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.