Triple

T12574034
Position Surface form Disambiguated ID Type / Status
Subject Timothy Gowers E271119 entity
Predicate notableWork P4 FINISHED
Object Gowers uniformity norms
Gowers uniformity norms are a family of higher-order norms in additive combinatorics used to measure the uniformity of functions and sequences, playing a central role in results such as Szemerédi’s theorem on arithmetic progressions.
E989311 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 uniformity norms | Statement: [Timothy Gowers, notableWork, Gowers uniformity norms]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Gowers uniformity norms
Context triple: [Timothy Gowers, notableWork, Gowers uniformity norms]
  • A. Szemerédi's theorem
    Szemerédi's theorem is a fundamental result in combinatorial number theory stating that any subset of the integers with positive upper density contains arbitrarily long arithmetic progressions.
  • B. Erdős discrepancy problem
    The Erdős discrepancy problem is a famous question in combinatorial number theory that asks whether every infinite ±1 sequence has arbitrarily large discrepancy along some homogeneous arithmetic progression.
  • C. Turán–Kubilius inequality
    The Turán–Kubilius inequality is a fundamental result in probabilistic number theory that provides bounds on the distribution of additive arithmetic functions.
  • D. Green–Tao theorem
    The Green–Tao theorem is a landmark result in number theory proving that the sequence of prime numbers contains arbitrarily long arithmetic progressions.
  • E. Three regularity results in harmonic analysis
    "Three regularity results in harmonic analysis" is the doctoral thesis of mathematician Terence Tao, focusing on advanced problems in harmonic analysis and the study of regularity properties of functions and operators.
  • 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 uniformity norms
Triple: [Timothy Gowers, notableWork, Gowers uniformity norms]
Generated description
Gowers uniformity norms are a family of higher-order norms in additive combinatorics used to measure the uniformity of functions and sequences, playing a central role in results such as Szemerédi’s theorem on arithmetic progressions.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Gowers uniformity norms
Target entity description: Gowers uniformity norms are a family of higher-order norms in additive combinatorics used to measure the uniformity of functions and sequences, playing a central role in results such as Szemerédi’s theorem on arithmetic progressions.
  • A. Szemerédi's theorem
    Szemerédi's theorem is a fundamental result in combinatorial number theory stating that any subset of the integers with positive upper density contains arbitrarily long arithmetic progressions.
  • B. Erdős discrepancy problem
    The Erdős discrepancy problem is a famous question in combinatorial number theory that asks whether every infinite ±1 sequence has arbitrarily large discrepancy along some homogeneous arithmetic progression.
  • C. Turán–Kubilius inequality
    The Turán–Kubilius inequality is a fundamental result in probabilistic number theory that provides bounds on the distribution of additive arithmetic functions.
  • D. Green–Tao theorem
    The Green–Tao theorem is a landmark result in number theory proving that the sequence of prime numbers contains arbitrarily long arithmetic progressions.
  • E. Three regularity results in harmonic analysis
    "Three regularity results in harmonic analysis" is the doctoral thesis of mathematician Terence Tao, focusing on advanced problems in harmonic analysis and the study of regularity properties of functions and operators.
  • 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.