Triple

T12574037
Position Surface form Disambiguated ID Type / Status
Subject Timothy Gowers E271119 entity
Predicate notableWork P4 FINISHED
Object Gowers dichotomy for Banach spaces
Gowers dichotomy for Banach spaces is a fundamental result in functional analysis that classifies infinite-dimensional Banach spaces by showing that each contains either a subspace with an unconditional basis or a hereditarily indecomposable subspace.
E989312 NE FINISHED

How this triple was built (4 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: Gowers dichotomy for Banach spaces | Statement: [Timothy Gowers, notableWork, Gowers dichotomy for Banach spaces]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Gowers dichotomy for Banach spaces
Context triple: [Timothy Gowers, notableWork, Gowers dichotomy for Banach spaces]
  • A. Bourgain–Tzafriri restricted invertibility principle
    The Bourgain–Tzafriri restricted invertibility principle is a fundamental result in functional analysis and operator theory that guarantees the existence of large, well-invertible submatrices within certain classes of linear operators.
  • B. New classes of Lp-spaces
    "New classes of Lp-spaces" is a mathematical work by Jean Bourgain that introduces and studies novel Banach space structures within the framework of Lp spaces, significantly advancing the theory of functional analysis.
  • C. Grothendieck inequality
    The Grothendieck inequality is a fundamental result in functional analysis and theoretical computer science that bounds certain bilinear forms and has deep implications for Banach space theory, operator theory, and approximation algorithms.
  • D. Orlicz spaces
    Orlicz spaces are a class of function spaces that generalize Lebesgue spaces by measuring integrability via convex Orlicz functions rather than fixed power exponents.
  • E. Banach–Saks theorem
    The Banach–Saks theorem is a result in functional analysis stating that every bounded sequence in a reflexive Banach space has a subsequence whose Cesàro means converge in norm.
  • F. None of above. chosen
  • G. Unsure - the case is ambiguous/there is not enough information to decide.
NEDg Description generation gpt-5.1
Instruction
Generate a one-sentence description of the target entity. 
You are given a context triple in the form (subject, predicate, object), where the object is the target entity. 
# Instructions
Use the triple to infer relevant information about the entity. Describe the entity based on what is most defining, well-known. 
Avoid repeating the information from the triple, unless really essential.
# Response Format
Return only the sentence: "Description: [one-sentence description of the target entity]"
Input
Entity: Gowers dichotomy for Banach spaces
Triple: [Timothy Gowers, notableWork, Gowers dichotomy for Banach spaces]
Generated description
Gowers dichotomy for Banach spaces is a fundamental result in functional analysis that classifies infinite-dimensional Banach spaces by showing that each contains either a subspace with an unconditional basis or a hereditarily indecomposable subspace.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Gowers dichotomy for Banach spaces
Target entity description: Gowers dichotomy for Banach spaces is a fundamental result in functional analysis that classifies infinite-dimensional Banach spaces by showing that each contains either a subspace with an unconditional basis or a hereditarily indecomposable subspace.
  • A. Bourgain–Tzafriri restricted invertibility principle
    The Bourgain–Tzafriri restricted invertibility principle is a fundamental result in functional analysis and operator theory that guarantees the existence of large, well-invertible submatrices within certain classes of linear operators.
  • B. New classes of Lp-spaces
    "New classes of Lp-spaces" is a mathematical work by Jean Bourgain that introduces and studies novel Banach space structures within the framework of Lp spaces, significantly advancing the theory of functional analysis.
  • C. Grothendieck inequality
    The Grothendieck inequality is a fundamental result in functional analysis and theoretical computer science that bounds certain bilinear forms and has deep implications for Banach space theory, operator theory, and approximation algorithms.
  • D. Orlicz spaces
    Orlicz spaces are a class of function spaces that generalize Lebesgue spaces by measuring integrability via convex Orlicz functions rather than fixed power exponents.
  • E. Banach–Saks theorem
    The Banach–Saks theorem is a result in functional analysis stating that every bounded sequence in a reflexive Banach space has a subsequence whose Cesàro means converge in norm.
  • F. None of above. chosen

Provenance (5 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_69d7bde87b648190bcd0266e9efde098 completed April 9, 2026, 2:55 p.m.
NER Named-entity recognition batch_69d954a629fc8190a1c3b6777aad4527 completed April 10, 2026, 7:51 p.m.
NED1 Entity disambiguation (via context triple) batch_69f65595826081908035655f7930f55a completed May 2, 2026, 7:50 p.m.
NEDg Description generation batch_69f656a86ff48190bd3debd30e11df80 completed May 2, 2026, 7:55 p.m.
NED2 Entity disambiguation (via description) batch_69f657aa1bf48190a884e0dfce31e30e completed May 2, 2026, 7:59 p.m.
Created at: April 9, 2026, 4:42 p.m.