Triple

T940257
Position Surface form Disambiguated ID Type / Status
Subject Karl Weierstrass E20288 entity
Predicate notableFor P22 FINISHED
Object epsilon–delta definition of limit
The epsilon–delta definition of limit is the rigorous formalization of the intuitive notion of a function approaching a value, forming the foundation of modern analysis and calculus.
E110604 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: epsilon–delta definition of limit | Statement: [Karl Weierstrass, notableFor, epsilon–delta definition of limit]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: epsilon–delta definition of limit
Context triple: [Karl Weierstrass, notableFor, epsilon–delta definition of limit]
  • A. Riemann–Lebesgue lemma
    The Riemann–Lebesgue lemma is a fundamental result in Fourier analysis stating that the Fourier coefficients (or transform) of an integrable function vanish at infinity.
  • B. Riemann sums
    Riemann sums are a fundamental method in calculus for approximating the area under a curve by summing the areas of a sequence of rectangles, forming the basis of the definition of the definite integral.
  • C. Ulam stability
    Ulam stability is a concept in the theory of functional equations that studies when approximate solutions imply the existence of exact solutions nearby, forming the basis of what is now called Hyers–Ulam stability.
  • D. inverse function theorem
    The inverse function theorem is a fundamental result in calculus and differential geometry that gives conditions under which a differentiable function has a locally defined differentiable inverse near a point where its derivative is invertible.
  • E. local existence and uniqueness theorem
    The local existence and uniqueness theorem is a fundamental result in differential equations that guarantees, under suitable conditions, a single solution passing through a given initial point, valid in some neighborhood of that point.
  • 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: epsilon–delta definition of limit
Triple: [Karl Weierstrass, notableFor, epsilon–delta definition of limit]
Generated description
The epsilon–delta definition of limit is the rigorous formalization of the intuitive notion of a function approaching a value, forming the foundation of modern analysis and calculus.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: epsilon–delta definition of limit
Target entity description: The epsilon–delta definition of limit is the rigorous formalization of the intuitive notion of a function approaching a value, forming the foundation of modern analysis and calculus.
  • A. Riemann–Lebesgue lemma
    The Riemann–Lebesgue lemma is a fundamental result in Fourier analysis stating that the Fourier coefficients (or transform) of an integrable function vanish at infinity.
  • B. Riemann sums
    Riemann sums are a fundamental method in calculus for approximating the area under a curve by summing the areas of a sequence of rectangles, forming the basis of the definition of the definite integral.
  • C. Ulam stability
    Ulam stability is a concept in the theory of functional equations that studies when approximate solutions imply the existence of exact solutions nearby, forming the basis of what is now called Hyers–Ulam stability.
  • D. inverse function theorem
    The inverse function theorem is a fundamental result in calculus and differential geometry that gives conditions under which a differentiable function has a locally defined differentiable inverse near a point where its derivative is invertible.
  • E. local existence and uniqueness theorem
    The local existence and uniqueness theorem is a fundamental result in differential equations that guarantees, under suitable conditions, a single solution passing through a given initial point, valid in some neighborhood of that point.
  • 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_69a493b0270c81909e6c9ce310f6aa55 completed March 1, 2026, 7:29 p.m.
NER Named-entity recognition batch_69a4b38b7da08190ac0853655dab678a completed March 1, 2026, 9:45 p.m.
NED1 Entity disambiguation (via context triple) batch_69a826e30c448190acc1457a63d27a4a completed March 4, 2026, 12:34 p.m.
NEDg Description generation batch_69a8343e16908190af102cfce025c31f completed March 4, 2026, 1:31 p.m.
NED2 Entity disambiguation (via description) batch_69a834f3a9288190a8cd28165379cec6 completed March 4, 2026, 1:34 p.m.
Created at: March 1, 2026, 7:40 p.m.