Triple
T10991383
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Fundamental Theorem of Calculus |
E259760
|
entity |
| Predicate | hasPart |
P35
|
FINISHED |
| Object |
First Fundamental Theorem of Calculus
The First Fundamental Theorem of Calculus states that if a function is continuous on an interval, then its definite integral over that interval can be computed using any of its antiderivatives evaluated at the endpoints.
|
E259760
|
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: First Fundamental Theorem of Calculus | Statement: [Fundamental Theorem of Calculus, hasPart, First Fundamental Theorem of Calculus]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: First Fundamental Theorem of Calculus Context triple: [Fundamental Theorem of Calculus, hasPart, First Fundamental Theorem of Calculus]
-
A.
Fundamental Theorem of Calculus
The Fundamental Theorem of Calculus links differentiation and integration by showing that the definite integral of a function can be computed using any of its antiderivatives.
-
B.
Cauchy’s mean value theorem
Cauchy’s mean value theorem is a fundamental result in real analysis that generalizes the standard mean value theorem by relating the rates of change of two differentiable functions on an interval.
-
C.
Riemann integral
The Riemann integral is a fundamental concept in calculus that defines the integral of a function as the limit of sums of function values over increasingly fine partitions of an interval.
-
D.
Leibniz rule
The Leibniz rule is a fundamental property of derivatives stating that the derivative of a product equals the sum of each factor’s derivative times the other factor.
-
E.
Fubini's theorem
Fubini's theorem is a fundamental result in measure theory that allows the evaluation of double integrals as iterated integrals under suitable integrability conditions.
- 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: First Fundamental Theorem of Calculus Triple: [Fundamental Theorem of Calculus, hasPart, First Fundamental Theorem of Calculus]
Generated description
The First Fundamental Theorem of Calculus states that if a function is continuous on an interval, then its definite integral over that interval can be computed using any of its antiderivatives evaluated at the endpoints.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: First Fundamental Theorem of Calculus Target entity description: The First Fundamental Theorem of Calculus states that if a function is continuous on an interval, then its definite integral over that interval can be computed using any of its antiderivatives evaluated at the endpoints.
-
A.
Fundamental Theorem of Calculus
chosen
The Fundamental Theorem of Calculus links differentiation and integration by showing that the definite integral of a function can be computed using any of its antiderivatives.
-
B.
Cauchy’s mean value theorem
Cauchy’s mean value theorem is a fundamental result in real analysis that generalizes the standard mean value theorem by relating the rates of change of two differentiable functions on an interval.
-
C.
Riemann integral
The Riemann integral is a fundamental concept in calculus that defines the integral of a function as the limit of sums of function values over increasingly fine partitions of an interval.
-
D.
Leibniz rule
The Leibniz rule is a fundamental property of derivatives stating that the derivative of a product equals the sum of each factor’s derivative times the other factor.
-
E.
Fubini's theorem
Fubini's theorem is a fundamental result in measure theory that allows the evaluation of double integrals as iterated integrals under suitable integrability conditions.
- F. None of above.
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_69d6aa8a6a548190a750f944ccdc8064 |
completed | April 8, 2026, 7:20 p.m. |
| NER | Named-entity recognition | batch_69d795d1e918819090c71f5a077fa15a |
completed | April 9, 2026, 12:04 p.m. |
| NED1 | Entity disambiguation (via context triple) | batch_69e34504ebec8190a78e4795765b0c24 |
completed | April 18, 2026, 8:47 a.m. |
| NEDg | Description generation | batch_69e3556fd3548190a33f04604be947cf |
completed | April 18, 2026, 9:57 a.m. |
| NED2 | Entity disambiguation (via description) | batch_69e3593b0f8481909ed7a90f8bb9839d |
completed | April 18, 2026, 10:13 a.m. |
Created at: April 8, 2026, 9:24 p.m.