Triple

T16232043
Position Surface form Disambiguated ID Type / Status
Subject Stanisław Mazur E394006 entity
Predicate notableWork P4 FINISHED
Object Scott–Mazur theorem
The Scott–Mazur theorem is a result in functional analysis that characterizes when a Banach space is reflexive in terms of the weak compactness of its closed unit ball.
E1200641 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: Scott–Mazur theorem | Statement: [Stanisław Mazur, notableWork, Scott–Mazur theorem]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Scott–Mazur theorem
Context triple: [Stanisław Mazur, notableWork, Scott–Mazur theorem]
  • A. 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.
  • B. Gelfand–Naimark theorem
    The Gelfand–Naimark theorem is a foundational result in functional analysis that characterizes C*-algebras as algebras of bounded operators on a Hilbert space (and, in the commutative case, as algebras of continuous functions on a locally compact Hausdorff space).
  • C. Mittag-Leffler theorem
    The Mittag-Leffler theorem is a fundamental result in complex analysis that characterizes meromorphic functions by allowing the construction of such functions with prescribed principal parts at given poles.
  • D. Bohr–Courant theorem
    The Bohr–Courant theorem is a classical result in analytic number theory describing the value distribution of Dirichlet series, particularly the Riemann zeta function, and serves as a precursor to modern universality theorems such as Voronin’s.
  • E. Banach–Stone theorem
    The Banach–Stone theorem is a fundamental result in functional analysis that characterizes compact Hausdorff spaces via isometric isomorphisms between their spaces of continuous real- or complex-valued functions.
  • 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: Scott–Mazur theorem
Triple: [Stanisław Mazur, notableWork, Scott–Mazur theorem]
Generated description
The Scott–Mazur theorem is a result in functional analysis that characterizes when a Banach space is reflexive in terms of the weak compactness of its closed unit ball.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Scott–Mazur theorem
Target entity description: The Scott–Mazur theorem is a result in functional analysis that characterizes when a Banach space is reflexive in terms of the weak compactness of its closed unit ball.
  • A. 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.
  • B. Gelfand–Naimark theorem
    The Gelfand–Naimark theorem is a foundational result in functional analysis that characterizes C*-algebras as algebras of bounded operators on a Hilbert space (and, in the commutative case, as algebras of continuous functions on a locally compact Hausdorff space).
  • C. Mittag-Leffler theorem
    The Mittag-Leffler theorem is a fundamental result in complex analysis that characterizes meromorphic functions by allowing the construction of such functions with prescribed principal parts at given poles.
  • D. Bohr–Courant theorem
    The Bohr–Courant theorem is a classical result in analytic number theory describing the value distribution of Dirichlet series, particularly the Riemann zeta function, and serves as a precursor to modern universality theorems such as Voronin’s.
  • E. Banach–Stone theorem
    The Banach–Stone theorem is a fundamental result in functional analysis that characterizes compact Hausdorff spaces via isometric isomorphisms between their spaces of continuous real- or complex-valued functions.
  • 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.