Triple

T17330262
Position Surface form Disambiguated ID Type / Status
Subject Lefschetz pencil E420793 entity
Predicate centralIn P4751 FINISHED
Object Picard–Lefschetz theory — NE ONNED1

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: Picard–Lefschetz theory | Statement: [Lefschetz pencil, centralIn, Picard–Lefschetz theory]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Picard–Lefschetz theory
Context triple: [Lefschetz pencil, centralIn, Picard–Lefschetz theory]
  • A. Picard–Lefschetz theory chosen
    Picard–Lefschetz theory is a branch of algebraic and symplectic geometry that studies how the topology of complex algebraic varieties changes under deformation, particularly via vanishing cycles and monodromy around singularities.
  • B. 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.
  • C. Lefschetz pencil
    A Lefschetz pencil is a geometric structure on an algebraic variety given by a one-parameter family of hyperplane sections with only isolated, well-controlled singularities, fundamental in the study of its topology and geometry.
  • D. 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.
  • E. Donaldson’s existence theorem for Lefschetz pencils
    Donaldson’s existence theorem for Lefschetz pencils is a fundamental result in symplectic geometry asserting that any compact symplectic 4-manifold admits a Lefschetz pencil structure compatible with its symplectic form.
  • F. None of above.
  • G. Unsure - the case is ambiguous/there is not enough information to decide.

Provenance (3 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.
NED1 Entity disambiguation (via context triple) batch_6a019550d3bc8190bda76e83edc81063 finalizing May 11, 2026, 8:37 a.m.
Created at: April 10, 2026, 5:43 a.m.