Triple
T4927386
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Weierstrass substitution |
E110609
|
entity |
| Predicate | relatedTo |
P37
|
FINISHED |
| Object |
Euler substitution
Euler substitution is a classical technique in integral calculus that simplifies integrals involving square roots of quadratic expressions by transforming them into rational functions through a specific change of variables.
|
E480876
|
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: Euler substitution | Statement: [Weierstrass substitution, relatedTo, Euler substitution]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Euler substitution Context triple: [Weierstrass substitution, relatedTo, Euler substitution]
-
A.
Weierstrass substitution
The Weierstrass substitution is a trigonometric substitution technique that transforms integrals involving sine and cosine into rational functions, simplifying their evaluation.
-
B.
Cauchy–Euler equation
The Cauchy–Euler equation is a type of linear ordinary differential equation with variable coefficients that often appears in problems with power-law or scale-invariant behavior.
-
C.
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.
-
D.
Euler’s theorem
Euler’s theorem is a fundamental result in number theory stating that for any integer a coprime to n, a raised to the power of φ(n) is congruent to 1 modulo n.
-
E.
Euler’s method of rearranging absolutely convergent series
Euler’s method of rearranging absolutely convergent series is a technique introduced by Leonhard Euler to systematically reorder and manipulate convergent infinite series in order to derive new identities and product expansions, such as those appearing in analytic number theory.
- 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: Euler substitution Triple: [Weierstrass substitution, relatedTo, Euler substitution]
Generated description
Euler substitution is a classical technique in integral calculus that simplifies integrals involving square roots of quadratic expressions by transforming them into rational functions through a specific change of variables.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Euler substitution Target entity description: Euler substitution is a classical technique in integral calculus that simplifies integrals involving square roots of quadratic expressions by transforming them into rational functions through a specific change of variables.
-
A.
Weierstrass substitution
The Weierstrass substitution is a trigonometric substitution technique that transforms integrals involving sine and cosine into rational functions, simplifying their evaluation.
-
B.
Cauchy–Euler equation
The Cauchy–Euler equation is a type of linear ordinary differential equation with variable coefficients that often appears in problems with power-law or scale-invariant behavior.
-
C.
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.
-
D.
Euler’s theorem
Euler’s theorem is a fundamental result in number theory stating that for any integer a coprime to n, a raised to the power of φ(n) is congruent to 1 modulo n.
-
E.
Euler’s method of rearranging absolutely convergent series
Euler’s method of rearranging absolutely convergent series is a technique introduced by Leonhard Euler to systematically reorder and manipulate convergent infinite series in order to derive new identities and product expansions, such as those appearing in analytic number theory.
- 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_69bd4415190c8190817bee7ec9f9f944 |
completed | March 20, 2026, 12:56 p.m. |
| NER | Named-entity recognition | batch_69bd7036d8e88190bc4be2975160da23 |
completed | March 20, 2026, 4:05 p.m. |
| NED1 | Entity disambiguation (via context triple) | batch_69be77ac88148190a51fa2e9085d6897 |
completed | March 21, 2026, 10:49 a.m. |
| NEDg | Description generation | batch_69be7847a378819081687ec783a8b862 |
completed | March 21, 2026, 10:51 a.m. |
| NED2 | Entity disambiguation (via description) | batch_69be7915a26c81909b21a128daebf5b3 |
completed | March 21, 2026, 10:55 a.m. |
Created at: March 20, 2026, 1:30 p.m.