Triple

T10216096
Position Surface form Disambiguated ID Type / Status
Subject Arnaud Denjoy E242444 entity
Predicate knownFor P22 FINISHED
Object Denjoy–Young–Saks theorem
The Denjoy–Young–Saks theorem is a result in real analysis that classifies the possible behaviors of the derivative of a real function at almost every point on the real line.
E850675 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: Denjoy–Young–Saks theorem | Statement: [Arnaud Denjoy, knownFor, Denjoy–Young–Saks theorem]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Denjoy–Young–Saks theorem
Context triple: [Arnaud Denjoy, knownFor, Denjoy–Young–Saks theorem]
  • A. Carathéodory existence theorem
    The Carathéodory existence theorem is a result in the theory of ordinary differential equations that guarantees the existence (and sometimes uniqueness) of solutions under weaker regularity conditions on the right-hand side than those required by classical theorems like Picard–Lindelöf.
  • B. Darboux theorem
    The Darboux theorem is a fundamental result in symplectic geometry stating that all symplectic manifolds are locally symplectomorphic to the standard symplectic space, implying that the symplectic form can always be put into a canonical local normal form.
  • C. Lebesgue differentiation theorem
    The Lebesgue differentiation theorem is a fundamental result in real analysis stating that, for an integrable function, the averages over shrinking neighborhoods converge almost everywhere to the function’s pointwise value.
  • D. Banach–Saks theorem
    The Banach–Saks theorem is a result in functional analysis stating that every bounded sequence in a reflexive Banach space has a subsequence whose Cesàro means converge in norm.
  • E. Du Bois-Reymond function
    The Du Bois-Reymond function is a classic example of a continuous but nowhere differentiable function, illustrating pathological behavior in real analysis.
  • 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: Denjoy–Young–Saks theorem
Triple: [Arnaud Denjoy, knownFor, Denjoy–Young–Saks theorem]
Generated description
The Denjoy–Young–Saks theorem is a result in real analysis that classifies the possible behaviors of the derivative of a real function at almost every point on the real line.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Denjoy–Young–Saks theorem
Target entity description: The Denjoy–Young–Saks theorem is a result in real analysis that classifies the possible behaviors of the derivative of a real function at almost every point on the real line.
  • A. Carathéodory existence theorem
    The Carathéodory existence theorem is a result in the theory of ordinary differential equations that guarantees the existence (and sometimes uniqueness) of solutions under weaker regularity conditions on the right-hand side than those required by classical theorems like Picard–Lindelöf.
  • B. Darboux theorem
    The Darboux theorem is a fundamental result in symplectic geometry stating that all symplectic manifolds are locally symplectomorphic to the standard symplectic space, implying that the symplectic form can always be put into a canonical local normal form.
  • C. Lebesgue differentiation theorem
    The Lebesgue differentiation theorem is a fundamental result in real analysis stating that, for an integrable function, the averages over shrinking neighborhoods converge almost everywhere to the function’s pointwise value.
  • D. Banach–Saks theorem
    The Banach–Saks theorem is a result in functional analysis stating that every bounded sequence in a reflexive Banach space has a subsequence whose Cesàro means converge in norm.
  • E. Du Bois-Reymond function
    The Du Bois-Reymond function is a classic example of a continuous but nowhere differentiable function, illustrating pathological behavior in real analysis.
  • 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_69d381ae26c48190985abd0e25ee5d04 completed April 6, 2026, 9:49 a.m.
NER Named-entity recognition batch_69d3aa2894d0819095704449ecc2db6c completed April 6, 2026, 12:42 p.m.
NED1 Entity disambiguation (via context triple) batch_69d6a804e8748190b4ebcfa9a0bb889f completed April 8, 2026, 7:09 p.m.
NEDg Description generation batch_69d6d0003434819093e3f82a556db79c completed April 8, 2026, 10 p.m.
NED2 Entity disambiguation (via description) batch_69d6df3c8f748190923db41ef1a9a03a completed April 8, 2026, 11:05 p.m.
Created at: April 6, 2026, 11:05 a.m.