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.