Triple

T27675314
Position Surface form Disambiguated ID Type / Status
Subject Gegenbauer polynomials E697761 entity
Predicate orthogonalityIntegral P76852 FINISHED
Object \int_{-1}^1 (1-x^2)^{\lambda-1/2} C_m^{(\lambda)}(x) C_n^{(\lambda)}(x) dx = 0 for m \neq 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: \int_{-1}^1 (1-x^2)^{\lambda-1/2} C_m^{(\lambda)}(x) C_n^{(\lambda)}(x) dx = 0 for m \neq n | Statement: [Gegenbauer polynomials, orthogonalityIntegral, \int_{-1}^1 (1-x^2)^{\lambda-1/2} C_m^{(\lambda)}(x) C_n^{(\lambda)}(x) dx = 0 for m \neq n]
PD Predicate disambiguation gpt-5-mini-2025-08-07
Target predicate: orthogonalityIntegral
Context triple: [Gegenbauer polynomials, orthogonalityIntegral, \int_{-1}^1 (1-x^2)^{\lambda-1/2} C_m^{(\lambda)}(x) C_n^{(\lambda)}(x) dx = 0 for m \neq n]
  • A. orthogonalityProperty chosen
    Indicates that one entity possesses the property of being orthogonal (i.e., at right angles or having zero inner product) with respect to another entity or a given reference.
  • B. orthonormalityRelation
    Indicates that a set of vectors are mutually orthogonal and each has unit length with respect to a given inner product.
  • C. integratedOver
    Indicates that a quantity or function has been mathematically integrated with respect to a specified variable or domain over a given interval or region.
  • D. integratesOn
    Indicates that one entity is designed to work seamlessly within, or be combined functionally with, another entity or platform.
  • E. integralTo
    Indicates that one entity is an essential, non-removable component or part of another entity, such that the whole depends on it to function or be complete.
  • 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_69f6562fd3488190be1acd8c526a28d2 completed May 2, 2026, 7:53 p.m.
PD Predicate disambiguation batch_69f651a931748190a637e631a52bbfaa completed May 2, 2026, 7:34 p.m.
Created at: April 27, 2026, 2:43 p.m.