Triple

T7338659
Position Surface form Disambiguated ID Type / Status
Subject Farey tessellation E169192 entity
Predicate relatedTo P37 FINISHED
Object Stern–Brocot tree
The Stern–Brocot tree is an infinite binary tree that systematically lists all positive rational numbers in lowest terms exactly once, ordered by increasing value.
E656695 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: Stern–Brocot tree | Statement: [Farey tessellation, relatedTo, Stern–Brocot tree]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Stern–Brocot tree
Context triple: [Farey tessellation, relatedTo, Stern–Brocot tree]
  • A. Sylvester sequence
    The Sylvester sequence is an integer sequence defined recursively where each term is one more than the product of all previous terms, yielding rapidly growing, pairwise coprime numbers closely related to Egyptian fraction representations.
  • B. Continued Fractions
    Continued Fractions is a classic mathematical monograph by Aleksandr Khinchin that systematically develops the theory and applications of continued fraction expansions in number theory and analysis.
  • C. Farey tessellation
    The Farey tessellation is a geometric partition of the hyperbolic plane into ideal triangles whose vertices correspond to rational numbers, closely linked to number theory and modular group actions.
  • D. Zeckendorf
    Zeckendorf is a surname most notably associated with American real estate developer William Zeckendorf and his influential role in mid-20th-century urban development.
  • E. Khinchin's constant
    Khinchin's constant is a mathematical constant that arises in metric number theory, describing the almost-sure geometric mean of the partial quotients in the continued fraction expansions of real numbers.
  • 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: Stern–Brocot tree
Triple: [Farey tessellation, relatedTo, Stern–Brocot tree]
Generated description
The Stern–Brocot tree is an infinite binary tree that systematically lists all positive rational numbers in lowest terms exactly once, ordered by increasing value.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Stern–Brocot tree
Target entity description: The Stern–Brocot tree is an infinite binary tree that systematically lists all positive rational numbers in lowest terms exactly once, ordered by increasing value.
  • A. Sylvester sequence
    The Sylvester sequence is an integer sequence defined recursively where each term is one more than the product of all previous terms, yielding rapidly growing, pairwise coprime numbers closely related to Egyptian fraction representations.
  • B. Continued Fractions
    Continued Fractions is a classic mathematical monograph by Aleksandr Khinchin that systematically develops the theory and applications of continued fraction expansions in number theory and analysis.
  • C. Farey tessellation
    The Farey tessellation is a geometric partition of the hyperbolic plane into ideal triangles whose vertices correspond to rational numbers, closely linked to number theory and modular group actions.
  • D. Zeckendorf
    Zeckendorf is a surname most notably associated with American real estate developer William Zeckendorf and his influential role in mid-20th-century urban development.
  • E. Khinchin's constant
    Khinchin's constant is a mathematical constant that arises in metric number theory, describing the almost-sure geometric mean of the partial quotients in the continued fraction expansions of real numbers.
  • 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_69c68a57710481909f0c1f3c6ebdb6f2 completed March 27, 2026, 1:47 p.m.
NER Named-entity recognition batch_69c6f0d702108190a00a3681ff6e67d4 completed March 27, 2026, 9:04 p.m.
NED1 Entity disambiguation (via context triple) batch_69c7ef266fd0819096cf3ece3fff6b90 completed March 28, 2026, 3:09 p.m.
NEDg Description generation batch_69c7efa4f5148190842f30988cbea94c completed March 28, 2026, 3:11 p.m.
NED2 Entity disambiguation (via description) batch_69c7f0092bac819080ded1863f99290a completed March 28, 2026, 3:13 p.m.
Created at: March 27, 2026, 3:04 p.m.