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.