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.