Triple

T10410817
Position Surface form Disambiguated ID Type / Status
Subject ICM E245382 entity
Predicate hasTrack P3284 FINISHED
Object geometry and topology
Geometry and topology is a major branch of mathematics focused on the properties, shapes, and structures of spaces, ranging from classical Euclidean geometry to abstract manifolds and their continuous deformations.
E862008 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: geometry and topology | Statement: [ICM, hasTrack, geometry and topology]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: geometry and topology
Context triple: [ICM, hasTrack, geometry and topology]
  • A. Three-dimensional geometry and topology
    Three-dimensional geometry and topology is a foundational mathematical monograph by William Thurston that develops the modern theory of 3-manifolds and introduces influential concepts such as hyperbolic structures and the geometrization viewpoint.
  • B. Topology
    "Topology" is a foundational mathematical text by Solomon Lefschetz that systematically develops the concepts and methods of algebraic topology.
  • C. 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.
  • D. Möbius geometry
    Möbius geometry is a branch of geometry that studies properties of figures invariant under Möbius (conformal) transformations of the extended complex plane or higher-dimensional spheres.
  • E. differential geometry
    Differential geometry is a branch of mathematics that uses the techniques of calculus and linear algebra to study the properties and curvature of smooth shapes and spaces such as curves, surfaces, and manifolds.
  • 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: geometry and topology
Triple: [ICM, hasTrack, geometry and topology]
Generated description
Geometry and topology is a major branch of mathematics focused on the properties, shapes, and structures of spaces, ranging from classical Euclidean geometry to abstract manifolds and their continuous deformations.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: geometry and topology
Target entity description: Geometry and topology is a major branch of mathematics focused on the properties, shapes, and structures of spaces, ranging from classical Euclidean geometry to abstract manifolds and their continuous deformations.
  • A. Three-dimensional geometry and topology
    Three-dimensional geometry and topology is a foundational mathematical monograph by William Thurston that develops the modern theory of 3-manifolds and introduces influential concepts such as hyperbolic structures and the geometrization viewpoint.
  • B. Topology
    "Topology" is a foundational mathematical text by Solomon Lefschetz that systematically develops the concepts and methods of algebraic topology.
  • C. 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.
  • D. Möbius geometry
    Möbius geometry is a branch of geometry that studies properties of figures invariant under Möbius (conformal) transformations of the extended complex plane or higher-dimensional spheres.
  • E. differential geometry
    Differential geometry is a branch of mathematics that uses the techniques of calculus and linear algebra to study the properties and curvature of smooth shapes and spaces such as curves, surfaces, and manifolds.
  • 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_69d381be340c8190b05998703d42d224 completed April 6, 2026, 9:49 a.m.
NER Named-entity recognition batch_69d4e9fb98748190a3a6c161edd8f400 completed April 7, 2026, 11:26 a.m.
NED1 Entity disambiguation (via context triple) batch_69d7fbfae96c8190ac496e9a1158afe4 completed April 9, 2026, 7:20 p.m.
NEDg Description generation batch_69d822d6a0188190a7ee6de5aab50486 completed April 9, 2026, 10:06 p.m.
NED2 Entity disambiguation (via description) batch_69d859e40bf88190a6dc8deed3049d31 completed April 10, 2026, 2:01 a.m.
Created at: April 6, 2026, 12:09 p.m.