Triple
T7421010
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | B-splines |
E171244
|
entity |
| Predicate | mathematicallyDefinedBy |
P12675
|
FINISHED |
| Object |
Cox–de Boor recursion formula
The Cox–de Boor recursion formula is a fundamental recursive definition used to construct and evaluate B-spline basis functions in numerical analysis and computer-aided geometric design.
|
E171244
|
NE FINISHED |
How this triple was built (5 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: Cox–de Boor recursion formula | Statement: [B-splines, mathematicallyDefinedBy, Cox–de Boor recursion formula]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Cox–de Boor recursion formula Context triple: [B-splines, mathematicallyDefinedBy, Cox–de Boor recursion formula]
-
A.
B-splines
B-splines are piecewise polynomial functions widely used in computer graphics and numerical analysis to create smooth, flexible curves and surfaces controlled by a set of control points.
-
B.
Catmull–Rom spline
The Catmull–Rom spline is a type of interpolating spline commonly used in computer graphics and animation to create smooth curves that pass through a given set of control points.
-
C.
Birkhoff interpolation
Birkhoff interpolation is a generalized form of polynomial interpolation that allows prescribing function and derivative values at selected points, not necessarily in a consecutive or complete pattern.
-
D.
Bernstein polynomials
Bernstein polynomials are a family of polynomials used in approximation theory that provide a constructive proof of the Weierstrass approximation theorem by uniformly approximating continuous functions on a closed interval.
-
E.
Carathéodory–Fejér interpolation
Carathéodory–Fejér interpolation is a classical result in complex analysis and approximation theory that concerns constructing analytic functions, typically with bounded or positive real part, that match prescribed initial Taylor coefficients.
- 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: Cox–de Boor recursion formula Triple: [B-splines, mathematicallyDefinedBy, Cox–de Boor recursion formula]
Generated description
The Cox–de Boor recursion formula is a fundamental recursive definition used to construct and evaluate B-spline basis functions in numerical analysis and computer-aided geometric design.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Cox–de Boor recursion formula Target entity description: The Cox–de Boor recursion formula is a fundamental recursive definition used to construct and evaluate B-spline basis functions in numerical analysis and computer-aided geometric design.
-
A.
B-splines
chosen
B-splines are piecewise polynomial functions widely used in computer graphics and numerical analysis to create smooth, flexible curves and surfaces controlled by a set of control points.
-
B.
Catmull–Rom spline
The Catmull–Rom spline is a type of interpolating spline commonly used in computer graphics and animation to create smooth curves that pass through a given set of control points.
-
C.
Birkhoff interpolation
Birkhoff interpolation is a generalized form of polynomial interpolation that allows prescribing function and derivative values at selected points, not necessarily in a consecutive or complete pattern.
-
D.
Bernstein polynomials
Bernstein polynomials are a family of polynomials used in approximation theory that provide a constructive proof of the Weierstrass approximation theorem by uniformly approximating continuous functions on a closed interval.
-
E.
Carathéodory–Fejér interpolation
Carathéodory–Fejér interpolation is a classical result in complex analysis and approximation theory that concerns constructing analytic functions, typically with bounded or positive real part, that match prescribed initial Taylor coefficients.
- F. None of above.
PD
Predicate disambiguation
gpt-5-mini-2025-08-07
Target predicate: mathematicallyDefinedBy Context triple: [B-splines, mathematicallyDefinedBy, Cox–de Boor recursion formula]
-
A.
mathematicallyExpressedBy
chosen
Indicates that something (such as a concept, quantity, or relationship) is represented or captured using a specific mathematical expression or formulation.
-
B.
mathematicallyFormulatedBy
Indicates that something (such as a concept, model, or theory) is expressed or defined using mathematical formulations created by a particular agent.
-
C.
mathematicallyFormulatedIn
Indicates that something is expressed, defined, or represented using mathematical formulas, equations, or formal mathematical structures within a given context.
-
D.
mathematicalObject
Indicates that the subject is a mathematical entity or construct, such as a number, function, set, or structure, within a mathematical context.
-
E.
mathematicallyUses
Indicates that one entity employs or applies another entity within a mathematical context, such as in a formula, proof, computation, or theoretical framework.
- F. None of above.
Provenance (6 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_69c68a625d048190af70eb8b63bec5a0 |
completed | March 27, 2026, 1:47 p.m. |
| NER | Named-entity recognition | batch_69c6f2ebc520819087cfc2eb9dda0e17 |
completed | March 27, 2026, 9:13 p.m. |
| NED1 | Entity disambiguation (via context triple) | batch_69c81ef7fc808190a564ab4d9d97ab37 |
completed | March 28, 2026, 6:33 p.m. |
| NEDg | Description generation | batch_69c81f9b565881909bebcc3112037f52 |
completed | March 28, 2026, 6:36 p.m. |
| NED2 | Entity disambiguation (via description) | batch_69c8207912f4819086e99ed441bee805 |
completed | March 28, 2026, 6:39 p.m. |
| PD | Predicate disambiguation | batch_69c6f0345040819094c5756dfa487faf |
completed | March 27, 2026, 9:01 p.m. |
Created at: March 27, 2026, 3:11 p.m.