Triple
T2866512
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Princeton Mathematical Series |
E63452
|
entity |
| Predicate | workIncluded |
P10663
|
FINISHED |
| Object |
"Algebraic Topology"
"Algebraic Topology" is a foundational mathematical text that develops topological concepts using algebraic methods such as homology and cohomology theories.
|
E305928
|
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: "Algebraic Topology" | Statement: [Princeton Mathematical Series, workIncluded, "Algebraic Topology"]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: "Algebraic Topology" Context triple: [Princeton Mathematical Series, workIncluded, "Algebraic Topology"]
-
A.
Alexandrov–Čech cohomology
Alexandrov–Čech cohomology is a topological cohomology theory that computes invariants of spaces using inverse limits over open covers, closely related to and often coinciding with sheaf cohomology.
-
B.
Introduction to Algebraic K-Theory
Introduction to Algebraic K-Theory is a foundational graduate-level textbook by John Milnor that systematically develops the basic concepts and techniques of algebraic K-theory in a concise and influential style.
-
C.
Categories for the Working Mathematician
Categories for the Working Mathematician is a foundational textbook in category theory that systematically develops the subject and its applications for professional mathematicians.
-
D.
Moscow school of topology
The Moscow school of topology was a prominent mathematical tradition centered in Moscow that made foundational contributions to general and algebraic topology in the 20th century.
-
E.
“K-Theory” (book with Friedrich Hirzebruch and others)
“K-Theory” is a foundational mathematical monograph co-authored by Michael Atiyah, Friedrich Hirzebruch, and others that systematically develops topological K-theory and its applications in geometry and topology.
- 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: "Algebraic Topology" Triple: [Princeton Mathematical Series, workIncluded, "Algebraic Topology"]
Generated description
"Algebraic Topology" is a foundational mathematical text that develops topological concepts using algebraic methods such as homology and cohomology theories.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: "Algebraic Topology" Target entity description: "Algebraic Topology" is a foundational mathematical text that develops topological concepts using algebraic methods such as homology and cohomology theories.
-
A.
Alexandrov–Čech cohomology
Alexandrov–Čech cohomology is a topological cohomology theory that computes invariants of spaces using inverse limits over open covers, closely related to and often coinciding with sheaf cohomology.
-
B.
Introduction to Algebraic K-Theory
Introduction to Algebraic K-Theory is a foundational graduate-level textbook by John Milnor that systematically develops the basic concepts and techniques of algebraic K-theory in a concise and influential style.
-
C.
Categories for the Working Mathematician
Categories for the Working Mathematician is a foundational textbook in category theory that systematically develops the subject and its applications for professional mathematicians.
-
D.
Moscow school of topology
The Moscow school of topology was a prominent mathematical tradition centered in Moscow that made foundational contributions to general and algebraic topology in the 20th century.
-
E.
“K-Theory” (book with Friedrich Hirzebruch and others)
“K-Theory” is a foundational mathematical monograph co-authored by Michael Atiyah, Friedrich Hirzebruch, and others that systematically develops topological K-theory and its applications in geometry and topology.
- 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_69ab4c42fb8c8190b36e161d47c03b81 |
completed | March 6, 2026, 9:50 p.m. |
| NER | Named-entity recognition | batch_69abe08c85c48190bd8c0f6680fca0c8 |
completed | March 7, 2026, 8:23 a.m. |
| NED1 | Entity disambiguation (via context triple) | batch_69b01da85930819092d19a5e712cfa18 |
completed | March 10, 2026, 1:33 p.m. |
| NEDg | Description generation | batch_69b01e34639c8190b1c6e8a14cd31d96 |
completed | March 10, 2026, 1:35 p.m. |
| NED2 | Entity disambiguation (via description) | batch_69b01f5a6784819089499926fb115d9c |
completed | March 10, 2026, 1:40 p.m. |
Created at: March 6, 2026, 10:02 p.m.