Triple

T4706377
Position Surface form Disambiguated ID Type / Status
Subject Ernst Eduard Kummer E104397 entity
Predicate knownFor P22 FINISHED
Object 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.
E463785 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: Kummer surfaces | Statement: [Ernst Eduard Kummer, knownFor, Kummer surfaces]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Kummer surfaces
Context triple: [Ernst Eduard Kummer, knownFor, Kummer surfaces]
  • A. 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.
  • B. Clebsch–Aronhold invariants
    The Clebsch–Aronhold invariants are classical algebraic invariants associated with binary forms, particularly quartic forms, that play a key role in invariant theory and the classification of algebraic curves.
  • C. Theorie der algebraischen Kurven
    "Theorie der algebraischen Kurven" is a foundational 19th-century mathematical treatise by Julius Plücker that systematically develops the geometry and classification of algebraic curves.
  • 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. 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.
  • 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: Kummer surfaces
Triple: [Ernst Eduard Kummer, knownFor, Kummer surfaces]
Generated description
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.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Kummer surfaces
Target entity description: 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.
  • A. 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.
  • B. Clebsch–Aronhold invariants
    The Clebsch–Aronhold invariants are classical algebraic invariants associated with binary forms, particularly quartic forms, that play a key role in invariant theory and the classification of algebraic curves.
  • C. Theorie der algebraischen Kurven
    "Theorie der algebraischen Kurven" is a foundational 19th-century mathematical treatise by Julius Plücker that systematically develops the geometry and classification of algebraic curves.
  • 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. 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.
  • 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_69bd43eac3c08190af7e4020c6c3704c completed March 20, 2026, 12:56 p.m.
NER Named-entity recognition batch_69bd63e9f0b88190820aa7fba2f91b6e completed March 20, 2026, 3:12 p.m.
NED1 Entity disambiguation (via context triple) batch_69be1067c6a081909fa06689ea66a8a4 completed March 21, 2026, 3:28 a.m.
NEDg Description generation batch_69be133c5a8c8190b3c0f066c4ab44a9 completed March 21, 2026, 3:40 a.m.
NED2 Entity disambiguation (via description) batch_69be13cafd1c8190aec0efe6328c25b8 completed March 21, 2026, 3:43 a.m.
Created at: March 20, 2026, 1:17 p.m.