Triple

T6337383
Position Surface form Disambiguated ID Type / Status
Subject Friedrich Hirzebruch E142524 entity
Predicate notableWork P4 FINISHED
Object Topological Methods in Algebraic Geometry
Topological Methods in Algebraic Geometry is a foundational mathematical monograph by Friedrich Hirzebruch that applies topological techniques, particularly characteristic classes and cobordism theory, to problems in algebraic geometry.
E586797 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: Topological Methods in Algebraic Geometry | Statement: [Friedrich Hirzebruch, notableWork, Topological Methods in Algebraic Geometry]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Topological Methods in Algebraic Geometry
Context triple: [Friedrich Hirzebruch, notableWork, Topological Methods in Algebraic Geometry]
  • A. Foundations of Algebraic Geometry
    Foundations of Algebraic Geometry is a landmark mathematical treatise that systematically developed the modern foundations of algebraic geometry and profoundly influenced the field’s subsequent evolution.
  • B. Chevalley’s theorem in algebraic geometry
    Chevalley’s theorem in algebraic geometry is a fundamental result stating that the image of a morphism of finite type between schemes (or varieties) is a constructible set, playing a key role in understanding how geometric properties behave under mappings.
  • C. 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.
  • D. Singular Points of Complex Hypersurfaces
    "Singular Points of Complex Hypersurfaces" is a foundational monograph in singularity theory that systematically studies the local and topological properties of singularities arising in complex algebraic and analytic hypersurfaces.
  • E. Brill–Noether theory
    Brill–Noether theory is a branch of algebraic geometry that studies linear series on algebraic curves, particularly the existence and dimension of spaces of special divisors and maps to projective spaces.
  • 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: Topological Methods in Algebraic Geometry
Triple: [Friedrich Hirzebruch, notableWork, Topological Methods in Algebraic Geometry]
Generated description
Topological Methods in Algebraic Geometry is a foundational mathematical monograph by Friedrich Hirzebruch that applies topological techniques, particularly characteristic classes and cobordism theory, to problems in algebraic geometry.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Topological Methods in Algebraic Geometry
Target entity description: Topological Methods in Algebraic Geometry is a foundational mathematical monograph by Friedrich Hirzebruch that applies topological techniques, particularly characteristic classes and cobordism theory, to problems in algebraic geometry.
  • A. Foundations of Algebraic Geometry
    Foundations of Algebraic Geometry is a landmark mathematical treatise that systematically developed the modern foundations of algebraic geometry and profoundly influenced the field’s subsequent evolution.
  • B. Chevalley’s theorem in algebraic geometry
    Chevalley’s theorem in algebraic geometry is a fundamental result stating that the image of a morphism of finite type between schemes (or varieties) is a constructible set, playing a key role in understanding how geometric properties behave under mappings.
  • C. 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.
  • D. Singular Points of Complex Hypersurfaces
    "Singular Points of Complex Hypersurfaces" is a foundational monograph in singularity theory that systematically studies the local and topological properties of singularities arising in complex algebraic and analytic hypersurfaces.
  • E. Brill–Noether theory
    Brill–Noether theory is a branch of algebraic geometry that studies linear series on algebraic curves, particularly the existence and dimension of spaces of special divisors and maps to projective spaces.
  • 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_69c008d4d8e88190ad301c05b08722ac completed March 22, 2026, 3:20 p.m.
NER Named-entity recognition batch_69c0654e11988190b708426d3003716a completed March 22, 2026, 9:55 p.m.
NED1 Entity disambiguation (via context triple) batch_69c604307b388190bbc59f5f57cb4bbe completed March 27, 2026, 4:14 a.m.
NEDg Description generation batch_69c606cb4d3c8190b8200ee8284cf1e7 completed March 27, 2026, 4:25 a.m.
NED2 Entity disambiguation (via description) batch_69c60741e7388190a8194d168a769cfd completed March 27, 2026, 4:27 a.m.
Created at: March 22, 2026, 4:30 p.m.