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.