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.