Triple
T16232045
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Stanisław Mazur |
E394006
|
entity |
| Predicate | notableWork |
P4
|
FINISHED |
| Object |
Mazur’s lemma
Mazur’s lemma is a fundamental result in functional analysis that provides conditions under which weak convergence in Banach spaces implies norm convergence of convex combinations of a sequence.
|
E1200643
|
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: Mazur’s lemma | Statement: [Stanisław Mazur, notableWork, Mazur’s lemma]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Mazur’s lemma Context triple: [Stanisław Mazur, notableWork, Mazur’s lemma]
-
A.
Riesz lemma
Riesz lemma is a fundamental result in functional analysis that characterizes how, in an infinite-dimensional normed space, one can find unit vectors that stay a fixed distance away from any given proper closed subspace.
-
B.
Banach–Mazur theorem
The Banach–Mazur theorem is a fundamental result in functional analysis that characterizes separable Banach spaces as isometrically isomorphic to closed subspaces of spaces of continuous functions on compact metric spaces.
-
C.
Banach–Saks theorem
The Banach–Saks theorem is a result in functional analysis stating that every bounded sequence in a reflexive Banach space has a subsequence whose Cesàro means converge in norm.
-
D.
Lax–Milgram theorem
The Lax–Milgram theorem is a fundamental result in functional analysis that guarantees the existence and uniqueness of solutions to certain linear boundary value problems via bounded, coercive bilinear forms on Hilbert spaces.
-
E.
Mazur control theorem
The Mazur control theorem is a fundamental result in Iwasawa theory that relates Selmer groups over infinite p-adic extensions to those over finite layers, allowing arithmetic information to be “controlled” across the tower.
- 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: Mazur’s lemma Triple: [Stanisław Mazur, notableWork, Mazur’s lemma]
Generated description
Mazur’s lemma is a fundamental result in functional analysis that provides conditions under which weak convergence in Banach spaces implies norm convergence of convex combinations of a sequence.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Mazur’s lemma Target entity description: Mazur’s lemma is a fundamental result in functional analysis that provides conditions under which weak convergence in Banach spaces implies norm convergence of convex combinations of a sequence.
-
A.
Riesz lemma
Riesz lemma is a fundamental result in functional analysis that characterizes how, in an infinite-dimensional normed space, one can find unit vectors that stay a fixed distance away from any given proper closed subspace.
-
B.
Banach–Mazur theorem
The Banach–Mazur theorem is a fundamental result in functional analysis that characterizes separable Banach spaces as isometrically isomorphic to closed subspaces of spaces of continuous functions on compact metric spaces.
-
C.
Banach–Saks theorem
The Banach–Saks theorem is a result in functional analysis stating that every bounded sequence in a reflexive Banach space has a subsequence whose Cesàro means converge in norm.
-
D.
Lax–Milgram theorem
The Lax–Milgram theorem is a fundamental result in functional analysis that guarantees the existence and uniqueness of solutions to certain linear boundary value problems via bounded, coercive bilinear forms on Hilbert spaces.
-
E.
Mazur control theorem
The Mazur control theorem is a fundamental result in Iwasawa theory that relates Selmer groups over infinite p-adic extensions to those over finite layers, allowing arithmetic information to be “controlled” across the tower.
- 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_69d87f204df88190a8f88923decf9835 |
completed | April 10, 2026, 4:40 a.m. |
| NER | Named-entity recognition | batch_69e23d29fa248190943f4c3f7808908b |
completed | April 17, 2026, 2:01 p.m. |
| NED1 | Entity disambiguation (via context triple) | batch_6a0007a0ab08819082aea4c312c9ffc7 |
completed | May 10, 2026, 4:20 a.m. |
| NEDg | Description generation | batch_6a00098ea3e48190b0744f1eafab9ce2 |
completed | May 10, 2026, 4:29 a.m. |
| NED2 | Entity disambiguation (via description) | batch_6a0009fb40a48190b82f6de80226d306 |
completed | May 10, 2026, 4:30 a.m. |
Created at: April 10, 2026, 5:04 a.m.