Triple

T10773244
Position Surface form Disambiguated ID Type / Status
Subject Grothendieck inequality E254132 entity
Predicate involvesConstant P9782 FINISHED
Object Grothendieck constant
The Grothendieck constant is a fundamental numerical constant in functional analysis and theoretical computer science that quantifies how much certain matrix norms or tensor products can differ between Hilbert space and classical settings.
E254132 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: Grothendieck constant | Statement: [Grothendieck inequality, involvesConstant, Grothendieck constant]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Grothendieck constant
Context triple: [Grothendieck inequality, involvesConstant, Grothendieck constant]
  • A. Grothendieck inequality
    The Grothendieck inequality is a fundamental result in functional analysis and theoretical computer science that bounds certain bilinear forms and has deep implications for Banach space theory, operator theory, and approximation algorithms.
  • B. 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.
  • C. Connes embedding problem
    The Connes embedding problem is a central open question in operator algebras and quantum theory that asks whether every separable II₁ factor can be approximated in a specific way by finite-dimensional matrix algebras.
  • D. Erdős discrepancy problem
    The Erdős discrepancy problem is a famous question in combinatorial number theory that asks whether every infinite ±1 sequence has arbitrarily large discrepancy along some homogeneous arithmetic progression.
  • E. Graham–Pollak theorem
    The Graham–Pollak theorem is a result in graph theory that states the edges of a complete graph on n vertices cannot be partitioned into fewer than n−1 complete bipartite subgraphs.
  • 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: Grothendieck constant
Triple: [Grothendieck inequality, involvesConstant, Grothendieck constant]
Generated description
The Grothendieck constant is a fundamental numerical constant in functional analysis and theoretical computer science that quantifies how much certain matrix norms or tensor products can differ between Hilbert space and classical settings.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Grothendieck constant
Target entity description: The Grothendieck constant is a fundamental numerical constant in functional analysis and theoretical computer science that quantifies how much certain matrix norms or tensor products can differ between Hilbert space and classical settings.
  • A. Grothendieck inequality chosen
    The Grothendieck inequality is a fundamental result in functional analysis and theoretical computer science that bounds certain bilinear forms and has deep implications for Banach space theory, operator theory, and approximation algorithms.
  • B. 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.
  • C. Connes embedding problem
    The Connes embedding problem is a central open question in operator algebras and quantum theory that asks whether every separable II₁ factor can be approximated in a specific way by finite-dimensional matrix algebras.
  • D. Erdős discrepancy problem
    The Erdős discrepancy problem is a famous question in combinatorial number theory that asks whether every infinite ±1 sequence has arbitrarily large discrepancy along some homogeneous arithmetic progression.
  • E. Graham–Pollak theorem
    The Graham–Pollak theorem is a result in graph theory that states the edges of a complete graph on n vertices cannot be partitioned into fewer than n−1 complete bipartite subgraphs.
  • F. None of above.

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.