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.