Triple

T940263
Position Surface form Disambiguated ID Type / Status
Subject Karl Weierstrass E20288 entity
Predicate notableFor P22 FINISHED
Object Weierstrass substitution
The Weierstrass substitution is a trigonometric substitution technique that transforms integrals involving sine and cosine into rational functions, simplifying their evaluation.
E110609 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: Weierstrass substitution | Statement: [Karl Weierstrass, notableFor, Weierstrass substitution]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Weierstrass substitution
Context triple: [Karl Weierstrass, notableFor, Weierstrass substitution]
  • A. Gauss’s constant
    Gauss’s constant is a mathematical constant arising in number theory and complex analysis, particularly in connection with the lemniscate and elliptic functions.
  • B. Peuterey Integral
    Peuterey Integral is a legendary, highly committing alpine climbing route that follows the full Peuterey ridge to the summit of Mont Blanc, renowned as one of the longest and most serious ridge climbs in the Alps.
  • 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. Riemann–Siegel formula
    The Riemann–Siegel formula is an asymptotic expression that efficiently approximates the Riemann zeta function on the critical line, playing a key role in the numerical study of its zeros.
  • E. 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.
  • 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: Weierstrass substitution
Triple: [Karl Weierstrass, notableFor, Weierstrass substitution]
Generated description
The Weierstrass substitution is a trigonometric substitution technique that transforms integrals involving sine and cosine into rational functions, simplifying their evaluation.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Weierstrass substitution
Target entity description: The Weierstrass substitution is a trigonometric substitution technique that transforms integrals involving sine and cosine into rational functions, simplifying their evaluation.
  • A. Gauss’s constant
    Gauss’s constant is a mathematical constant arising in number theory and complex analysis, particularly in connection with the lemniscate and elliptic functions.
  • B. Peuterey Integral
    Peuterey Integral is a legendary, highly committing alpine climbing route that follows the full Peuterey ridge to the summit of Mont Blanc, renowned as one of the longest and most serious ridge climbs in the Alps.
  • 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. Riemann–Siegel formula
    The Riemann–Siegel formula is an asymptotic expression that efficiently approximates the Riemann zeta function on the critical line, playing a key role in the numerical study of its zeros.
  • E. 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.
  • 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.