Triple

T12574038
Position Surface form Disambiguated ID Type / Status
Subject Timothy Gowers E271119 entity
Predicate notableWork P4 FINISHED
Object Gowers inverse theorem in additive combinatorics
The Gowers inverse theorem in additive combinatorics is a fundamental result that characterizes functions with large Gowers uniformity norms by showing they must correlate with structured objects such as polynomial phase functions, underpinning much of modern higher-order Fourier analysis.
E992627 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 inverse theorem in additive combinatorics | Statement: [Timothy Gowers, notableWork, Gowers inverse theorem in additive combinatorics]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Gowers inverse theorem in additive combinatorics
Context triple: [Timothy Gowers, notableWork, Gowers inverse theorem in additive combinatorics]
  • A. 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.
  • B. Gowers–Hatami stability theorem
    The Gowers–Hatami stability theorem is a result in functional analysis and group theory that characterizes when approximate representations of finite groups are close to genuine representations, providing a quantitative form of stability for such structures.
  • C. 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.
  • D. 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.
  • E. 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.
  • 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 inverse theorem in additive combinatorics
Triple: [Timothy Gowers, notableWork, Gowers inverse theorem in additive combinatorics]
Generated description
The Gowers inverse theorem in additive combinatorics is a fundamental result that characterizes functions with large Gowers uniformity norms by showing they must correlate with structured objects such as polynomial phase functions, underpinning much of modern higher-order Fourier analysis.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Gowers inverse theorem in additive combinatorics
Target entity description: The Gowers inverse theorem in additive combinatorics is a fundamental result that characterizes functions with large Gowers uniformity norms by showing they must correlate with structured objects such as polynomial phase functions, underpinning much of modern higher-order Fourier analysis.
  • A. 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.
  • B. Gowers–Hatami stability theorem
    The Gowers–Hatami stability theorem is a result in functional analysis and group theory that characterizes when approximate representations of finite groups are close to genuine representations, providing a quantitative form of stability for such structures.
  • C. 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.
  • D. 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.
  • E. 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.
  • 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_69f65eb8ec888190b46a0b48840efd20 completed May 2, 2026, 8:29 p.m.
NEDg Description generation batch_69f660294004819089714099a08085f6 completed May 2, 2026, 8:35 p.m.
NED2 Entity disambiguation (via description) batch_69f6613ce1108190851cf8491fe666c8 completed May 2, 2026, 8:40 p.m.
Created at: April 9, 2026, 4:42 p.m.