Triple

T17330261
Position Surface form Disambiguated ID Type / Status
Subject Lefschetz pencil E420793 entity
Predicate hasGeneralization P2372 FINISHED
Object Lefschetz fibration in symplectic geometry — NE NERFINISHED

How this triple was built (2 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: Lefschetz fibration in symplectic geometry | Statement: [Lefschetz pencil, hasGeneralization, Lefschetz fibration in symplectic geometry]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Lefschetz fibration in symplectic geometry
Context triple: [Lefschetz pencil, hasGeneralization, Lefschetz fibration in symplectic geometry]
  • A. Lefschetz fibration chosen
    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. Introduction to Symplectic Topology
    Introduction to Symplectic Topology is a foundational graduate-level textbook that systematically develops the theory and applications of symplectic manifolds and symplectic geometry.
  • C. McDuff–Salamon theory of J-holomorphic curves
    The McDuff–Salamon theory of J-holomorphic curves is a foundational framework in symplectic geometry that systematically develops the analysis, topology, and applications of pseudoholomorphic curves in symplectic manifolds.
  • D. The geometry of four-manifolds
    The Geometry of Four-Manifolds is a foundational monograph in differential geometry that develops the theory of smooth four-dimensional manifolds using gauge theory and Yang–Mills instantons.
  • E. 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.
  • F. None of above.
  • G. Unsure - the case is ambiguous/there is not enough information to decide.

Provenance (2 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_69d889d3adc881909319f1edb8d2a956 completed April 10, 2026, 5:25 a.m.
NER Named-entity recognition batch_69e439d5c788819092bdc4d3de0ec958 completed April 19, 2026, 2:11 a.m.
Created at: April 10, 2026, 5:43 a.m.