Triple

T11411573
Position Surface form Disambiguated ID Type / Status
Subject Gelfand–Naimark theorem E270382 entity
Predicate isRelatedTo P37 FINISHED
Object Stone representation theorem
The Stone representation theorem is a fundamental result in mathematical logic and topology that represents every Boolean algebra as an algebra of clopen sets in a totally disconnected compact Hausdorff (Stone) space.
E924199 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: Stone representation theorem | Statement: [Gelfand–Naimark theorem, isRelatedTo, Stone representation theorem]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Stone representation theorem
Context triple: [Gelfand–Naimark theorem, isRelatedTo, Stone representation theorem]
  • A. Khinchin's representation theorem
    Khinchin's representation theorem is a result in probability theory that characterizes stationary stochastic processes by representing them in terms of simpler, more fundamental random components.
  • B. Birkhoff’s representation theorem for finite distributive lattices
    Birkhoff’s representation theorem for finite distributive lattices is a fundamental result in lattice theory that characterizes every finite distributive lattice as isomorphic to the lattice of lower (order) ideals of a finite poset.
  • C. Szekeres–Lindström theorem
    The Szekeres–Lindström theorem is a result in combinatorics that characterizes the maximum size of intersecting families of subsets, serving as a precursor to and special case of the Erdős–Ko–Rado theorem.
  • D. 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).
  • E. Birkhoff–von Neumann theorem
    The Birkhoff–von Neumann theorem is a fundamental result in matrix theory and combinatorics stating that every doubly stochastic matrix can be expressed as a convex combination of permutation matrices.
  • 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: Stone representation theorem
Triple: [Gelfand–Naimark theorem, isRelatedTo, Stone representation theorem]
Generated description
The Stone representation theorem is a fundamental result in mathematical logic and topology that represents every Boolean algebra as an algebra of clopen sets in a totally disconnected compact Hausdorff (Stone) space.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Stone representation theorem
Target entity description: The Stone representation theorem is a fundamental result in mathematical logic and topology that represents every Boolean algebra as an algebra of clopen sets in a totally disconnected compact Hausdorff (Stone) space.
  • A. Khinchin's representation theorem
    Khinchin's representation theorem is a result in probability theory that characterizes stationary stochastic processes by representing them in terms of simpler, more fundamental random components.
  • B. Birkhoff’s representation theorem for finite distributive lattices
    Birkhoff’s representation theorem for finite distributive lattices is a fundamental result in lattice theory that characterizes every finite distributive lattice as isomorphic to the lattice of lower (order) ideals of a finite poset.
  • C. Szekeres–Lindström theorem
    The Szekeres–Lindström theorem is a result in combinatorics that characterizes the maximum size of intersecting families of subsets, serving as a precursor to and special case of the Erdős–Ko–Rado theorem.
  • D. 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).
  • E. Birkhoff–von Neumann theorem
    The Birkhoff–von Neumann theorem is a fundamental result in matrix theory and combinatorics stating that every doubly stochastic matrix can be expressed as a convex combination of permutation matrices.
  • 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_69d6aaddeaa8819088b30ef7b50598c9 completed April 8, 2026, 7:22 p.m.
NER Named-entity recognition batch_69d8015017d08190b4020c76545556d6 completed April 9, 2026, 7:43 p.m.
NED1 Entity disambiguation (via context triple) batch_69e5b855f0508190a2e57ef9407ddb1a completed April 20, 2026, 5:23 a.m.
NEDg Description generation batch_69e5c28d3824819097ff84cb4e13c923 completed April 20, 2026, 6:07 a.m.
NED2 Entity disambiguation (via description) batch_69e5c451c6c88190bcbb1f54ede35d29 completed April 20, 2026, 6:14 a.m.
Created at: April 8, 2026, 9:34 p.m.