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.