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.