Triple

T22328663
Position Surface form Disambiguated ID Type / Status
Subject Strominger–Yau–Zaslow conjecture E551966 entity
Predicate involves P1256 FINISHED
Object SYZ fibration
An SYZ fibration is a special Lagrangian torus fibration on a Calabi–Yau manifold that underlies the geometric explanation of mirror symmetry in the Strominger–Yau–Zaslow conjecture.
E551966 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: SYZ fibration | Statement: [Strominger–Yau–Zaslow conjecture, involves, SYZ fibration]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: SYZ fibration
Context triple: [Strominger–Yau–Zaslow conjecture, involves, SYZ fibration]
  • A. Lefschetz fibration
    A Lefschetz fibration is a smooth map from a higher-dimensional manifold to a lower-dimensional one whose singularities are modeled on complex Morse-type critical points, playing a central role in symplectic and complex geometry.
  • B. Strominger–Yau–Zaslow conjecture
    The Strominger–Yau–Zaslow conjecture is a proposal in mirror symmetry stating that mirror pairs of Calabi–Yau manifolds can be understood as dual special Lagrangian torus fibrations, providing a geometric explanation of mirror symmetry.
  • C. Milnor fibration
    Milnor fibration is a fundamental construction in singularity theory and differential topology that describes how the complement of a complex hypersurface singularity fibers over the circle, revealing the local topological structure of the singularity.
  • D. Hitchin fibration
    The Hitchin fibration is a fundamental geometric structure in the theory of Higgs bundles that organizes their moduli space into an algebraically completely integrable system with deep connections to representation theory and the geometric Langlands program.
  • E. 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.
  • 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: SYZ fibration
Triple: [Strominger–Yau–Zaslow conjecture, involves, SYZ fibration]
Generated description
An SYZ fibration is a special Lagrangian torus fibration on a Calabi–Yau manifold that underlies the geometric explanation of mirror symmetry in the Strominger–Yau–Zaslow conjecture.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: SYZ fibration
Target entity description: An SYZ fibration is a special Lagrangian torus fibration on a Calabi–Yau manifold that underlies the geometric explanation of mirror symmetry in the Strominger–Yau–Zaslow conjecture.
  • A. Lefschetz fibration
    A Lefschetz fibration is a smooth map from a higher-dimensional manifold to a lower-dimensional one whose singularities are modeled on complex Morse-type critical points, playing a central role in symplectic and complex geometry.
  • B. Strominger–Yau–Zaslow conjecture chosen
    The Strominger–Yau–Zaslow conjecture is a proposal in mirror symmetry stating that mirror pairs of Calabi–Yau manifolds can be understood as dual special Lagrangian torus fibrations, providing a geometric explanation of mirror symmetry.
  • C. Milnor fibration
    Milnor fibration is a fundamental construction in singularity theory and differential topology that describes how the complement of a complex hypersurface singularity fibers over the circle, revealing the local topological structure of the singularity.
  • D. Hitchin fibration
    The Hitchin fibration is a fundamental geometric structure in the theory of Higgs bundles that organizes their moduli space into an algebraically completely integrable system with deep connections to representation theory and the geometric Langlands program.
  • E. 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.
  • 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_69e11e482f788190b78d1588fc26d606 completed April 16, 2026, 5:37 p.m.
NER Named-entity recognition batch_69f15769fdb48190b84e0c019ab63579 completed April 29, 2026, 12:57 a.m.
NED1 Entity disambiguation (via context triple) batch_6a0ad523ecec8190a85eb932288965fb completed May 18, 2026, 9 a.m.
NEDg Description generation batch_6a0ad992b43c8190b0e409d64db83308 completed May 18, 2026, 9:19 a.m.
NED2 Entity disambiguation (via description) batch_6a0adac48bec8190989dd7c5e28d283a completed May 18, 2026, 9:24 a.m.
Created at: April 16, 2026, 8:43 p.m.