Triple

T11219276
Position Surface form Disambiguated ID Type / Status
Subject Milnor fibration E265516 entity
Predicate relatedTo P37 FINISHED
Object Milnor fiber
The Milnor fiber is a smooth manifold obtained by intersecting a small sphere with a nearby regular level set of a complex hypersurface singularity, capturing the local topological structure of the singularity.
E265516 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: Milnor fiber | Statement: [Milnor fibration, relatedTo, Milnor fiber]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Milnor fiber
Context triple: [Milnor fibration, relatedTo, Milnor fiber]
  • A. 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.
  • B. 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.
  • C. Milnor number
    The Milnor number is an invariant in singularity theory that measures the complexity of an isolated critical point of a complex hypersurface or function.
  • D. Picard–Lefschetz theory
    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.
  • E. Singular Points of Complex Hypersurfaces
    "Singular Points of Complex Hypersurfaces" is a foundational monograph in singularity theory that systematically studies the local and topological properties of singularities arising in complex algebraic and analytic hypersurfaces.
  • 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: Milnor fiber
Triple: [Milnor fibration, relatedTo, Milnor fiber]
Generated description
The Milnor fiber is a smooth manifold obtained by intersecting a small sphere with a nearby regular level set of a complex hypersurface singularity, capturing the local topological structure of the singularity.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Milnor fiber
Target entity description: The Milnor fiber is a smooth manifold obtained by intersecting a small sphere with a nearby regular level set of a complex hypersurface singularity, capturing the local topological structure of the singularity.
  • A. Milnor fibration chosen
    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.
  • B. 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.
  • C. Milnor number
    The Milnor number is an invariant in singularity theory that measures the complexity of an isolated critical point of a complex hypersurface or function.
  • D. Picard–Lefschetz theory
    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.
  • E. Singular Points of Complex Hypersurfaces
    "Singular Points of Complex Hypersurfaces" is a foundational monograph in singularity theory that systematically studies the local and topological properties of singularities arising in complex algebraic and analytic hypersurfaces.
  • 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_69d6aac59460819089b9848b27f57848 completed April 8, 2026, 7:21 p.m.
NER Named-entity recognition batch_69d7e8eb84c48190b4f3bede254afde2 completed April 9, 2026, 5:59 p.m.
NED1 Entity disambiguation (via context triple) batch_69e4cc3ced708190adf7276865cfa715 completed April 19, 2026, 12:36 p.m.
NEDg Description generation batch_69e4d9e87508819080932fac06fb754d completed April 19, 2026, 1:34 p.m.
NED2 Entity disambiguation (via description) batch_69e4dda28b0081909245b65faae3533b completed April 19, 2026, 1:50 p.m.
Created at: April 8, 2026, 9:30 p.m.