Triple

T7685048
Position Surface form Disambiguated ID Type / Status
Subject Lev Pontryagin E174094 entity
Predicate notableWork P4 FINISHED
Object Foundations of Combinatorial Topology
Foundations of Combinatorial Topology is a seminal mathematical monograph by Lev Pontryagin that systematically develops the methods and results of early 20th-century combinatorial (algebraic) topology.
E681629 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 Combinatorial Topology | Statement: [Lev Pontryagin, notableWork, Foundations of Combinatorial Topology]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Foundations of Combinatorial Topology
Context triple: [Lev Pontryagin, notableWork, Foundations of Combinatorial Topology]
  • A. Topologie (with Heinz Hopf)
    "Topologie" is a foundational 1935 textbook on general topology co-authored by Pavel Alexandrov and Heinz Hopf that helped shape the modern development of the field.
  • B. 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.
  • C. 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.
  • D. "Topologie" (with W. Hurewicz)
    "Topologie" (with W. Hurewicz) is a foundational textbook in topology co-authored by Heinz Hopf and Witold Hurewicz that helped shape the modern development and teaching of the subject.
  • E. L’Analysis Situs et la Géométrie Algébrique
    L’Analysis Situs et la Géométrie Algébrique is a foundational mathematical treatise that helped establish modern algebraic topology and its connections with algebraic geometry.
  • 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 Combinatorial Topology
Triple: [Lev Pontryagin, notableWork, Foundations of Combinatorial Topology]
Generated description
Foundations of Combinatorial Topology is a seminal mathematical monograph by Lev Pontryagin that systematically develops the methods and results of early 20th-century combinatorial (algebraic) topology.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Foundations of Combinatorial Topology
Target entity description: Foundations of Combinatorial Topology is a seminal mathematical monograph by Lev Pontryagin that systematically develops the methods and results of early 20th-century combinatorial (algebraic) topology.
  • A. Topologie (with Heinz Hopf)
    "Topologie" is a foundational 1935 textbook on general topology co-authored by Pavel Alexandrov and Heinz Hopf that helped shape the modern development of the field.
  • B. 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.
  • C. 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.
  • D. "Topologie" (with W. Hurewicz)
    "Topologie" (with W. Hurewicz) is a foundational textbook in topology co-authored by Heinz Hopf and Witold Hurewicz that helped shape the modern development and teaching of the subject.
  • E. L’Analysis Situs et la Géométrie Algébrique
    L’Analysis Situs et la Géométrie Algébrique is a foundational mathematical treatise that helped establish modern algebraic topology and its connections with algebraic geometry.
  • 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_69c6995840408190a19de6c51090f46f completed March 27, 2026, 2:51 p.m.
NER Named-entity recognition batch_69c7022118908190a3a93cfda79be0a4 completed March 27, 2026, 10:18 p.m.
NED1 Entity disambiguation (via context triple) batch_69c8a25c2a308190908ffdd2f0b7262f completed March 29, 2026, 3:54 a.m.
NEDg Description generation batch_69c8a37c995881908c71791c6cc002f3 completed March 29, 2026, 3:58 a.m.
NED2 Entity disambiguation (via description) batch_69c8a3fe63a4819086bcb5f80cdbd30b completed March 29, 2026, 4:01 a.m.
Created at: March 27, 2026, 4:02 p.m.