Triple

T6709028
Position Surface form Disambiguated ID Type / Status
Subject Simon Donaldson E153081 entity
Predicate notableWork P4 FINISHED
Object 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.
E613809 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: The geometry of four-manifolds | Statement: [Simon Donaldson, notableWork, The geometry of four-manifolds]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: The geometry of four-manifolds
Context triple: [Simon Donaldson, notableWork, The geometry of four-manifolds]
  • 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. Foliations of Three-Manifolds Which Are Circle Bundles
    "Foliations of Three-Manifolds Which Are Circle Bundles" is William Thurston’s influential 1972 doctoral dissertation in geometric topology, where he developed foundational ideas about the structure and classification of foliations on 3-manifolds.
  • C. Donaldson invariants
    Donaldson invariants are sophisticated topological invariants of smooth four-dimensional manifolds derived from moduli spaces of anti-self-dual connections, central to the study of 4-manifold differential topology.
  • D. Hirzebruch signature theorem
    The Hirzebruch signature theorem is a fundamental result in differential topology that expresses the signature of a smooth, compact, oriented 4k-dimensional manifold as a polynomial in its Pontryagin classes.
  • E. Topological Methods in Algebraic Geometry
    Topological Methods in Algebraic Geometry is a foundational mathematical monograph by Friedrich Hirzebruch that applies topological techniques, particularly characteristic classes and cobordism theory, to problems in 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: The geometry of four-manifolds
Triple: [Simon Donaldson, notableWork, The geometry of four-manifolds]
Generated description
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.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: The geometry of four-manifolds
Target entity description: 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.
  • 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. Foliations of Three-Manifolds Which Are Circle Bundles
    "Foliations of Three-Manifolds Which Are Circle Bundles" is William Thurston’s influential 1972 doctoral dissertation in geometric topology, where he developed foundational ideas about the structure and classification of foliations on 3-manifolds.
  • C. Donaldson invariants
    Donaldson invariants are sophisticated topological invariants of smooth four-dimensional manifolds derived from moduli spaces of anti-self-dual connections, central to the study of 4-manifold differential topology.
  • D. Hirzebruch signature theorem
    The Hirzebruch signature theorem is a fundamental result in differential topology that expresses the signature of a smooth, compact, oriented 4k-dimensional manifold as a polynomial in its Pontryagin classes.
  • E. Topological Methods in Algebraic Geometry
    Topological Methods in Algebraic Geometry is a foundational mathematical monograph by Friedrich Hirzebruch that applies topological techniques, particularly characteristic classes and cobordism theory, to problems in algebraic geometry.
  • F. None of above. chosen

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_69c68808d8d8819087369015270788fe completed March 27, 2026, 1:37 p.m.
NER Named-entity recognition batch_69c6d105b49c8190932246a727e2c513 completed March 27, 2026, 6:48 p.m.
NED1 Entity disambiguation (via context triple) batch_69c7008e6b308190a3d5db2bf4a469c4 completed March 27, 2026, 10:11 p.m.
NEDg Description generation batch_69c701be78cc8190a0848ea60908d129 completed March 27, 2026, 10:16 p.m.
NED2 Entity disambiguation (via description) batch_69c7021b27288190866aef500198479d completed March 27, 2026, 10:18 p.m.
Created at: March 27, 2026, 2:06 p.m.