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.