Triple
T19319680
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | An Introduction to the Mathematical Theory of Finite Elements |
E483186
|
entity |
| Predicate | topic |
P261
|
FINISHED |
| Object |
Céa’s lemma
Céa’s lemma is a fundamental result in finite element analysis that provides an a priori error estimate by bounding the approximation error in terms of the best possible error in the chosen finite-dimensional space.
|
E1369967
|
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: Céa’s lemma | Statement: [An Introduction to the Mathematical Theory of Finite Elements, topic, Céa’s lemma]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Céa’s lemma Context triple: [An Introduction to the Mathematical Theory of Finite Elements, topic, Céa’s lemma]
-
A.
Bailey lemma
The Bailey lemma is a key result in the theory of basic hypergeometric series that provides a systematic method for generating Rogers–Ramanujan-type identities and other q-series relations.
-
B.
Ky Fan’s lemma
Ky Fan’s lemma is a combinatorial topological result that generalizes Tucker’s lemma and provides conditions guaranteeing the existence of certain balanced or fully labeled simplices in labeled triangulations of spheres or simplices.
-
C.
Kummer's lemma
Kummer's lemma is a result in algebraic number theory that provides conditions on ideal factorization in cyclotomic fields, particularly relating to divisibility properties of class numbers and units.
-
D.
Robbins lemma
Robbins lemma is a result in probability theory that provides a bound on the expected maximum of partial sums of independent random variables, named after mathematician Herbert Robbins.
-
E.
Chevalley–Warning theorem
The Chevalley–Warning theorem is a result in number theory and algebraic geometry that gives conditions under which systems of polynomial equations over finite fields must have nontrivial solutions.
- 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: Céa’s lemma Triple: [An Introduction to the Mathematical Theory of Finite Elements, topic, Céa’s lemma]
Generated description
Céa’s lemma is a fundamental result in finite element analysis that provides an a priori error estimate by bounding the approximation error in terms of the best possible error in the chosen finite-dimensional space.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Céa’s lemma Target entity description: Céa’s lemma is a fundamental result in finite element analysis that provides an a priori error estimate by bounding the approximation error in terms of the best possible error in the chosen finite-dimensional space.
-
A.
Bailey lemma
The Bailey lemma is a key result in the theory of basic hypergeometric series that provides a systematic method for generating Rogers–Ramanujan-type identities and other q-series relations.
-
B.
Ky Fan’s lemma
Ky Fan’s lemma is a combinatorial topological result that generalizes Tucker’s lemma and provides conditions guaranteeing the existence of certain balanced or fully labeled simplices in labeled triangulations of spheres or simplices.
-
C.
Kummer's lemma
Kummer's lemma is a result in algebraic number theory that provides conditions on ideal factorization in cyclotomic fields, particularly relating to divisibility properties of class numbers and units.
-
D.
Robbins lemma
Robbins lemma is a result in probability theory that provides a bound on the expected maximum of partial sums of independent random variables, named after mathematician Herbert Robbins.
-
E.
Chevalley–Warning theorem
The Chevalley–Warning theorem is a result in number theory and algebraic geometry that gives conditions under which systems of polynomial equations over finite fields must have nontrivial solutions.
- 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_69d8e8d13e3c81909d91d1d5ec37c095 |
completed | April 10, 2026, 12:10 p.m. |
| NER | Named-entity recognition | batch_69e60d87a0088190a60201b1f388089e |
completed | April 20, 2026, 11:27 a.m. |
| NED1 | Entity disambiguation (via context triple) | batch_6a0714640aa481909bd6b1ca617f35a7 |
completed | May 15, 2026, 12:41 p.m. |
| NEDg | Description generation | batch_6a0714eb6a0c8190bec7ae8ef785a4ab |
completed | May 15, 2026, 12:43 p.m. |
| NED2 | Entity disambiguation (via description) | batch_6a0718ee8adc8190a74685f9783ba5d5 |
completed | May 15, 2026, 1 p.m. |
Created at: April 10, 2026, 1:32 p.m.