Triple

T13012659
Position Surface form Disambiguated ID Type / Status
Subject Herbert Robbins E322458 entity
Predicate knownFor P22 FINISHED
Object Robbins lemma
Robbins lemma is a result in probability theory that provides a bound on the expected maximum of partial sums of independent random variables, named after mathematician Herbert Robbins.
E1015499 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: Robbins lemma | Statement: [Herbert Robbins, knownFor, Robbins lemma]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Robbins lemma
Context triple: [Herbert Robbins, knownFor, Robbins lemma]
  • A. Bailey lemma
    The Bailey lemma is a key result in the theory of basic hypergeometric series that provides a systematic method for generating Rogers–Ramanujan-type identities and other q-series relations.
  • B. Tucker’s lemma
    Tucker’s lemma is a combinatorial analog of the Borsuk–Ulam theorem that provides conditions guaranteeing the existence of certain complementary edge labels in triangulated spheres.
  • C. Ky Fan’s lemma
    Ky Fan’s lemma is a combinatorial topological result that generalizes Tucker’s lemma and provides conditions guaranteeing the existence of certain balanced or fully labeled simplices in labeled triangulations of spheres or simplices.
  • D. Sperner's lemma
    Sperner's lemma is a fundamental result in combinatorial topology that guarantees the existence of a fully labeled simplex in certain labeled triangulations, and is widely used to prove fixed-point and equilibrium theorems.
  • E. Beppo Levi's lemma
    Beppo Levi's lemma, also known as the monotone convergence theorem, is a fundamental result in measure theory that guarantees the convergence of integrals for non-decreasing sequences of non-negative measurable 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: Robbins lemma
Triple: [Herbert Robbins, knownFor, Robbins lemma]
Generated description
Robbins lemma is a result in probability theory that provides a bound on the expected maximum of partial sums of independent random variables, named after mathematician Herbert Robbins.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Robbins lemma
Target entity description: Robbins lemma is a result in probability theory that provides a bound on the expected maximum of partial sums of independent random variables, named after mathematician Herbert Robbins.
  • A. Bailey lemma
    The Bailey lemma is a key result in the theory of basic hypergeometric series that provides a systematic method for generating Rogers–Ramanujan-type identities and other q-series relations.
  • B. Tucker’s lemma
    Tucker’s lemma is a combinatorial analog of the Borsuk–Ulam theorem that provides conditions guaranteeing the existence of certain complementary edge labels in triangulated spheres.
  • C. Ky Fan’s lemma
    Ky Fan’s lemma is a combinatorial topological result that generalizes Tucker’s lemma and provides conditions guaranteeing the existence of certain balanced or fully labeled simplices in labeled triangulations of spheres or simplices.
  • D. Sperner's lemma
    Sperner's lemma is a fundamental result in combinatorial topology that guarantees the existence of a fully labeled simplex in certain labeled triangulations, and is widely used to prove fixed-point and equilibrium theorems.
  • E. Beppo Levi's lemma
    Beppo Levi's lemma, also known as the monotone convergence theorem, is a fundamental result in measure theory that guarantees the convergence of integrals for non-decreasing sequences of non-negative measurable 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_69d807657e8c8190bd9435ee2f823845 completed April 9, 2026, 8:09 p.m.
NER Named-entity recognition batch_69d97ecbb8f4819094d55eb07cb5ad97 completed April 10, 2026, 10:50 p.m.
NED1 Entity disambiguation (via context triple) batch_69f6c10d5b9881909db688c1ab0e6a77 completed May 3, 2026, 3:29 a.m.
NEDg Description generation batch_69f6c277e6248190870b3bf9869716a7 completed May 3, 2026, 3:35 a.m.
NED2 Entity disambiguation (via description) batch_69f6c38bc0b08190b76cb0853d99ad82 completed May 3, 2026, 3:39 a.m.
Created at: April 9, 2026, 8:49 p.m.