Triple
T10773258
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Grothendieck inequality |
E254132
|
entity |
| Predicate | relatedTo |
P37
|
FINISHED |
| Object |
Pisier’s factorization theorems
Pisier’s factorization theorems are fundamental results in functional analysis and operator theory that provide deep factorization properties for linear and multilinear operators on Banach spaces, extending and refining ideas related to Grothendieck-type inequalities.
|
E884928
|
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: Pisier’s factorization theorems | Statement: [Grothendieck inequality, relatedTo, Pisier’s factorization theorems]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Pisier’s factorization theorems Context triple: [Grothendieck inequality, relatedTo, Pisier’s factorization theorems]
-
A.
Sylvester’s theorem on partitions
Sylvester’s theorem on partitions is a result in number theory that provides a systematic way to count integer partitions subject to certain congruence or restriction conditions, forming part of the foundational work in partition theory.
-
B.
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.
-
C.
Fellini–Rota collaborations
The Fellini–Rota collaborations are the celebrated series of film projects in which Italian director Federico Fellini worked closely with composer Nino Rota to create some of the most iconic and influential soundtracks in cinema history.
-
D.
Legendre’s formula for valuations of factorials
Legendre’s formula for valuations of factorials is a number-theoretic result that expresses the exponent of a prime in the prime factorization of n! as a sum of integer divisions of n by successive powers of that prime.
-
E.
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.
- 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: Pisier’s factorization theorems Triple: [Grothendieck inequality, relatedTo, Pisier’s factorization theorems]
Generated description
Pisier’s factorization theorems are fundamental results in functional analysis and operator theory that provide deep factorization properties for linear and multilinear operators on Banach spaces, extending and refining ideas related to Grothendieck-type inequalities.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Pisier’s factorization theorems Target entity description: Pisier’s factorization theorems are fundamental results in functional analysis and operator theory that provide deep factorization properties for linear and multilinear operators on Banach spaces, extending and refining ideas related to Grothendieck-type inequalities.
-
A.
Sylvester’s theorem on partitions
Sylvester’s theorem on partitions is a result in number theory that provides a systematic way to count integer partitions subject to certain congruence or restriction conditions, forming part of the foundational work in partition theory.
-
B.
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.
-
C.
Fellini–Rota collaborations
The Fellini–Rota collaborations are the celebrated series of film projects in which Italian director Federico Fellini worked closely with composer Nino Rota to create some of the most iconic and influential soundtracks in cinema history.
-
D.
Legendre’s formula for valuations of factorials
Legendre’s formula for valuations of factorials is a number-theoretic result that expresses the exponent of a prime in the prime factorization of n! as a sum of integer divisions of n by successive powers of that prime.
-
E.
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.
- 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_69d6aa5f54f4819082d0bbcb6f8797e6 |
completed | April 8, 2026, 7:19 p.m. |
| NER | Named-entity recognition | batch_69d7329b27748190bd0e2569c7972fd1 |
completed | April 9, 2026, 5:01 a.m. |
| NED1 | Entity disambiguation (via context triple) | batch_69de238559b48190abc759e744ab0f8e |
completed | April 14, 2026, 11:22 a.m. |
| NEDg | Description generation | batch_69de271fb08c8190a44c547083226fd8 |
completed | April 14, 2026, 11:38 a.m. |
| NED2 | Entity disambiguation (via description) | batch_69de2cecc24c8190a240366e0600426a |
completed | April 14, 2026, 12:02 p.m. |
Created at: April 8, 2026, 9:16 p.m.