Triple

T20627327
Position Surface form Disambiguated ID Type / Status
Subject Darboux theorem E506852 entity
Predicate relatedTo P37 FINISHED
Object Moser trick
Moser trick is a technique in symplectic geometry that uses a time-dependent flow to show that certain families of differential forms are equivalent, and is a key tool in proving results like Darboux’s theorem.
E1440915 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: Moser trick | Statement: [Darboux theorem, relatedTo, Moser trick]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Moser trick
Context triple: [Darboux theorem, relatedTo, Moser trick]
  • A. Turán's method
    Turán's method is a powerful technique in analytic and probabilistic number theory that uses inequalities for power sums of sequences to derive bounds for arithmetic functions and related quantities.
  • B. Grothendieck inequality
    The Grothendieck inequality is a fundamental result in functional analysis and theoretical computer science that bounds certain bilinear forms and has deep implications for Banach space theory, operator theory, and approximation algorithms.
  • C. Calderón transference principle
    The Calderón transference principle is a fundamental result in harmonic analysis that allows boundedness properties of operators on one group (often the real line or integers) to be transferred to analogous operators on more general groups or measure spaces.
  • D. 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.
  • E. 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.
  • 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: Moser trick
Triple: [Darboux theorem, relatedTo, Moser trick]
Generated description
Moser trick is a technique in symplectic geometry that uses a time-dependent flow to show that certain families of differential forms are equivalent, and is a key tool in proving results like Darboux’s theorem.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Moser trick
Target entity description: Moser trick is a technique in symplectic geometry that uses a time-dependent flow to show that certain families of differential forms are equivalent, and is a key tool in proving results like Darboux’s theorem.
  • A. Turán's method
    Turán's method is a powerful technique in analytic and probabilistic number theory that uses inequalities for power sums of sequences to derive bounds for arithmetic functions and related quantities.
  • B. Grothendieck inequality
    The Grothendieck inequality is a fundamental result in functional analysis and theoretical computer science that bounds certain bilinear forms and has deep implications for Banach space theory, operator theory, and approximation algorithms.
  • C. Calderón transference principle
    The Calderón transference principle is a fundamental result in harmonic analysis that allows boundedness properties of operators on one group (often the real line or integers) to be transferred to analogous operators on more general groups or measure spaces.
  • D. 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.
  • E. 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.
  • 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_69e0b4bd4a0081908d4e97a590a33fb2 completed April 16, 2026, 10:06 a.m.
NER Named-entity recognition batch_69e6abe645888190b639ebedc5b3041a completed April 20, 2026, 10:42 p.m.
NED1 Entity disambiguation (via context triple) batch_6a08bb1d9fc881909afe38600d8556b1 completed May 16, 2026, 6:44 p.m.
NEDg Description generation batch_6a08bbb64c40819080b2ea24d1f774ff completed May 16, 2026, 6:47 p.m.
NED2 Entity disambiguation (via description) batch_6a08bc4ea25881909fa71fe2f1b6ddb4 completed May 16, 2026, 6:49 p.m.
Created at: April 16, 2026, 11:42 a.m.