Triple
T16876265
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Gian-Carlo Rota |
E421307
|
entity |
| Predicate | notableWork |
P4
|
FINISHED |
| Object |
Foundations of Combinatorics via Linear Algebra
Foundations of Combinatorics via Linear Algebra is a seminal textbook by Gian-Carlo Rota that develops key topics in combinatorics through the methods and perspective of linear algebra.
|
E1237906
|
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: Foundations of Combinatorics via Linear Algebra | Statement: [Gian-Carlo Rota, notableWork, Foundations of Combinatorics via Linear Algebra]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Foundations of Combinatorics via Linear Algebra Context triple: [Gian-Carlo Rota, notableWork, Foundations of Combinatorics via Linear Algebra]
-
A.
Foundations of Combinatorial Theory
Foundations of Combinatorial Theory is a seminal mathematical work by Gian-Carlo Rota that helped establish modern combinatorics as a rigorous and unified field of study.
-
B.
Combinatorial Nullstellensatz
Combinatorial Nullstellensatz is a powerful algebraic tool in combinatorics that uses polynomial methods over fields to derive results about combinatorial structures, such as existence and counting theorems.
-
C.
The Twelvefold Way
The Twelvefold Way is a framework in combinatorics that systematically classifies twelve fundamental ways of counting functions between finite sets under various labeling and structural constraints.
-
D.
Introduction to Graph Theory
Introduction to Graph Theory is a widely used textbook that provides a clear and accessible introduction to the fundamental concepts and techniques of graph theory.
-
E.
Erdős on Graphs: His Legacy
Erdős on Graphs: His Legacy is a mathematical monograph by Fan Chung and Ronald Graham that surveys and extends Paul Erdős’s influential work in graph theory and combinatorics.
- 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: Foundations of Combinatorics via Linear Algebra Triple: [Gian-Carlo Rota, notableWork, Foundations of Combinatorics via Linear Algebra]
Generated description
Foundations of Combinatorics via Linear Algebra is a seminal textbook by Gian-Carlo Rota that develops key topics in combinatorics through the methods and perspective of linear algebra.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Foundations of Combinatorics via Linear Algebra Target entity description: Foundations of Combinatorics via Linear Algebra is a seminal textbook by Gian-Carlo Rota that develops key topics in combinatorics through the methods and perspective of linear algebra.
-
A.
Foundations of Combinatorial Theory
Foundations of Combinatorial Theory is a seminal mathematical work by Gian-Carlo Rota that helped establish modern combinatorics as a rigorous and unified field of study.
-
B.
Combinatorial Nullstellensatz
Combinatorial Nullstellensatz is a powerful algebraic tool in combinatorics that uses polynomial methods over fields to derive results about combinatorial structures, such as existence and counting theorems.
-
C.
The Twelvefold Way
The Twelvefold Way is a framework in combinatorics that systematically classifies twelve fundamental ways of counting functions between finite sets under various labeling and structural constraints.
-
D.
Introduction to Graph Theory
Introduction to Graph Theory is a widely used textbook that provides a clear and accessible introduction to the fundamental concepts and techniques of graph theory.
-
E.
Erdős on Graphs: His Legacy
Erdős on Graphs: His Legacy is a mathematical monograph by Fan Chung and Ronald Graham that surveys and extends Paul Erdős’s influential work in graph theory and combinatorics.
- 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_69d889d470fc8190b4aec199636c0c56 |
completed | April 10, 2026, 5:25 a.m. |
| NER | Named-entity recognition | batch_69e3b7f646308190b5e277b5f51cd315 |
completed | April 18, 2026, 4:57 p.m. |
| NED1 | Entity disambiguation (via context triple) | batch_6a00c2b4abd08190841c5bb0b0eaa177 |
completed | May 10, 2026, 5:39 p.m. |
| NEDg | Description generation | batch_6a00c355f4108190a4209599bf5f50da |
completed | May 10, 2026, 5:41 p.m. |
| NED2 | Entity disambiguation (via description) | batch_6a00c413314881909e308588af09ce2a |
completed | May 10, 2026, 5:44 p.m. |
Created at: April 10, 2026, 5:29 a.m.