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.