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.