Triple
T27675258
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Chebyshev polynomials of the first kind |
E697760
|
entity |
| Predicate | zerosLocation |
P162941
|
FINISHED |
| Object | x_k = \cos\left(\frac{(2k-1)\pi}{2n}\right), k=1,…,n |
—
|
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: x_k = \cos\left(\frac{(2k-1)\pi}{2n}\right), k=1,…,n | Statement: [Chebyshev polynomials of the first kind, zerosLocation, x_k = \cos\left(\frac{(2k-1)\pi}{2n}\right), k=1,…,n]
PD
Predicate disambiguation
gpt-5-mini-2025-08-07
Target predicate: zerosLocation
Context triple: [Chebyshev polynomials of the first kind, zerosLocation, x_k = \cos\left(\frac{(2k-1)\pi}{2n}\right), k=1,…,n]
-
A.
nontrivialZerosRegion
Indicates that the nontrivial zeros of a function (typically the Riemann zeta function) lie within a specified region of the complex plane.
-
B.
orderOfPoleAt
Indicates the location or index at which a function has a pole of a specified order.
-
C.
hasOrderOfPoleAtLatticePoints
Indicates that a function has poles of specified orders at each point of a given lattice in its domain.
-
D.
deltaLocation
Indicates a change or difference between two locations, typically specifying how one location has shifted relative to another.
-
E.
bitLocation
Indicates the specific position or index of a bit within a binary sequence or data structure.
- F. None of above. chosen
Provenance (4 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_69f63532e35881909bfe0a8a315e2efe |
completed | May 2, 2026, 5:32 p.m. |
| PD | Predicate disambiguation | batch_69f62c1a92648190835a2c5250d8c758 |
completed | May 2, 2026, 4:53 p.m. |
| PDg | Predicate description generation | batch_69f6305219f08190b55f6193a4a49984 |
completed | May 2, 2026, 5:11 p.m. |
Created at: April 27, 2026, 2:43 p.m.