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.