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.