Triple
T16249781
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Steinhaus theorem |
E394469
|
entity |
| Predicate | relatedTo |
P37
|
FINISHED |
| Object |
Ruzsa triangle inequality
The Ruzsa triangle inequality is a fundamental result in additive combinatorics that bounds the size of sumsets and difference sets, playing a key role in understanding the structure of sets with small sumset growth.
|
E1202382
|
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: Ruzsa triangle inequality | Statement: [Steinhaus theorem, relatedTo, Ruzsa triangle inequality]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Ruzsa triangle inequality Context triple: [Steinhaus theorem, relatedTo, Ruzsa triangle inequality]
-
A.
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.
-
B.
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.
-
C.
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.
-
D.
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.
-
E.
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.
- 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: Ruzsa triangle inequality Triple: [Steinhaus theorem, relatedTo, Ruzsa triangle inequality]
Generated description
The Ruzsa triangle inequality is a fundamental result in additive combinatorics that bounds the size of sumsets and difference sets, playing a key role in understanding the structure of sets with small sumset growth.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Ruzsa triangle inequality Target entity description: The Ruzsa triangle inequality is a fundamental result in additive combinatorics that bounds the size of sumsets and difference sets, playing a key role in understanding the structure of sets with small sumset growth.
-
A.
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.
-
B.
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.
-
C.
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.
-
D.
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.
-
E.
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.
- 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_69d87f2171208190951025e526947816 |
completed | April 10, 2026, 4:40 a.m. |
| NER | Named-entity recognition | batch_69e2459606f88190a53905186f7f73be |
completed | April 17, 2026, 2:37 p.m. |
| NED1 | Entity disambiguation (via context triple) | batch_6a000ee568a48190835ce76f84461044 |
completed | May 10, 2026, 4:51 a.m. |
| NEDg | Description generation | batch_6a0011995ff481908bbca9f9cfb41bf0 |
completed | May 10, 2026, 5:03 a.m. |
| NED2 | Entity disambiguation (via description) | batch_6a0012669ff48190884367b92962a6d4 |
completed | May 10, 2026, 5:06 a.m. |
Created at: April 10, 2026, 5:04 a.m.