Triple

T5837293
Position Surface form Disambiguated ID Type / Status
Subject Calabi–Yau manifold E129502 entity
Predicate example P1259 FINISHED
Object K3 surface
A K3 surface is a compact, complex, two-dimensional algebraic surface with trivial canonical bundle and no global holomorphic 1-forms, serving as a fundamental example in algebraic geometry and string theory.
E129502 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: K3 surface | Statement: [Calabi–Yau manifold, example, K3 surface]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: K3 surface
Context triple: [Calabi–Yau manifold, example, K3 surface]
  • 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. Calabi–Yau manifold
    A Calabi–Yau manifold is a special type of complex manifold with vanishing first Chern class that plays a central role in string theory compactifications and complex algebraic geometry.
  • C. Fermat surface
    A Fermat surface is an algebraic surface in projective space defined by a homogeneous equation where each variable appears with the same exponent, generalizing the notion of Fermat curves to higher dimensions.
  • D. Kähler manifold
    A Kähler manifold is a complex manifold equipped with a Hermitian metric whose associated symplectic form is closed, making it simultaneously a complex, Riemannian, and symplectic manifold in a compatible way.
  • E. 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.
  • 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: K3 surface
Triple: [Calabi–Yau manifold, example, K3 surface]
Generated description
A K3 surface is a compact, complex, two-dimensional algebraic surface with trivial canonical bundle and no global holomorphic 1-forms, serving as a fundamental example in algebraic geometry and string theory.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: K3 surface
Target entity description: A K3 surface is a compact, complex, two-dimensional algebraic surface with trivial canonical bundle and no global holomorphic 1-forms, serving as a fundamental example in algebraic geometry and string theory.
  • 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. Calabi–Yau manifold chosen
    A Calabi–Yau manifold is a special type of complex manifold with vanishing first Chern class that plays a central role in string theory compactifications and complex algebraic geometry.
  • C. Fermat surface
    A Fermat surface is an algebraic surface in projective space defined by a homogeneous equation where each variable appears with the same exponent, generalizing the notion of Fermat curves to higher dimensions.
  • D. Kähler manifold
    A Kähler manifold is a complex manifold equipped with a Hermitian metric whose associated symplectic form is closed, making it simultaneously a complex, Riemannian, and symplectic manifold in a compatible way.
  • E. 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.
  • F. None of above.

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_69c0084af79c81908af128ccc29983d0 completed March 22, 2026, 3:18 p.m.
NER Named-entity recognition batch_69c034a48750819099ae917ae2b54e6d completed March 22, 2026, 6:27 p.m.
NED1 Entity disambiguation (via context triple) batch_69c0a19a6554819086cdae499f4d2247 completed March 23, 2026, 2:12 a.m.
NEDg Description generation batch_69c0a5ce005c8190a7da8d337caa089c completed March 23, 2026, 2:30 a.m.
NED2 Entity disambiguation (via description) batch_69c0a62cadf481909007a2a16cd36dbf completed March 23, 2026, 2:32 a.m.
Created at: March 22, 2026, 3:54 p.m.