Triple
T10803781
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Raj Chandra Bose |
E254909
|
entity |
| Predicate | notableWork |
P4
|
FINISHED |
| Object |
Bose–Nair theorem
The Bose–Nair theorem is a result in combinatorial design theory that provides conditions for the existence and construction of certain balanced incomplete block designs, contributing to the foundations of modern combinatorics and coding theory.
|
E886601
|
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: Bose–Nair theorem | Statement: [Raj Chandra Bose, notableWork, Bose–Nair theorem]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Bose–Nair theorem Context triple: [Raj Chandra Bose, notableWork, Bose–Nair theorem]
-
A.
Kesten’s theorem
Kesten’s theorem is a fundamental result in probability theory that characterizes when a random walk on a group is transient or recurrent, with deep implications for random walks on groups and percolation theory.
-
B.
Busemann–Feller theorem
The Busemann–Feller theorem is a result in geometric measure theory that characterizes when a metric space is geodesic by relating distance properties to the existence of shortest paths between points.
-
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.
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.
-
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: Bose–Nair theorem Triple: [Raj Chandra Bose, notableWork, Bose–Nair theorem]
Generated description
The Bose–Nair theorem is a result in combinatorial design theory that provides conditions for the existence and construction of certain balanced incomplete block designs, contributing to the foundations of modern combinatorics and coding theory.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Bose–Nair theorem Target entity description: The Bose–Nair theorem is a result in combinatorial design theory that provides conditions for the existence and construction of certain balanced incomplete block designs, contributing to the foundations of modern combinatorics and coding theory.
-
A.
Kesten’s theorem
Kesten’s theorem is a fundamental result in probability theory that characterizes when a random walk on a group is transient or recurrent, with deep implications for random walks on groups and percolation theory.
-
B.
Busemann–Feller theorem
The Busemann–Feller theorem is a result in geometric measure theory that characterizes when a metric space is geodesic by relating distance properties to the existence of shortest paths between points.
-
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.
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.
-
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_69d6aa61c15c8190a1839550c56e75e1 |
completed | April 8, 2026, 7:20 p.m. |
| NER | Named-entity recognition | batch_69d73370e7388190885b104fc883456e |
completed | April 9, 2026, 5:04 a.m. |
| NED1 | Entity disambiguation (via context triple) | batch_69de567a7ea0819088a2fa10f8367d89 |
completed | April 14, 2026, 3 p.m. |
| NEDg | Description generation | batch_69de5eaf3cc08190935cb6ddf2020166 |
completed | April 14, 2026, 3:35 p.m. |
| NED2 | Entity disambiguation (via description) | batch_69de63a902f4819089845bc6d7469c6b |
completed | April 14, 2026, 3:56 p.m. |
Created at: April 8, 2026, 9:18 p.m.