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.