Triple
T16876410
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Finite Operator Calculus |
E421310
|
entity |
| Predicate | usesConcept |
P531
|
FINISHED |
| Object |
umbral calculus
Umbral calculus is a mathematical framework that manipulates sequences of polynomials and linear operators using symbolic rules that resemble the manipulation of powers in classical algebra.
|
E1237908
|
NE FINISHED |
How this triple was built (4 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: umbral calculus | Statement: [Finite Operator Calculus, usesConcept, umbral calculus]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: umbral calculus Context triple: [Finite Operator Calculus, usesConcept, umbral calculus]
-
A.
Mueller calculus
Mueller calculus is a mathematical framework in polarization optics that uses matrix operations to describe how optical elements transform the Stokes parameters of light.
-
B.
Euler–Maclaurin summation formula
The Euler–Maclaurin summation formula is a fundamental result in analysis that connects sums and integrals, providing powerful asymptotic expansions and error estimates for approximating series by integrals.
-
C.
Bernoulli polynomials
Bernoulli polynomials are a sequence of polynomials deeply connected to number theory and analysis, appearing in the study of special functions, series expansions, and the evaluation of sums of powers of integers.
-
D.
Bernoulli numbers
Bernoulli numbers are a sequence of rational numbers that play a central role in number theory and analysis, especially in formulas for sums of powers of integers and in the study of special functions like the Riemann zeta function.
-
E.
Gauss hypergeometric function
The Gauss hypergeometric function is a special function defined by a power series that generalizes many elementary and higher transcendental functions and plays a central role in mathematical analysis, differential equations, and mathematical physics.
- 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: umbral calculus Triple: [Finite Operator Calculus, usesConcept, umbral calculus]
Generated description
Umbral calculus is a mathematical framework that manipulates sequences of polynomials and linear operators using symbolic rules that resemble the manipulation of powers in classical algebra.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: umbral calculus Target entity description: Umbral calculus is a mathematical framework that manipulates sequences of polynomials and linear operators using symbolic rules that resemble the manipulation of powers in classical algebra.
-
A.
Mueller calculus
Mueller calculus is a mathematical framework in polarization optics that uses matrix operations to describe how optical elements transform the Stokes parameters of light.
-
B.
Euler–Maclaurin summation formula
The Euler–Maclaurin summation formula is a fundamental result in analysis that connects sums and integrals, providing powerful asymptotic expansions and error estimates for approximating series by integrals.
-
C.
Bernoulli polynomials
Bernoulli polynomials are a sequence of polynomials deeply connected to number theory and analysis, appearing in the study of special functions, series expansions, and the evaluation of sums of powers of integers.
-
D.
Bernoulli numbers
Bernoulli numbers are a sequence of rational numbers that play a central role in number theory and analysis, especially in formulas for sums of powers of integers and in the study of special functions like the Riemann zeta function.
-
E.
Gauss hypergeometric function
The Gauss hypergeometric function is a special function defined by a power series that generalizes many elementary and higher transcendental functions and plays a central role in mathematical analysis, differential equations, and mathematical physics.
- F. None of above. chosen
Provenance (5 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_69d889d470fc8190b4aec199636c0c56 |
completed | April 10, 2026, 5:25 a.m. |
| NER | Named-entity recognition | batch_69e3b7f704a081909921d00b3c470472 |
completed | April 18, 2026, 4:57 p.m. |
| NED1 | Entity disambiguation (via context triple) | batch_6a00c2b4abd08190841c5bb0b0eaa177 |
completed | May 10, 2026, 5:39 p.m. |
| NEDg | Description generation | batch_6a00c355f4108190a4209599bf5f50da |
completed | May 10, 2026, 5:41 p.m. |
| NED2 | Entity disambiguation (via description) | batch_6a00c413314881909e308588af09ce2a |
completed | May 10, 2026, 5:44 p.m. |
Created at: April 10, 2026, 5:29 a.m.