Triple
T27675245
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Chebyshev polynomials of the first kind |
E697760
|
entity |
| Predicate | hasTrigonometricDefinition |
P114498
|
FINISHED |
| Object | T_n(\cos \theta) = \cos(n\theta) |
—
|
LITERAL FINISHED |
How this triple was built (2 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: T_n(\cos \theta) = \cos(n\theta) | Statement: [Chebyshev polynomials of the first kind, hasTrigonometricDefinition, T_n(\cos \theta) = \cos(n\theta)]
PD
Predicate disambiguation
gpt-5-mini-2025-08-07
Target predicate: hasTrigonometricDefinition Context triple: [Chebyshev polynomials of the first kind, hasTrigonometricDefinition, T_n(\cos \theta) = \cos(n\theta)]
-
A.
hasTriangleAngle
Indicates that a triangle possesses a specific angle as one of its interior angles.
-
B.
usesIrrationalAngle
Indicates that the relationship or action involves an angle whose measure is an irrational number (i.e., cannot be expressed as a ratio of integers).
-
C.
mathematicallyDefinedAs
chosen
Indicates that one entity is precisely specified or characterized in terms of another using a formal mathematical definition or expression.
-
D.
hasMathematicalProperty
Indicates that one entity possesses or exhibits a specific mathematical property or characteristic.
-
E.
hasTypicalAngle
Indicates that there is a characteristic or commonly occurring angle associated with the relationship between the entities.
- F. None of above.
Provenance (3 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_69ef590d458c81909583290c3cd0478b |
completed | April 27, 2026, 12:39 p.m. |
| NER | Named-entity recognition | batch_69fd2a215d6c8190a1a428ccaee603f1 |
completed | May 8, 2026, 12:11 a.m. |
| PD | Predicate disambiguation | batch_69fd28ef19688190bb8370f2812a43e7 |
completed | May 8, 2026, 12:06 a.m. |
Created at: April 27, 2026, 2:43 p.m.