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.