Triple

T9838897
Position Surface form Disambiguated ID Type / Status
Subject de Bruijn–van Aardenne–Ehrenfest theorem E239170 entity
Predicate relatedTo P37 FINISHED
Object BEST theorem
The BEST theorem is a result in graph theory that gives a formula for counting the number of distinct Eulerian circuits in a directed graph using spanning arborescences and vertex degrees.
E824089 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: BEST theorem | Statement: [de Bruijn–van Aardenne–Ehrenfest theorem, relatedTo, BEST theorem]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: BEST theorem
Context triple: [de Bruijn–van Aardenne–Ehrenfest theorem, relatedTo, BEST theorem]
  • A. Teorema
    Teorema is a 1968 Italian art-house drama film directed by Pier Paolo Pasolini, known for its enigmatic, allegorical exploration of sexuality, faith, and bourgeois emptiness.
  • B. Page theorem
    The Page theorem is a result in quantum information theory and black hole physics that predicts how the entanglement entropy of a subsystem typically evolves, underpinning the characteristic "Page curve" behavior in discussions of the black hole information paradox.
  • C. Best
    Best is a common English surname borne by numerous notable individuals across sports, arts, and public life.
  • D. Best
    Best is a town and municipality in the southern Netherlands, located in the province of North Brabant near the city of Eindhoven.
  • E. Thales’ theorem
    Thales’ theorem is a fundamental result in Euclidean geometry stating that any angle inscribed in a semicircle is a right angle.
  • 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: BEST theorem
Triple: [de Bruijn–van Aardenne–Ehrenfest theorem, relatedTo, BEST theorem]
Generated description
The BEST theorem is a result in graph theory that gives a formula for counting the number of distinct Eulerian circuits in a directed graph using spanning arborescences and vertex degrees.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: BEST theorem
Target entity description: The BEST theorem is a result in graph theory that gives a formula for counting the number of distinct Eulerian circuits in a directed graph using spanning arborescences and vertex degrees.
  • A. Teorema
    Teorema is a 1968 Italian art-house drama film directed by Pier Paolo Pasolini, known for its enigmatic, allegorical exploration of sexuality, faith, and bourgeois emptiness.
  • B. Page theorem
    The Page theorem is a result in quantum information theory and black hole physics that predicts how the entanglement entropy of a subsystem typically evolves, underpinning the characteristic "Page curve" behavior in discussions of the black hole information paradox.
  • C. Best
    Best is a common English surname borne by numerous notable individuals across sports, arts, and public life.
  • D. Best
    Best is a town and municipality in the southern Netherlands, located in the province of North Brabant near the city of Eindhoven.
  • E. Thales’ theorem
    Thales’ theorem is a fundamental result in Euclidean geometry stating that any angle inscribed in a semicircle is a right angle.
  • 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_69ca84e314108190978324a4bdb959f8 completed March 30, 2026, 2:12 p.m.
NER Named-entity recognition batch_69cdb34921b881909836ba0f5b42a27b completed April 2, 2026, 12:07 a.m.
NED1 Entity disambiguation (via context triple) batch_69d1d5d145ac8190ad10a4328216ef54 completed April 5, 2026, 3:24 a.m.
NEDg Description generation batch_69d1d6bb23cc81909efbeccf147018e8 completed April 5, 2026, 3:27 a.m.
NED2 Entity disambiguation (via description) batch_69d1d726e58c819090135d1ff275d2d8 completed April 5, 2026, 3:29 a.m.
Created at: March 30, 2026, 8:33 p.m.