Triple

T11411519
Position Surface form Disambiguated ID Type / Status
Subject Gelfand representation of commutative C*-algebras E270381 entity
Predicate relatesTo P37 FINISHED
Object Riesz 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 representation theorem | Statement: [Gelfand representation of commutative C*-algebras, relatesTo, Riesz representation theorem]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Riesz representation theorem
Context triple: [Gelfand representation of commutative C*-algebras, relatesTo, Riesz 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. Riesz–Fischer theorem
    The Riesz–Fischer theorem is a fundamental result in functional analysis that establishes the equivalence between square-summable sequences and square-integrable functions, providing the foundation for the Hilbert space structure of L² spaces.
  • C. 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).
  • D. Riesz lemma
    Riesz lemma is a fundamental result in functional analysis that characterizes how, in an infinite-dimensional normed space, one can find unit vectors that stay a fixed distance away from any given proper closed subspace.
  • E. 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.
  • 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_69d6aaddeaa8819088b30ef7b50598c9 completed April 8, 2026, 7:22 p.m.
NER Named-entity recognition batch_69d8015017d08190b4020c76545556d6 completed April 9, 2026, 7:43 p.m.
NED1 Entity disambiguation (via context triple) batch_69e5b855f0508190a2e57ef9407ddb1a completed April 20, 2026, 5:23 a.m.
Created at: April 8, 2026, 9:34 p.m.