundational result in functional analysis that characterizes C*-algebras as algebras of bounded operators on a Hilbert space (and, in the commutative case, as algebras of continuous functions on a locally compact Hausdorff space).
  • C. Banach–Stone theorem
    The Banach–Stone theorem is a fundamental result in functional analysis that characterizes compact Hausdorff spaces via isometric isomorphisms between their spaces of continuous real- or complex-valued functions.
  • D. Krein–Milman theorem
    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.
  • E. Carathéodory’s extension theorem
    Carathéodory’s extension theorem is a fundamental result in measure theory that guarantees a unique extension of a pre-measure defined on an algebra of sets to a complete measure on the generated σ-algebra.
  • 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_69ca834ca1c88190a11ffb0200342fac completed March 30, 2026, 2:06 p.m.
NER Named-entity recognition batch_69cc47944d1c819081f448f14d04bf9d completed March 31, 2026, 10:15 p.m.
NED1 Entity disambiguation (via context triple) batch_69cebc340528819085c80b69d6d32a34 completed April 2, 2026, 6:57 p.m.
Created at: March 30, 2026, 6:28 p.m.