Triple

T6337355
Position Surface form Disambiguated ID Type / Status
Subject Friedrich Hirzebruch E142524 entity
Predicate knownFor P22 FINISHED
Object Hirzebruch surfaces
Hirzebruch surfaces are a family of complex algebraic surfaces that serve as fundamental examples in algebraic geometry and the classification of complex surfaces.
E586791 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: Hirzebruch surfaces | Statement: [Friedrich Hirzebruch, knownFor, Hirzebruch surfaces]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Hirzebruch surfaces
Context triple: [Friedrich Hirzebruch, knownFor, Hirzebruch surfaces]
  • A. Kummer surfaces
    Kummer surfaces are special quartic algebraic surfaces in projective three-space characterized by having 16 ordinary double points, extensively studied in the context of complex geometry and abelian varieties.
  • B. Clebsch diagonal surfaces
    Clebsch diagonal surfaces are classical 19th-century algebraic surfaces in projective three-space, famous as the first explicit smooth cubic surface with all 27 lines defined over the real numbers.
  • C. Hirzebruch–Riemann–Roch theorem
    The Hirzebruch–Riemann–Roch theorem is a fundamental result in algebraic geometry and topology that expresses the holomorphic Euler characteristic of a complex manifold in terms of characteristic classes, unifying and extending classical Riemann–Roch type formulas.
  • D. Grothendieck–Ogg–Shafarevich formula
    The Grothendieck–Ogg–Shafarevich formula is a result in arithmetic geometry that relates the Euler characteristic of an ℓ-adic sheaf on a curve over a finite field to local invariants such as conductors and ramification data.
  • E. Chern classes
    Chern classes are fundamental topological invariants in differential and algebraic geometry that classify complex vector bundles and capture their curvature and twisting properties.
  • 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: Hirzebruch surfaces
Triple: [Friedrich Hirzebruch, knownFor, Hirzebruch surfaces]
Generated description
Hirzebruch surfaces are a family of complex algebraic surfaces that serve as fundamental examples in algebraic geometry and the classification of complex surfaces.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Hirzebruch surfaces
Target entity description: Hirzebruch surfaces are a family of complex algebraic surfaces that serve as fundamental examples in algebraic geometry and the classification of complex surfaces.
  • A. Kummer surfaces
    Kummer surfaces are special quartic algebraic surfaces in projective three-space characterized by having 16 ordinary double points, extensively studied in the context of complex geometry and abelian varieties.
  • B. Clebsch diagonal surfaces
    Clebsch diagonal surfaces are classical 19th-century algebraic surfaces in projective three-space, famous as the first explicit smooth cubic surface with all 27 lines defined over the real numbers.
  • C. Hirzebruch–Riemann–Roch theorem
    The Hirzebruch–Riemann–Roch theorem is a fundamental result in algebraic geometry and topology that expresses the holomorphic Euler characteristic of a complex manifold in terms of characteristic classes, unifying and extending classical Riemann–Roch type formulas.
  • D. Grothendieck–Ogg–Shafarevich formula
    The Grothendieck–Ogg–Shafarevich formula is a result in arithmetic geometry that relates the Euler characteristic of an ℓ-adic sheaf on a curve over a finite field to local invariants such as conductors and ramification data.
  • E. Chern classes
    Chern classes are fundamental topological invariants in differential and algebraic geometry that classify complex vector bundles and capture their curvature and twisting properties.
  • 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_69c0654c63508190b51f7b622388e5ad 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.