Triple

T11219560
Position Surface form Disambiguated ID Type / Status
Subject Morse theory E265522 entity
Predicate hasVariant P455 FINISHED
Object Morse–Bott theory
Morse–Bott theory is a generalization of Morse theory that allows critical points of a smooth function to form non-isolated submanifolds while still yielding powerful topological information about the underlying manifold.
E265522 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: Morse–Bott theory | Statement: [Morse theory, hasVariant, Morse–Bott theory]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Morse–Bott theory
Context triple: [Morse theory, hasVariant, Morse–Bott theory]
  • A. Morse Theory
    Morse Theory is a branch of differential topology that studies the relationship between the topology of manifolds and the critical points of smooth real-valued functions defined on them.
  • B. Introduction to Symplectic Topology
    Introduction to Symplectic Topology is a foundational graduate-level textbook that systematically develops the theory and applications of symplectic manifolds and symplectic geometry.
  • C. Arnold conjecture
    The Arnold conjecture is a central statement in symplectic geometry predicting a lower bound on the number of fixed points of Hamiltonian diffeomorphisms in terms of the topology of the underlying manifold.
  • D. Floer theory
    Floer theory is a branch of symplectic geometry and low-dimensional topology that extends Morse-theoretic ideas to infinite-dimensional spaces, providing powerful tools for studying periodic orbits, Lagrangian intersections, and invariants such as Floer homology.
  • E. McDuff–Salamon theory of J-holomorphic curves
    The McDuff–Salamon theory of J-holomorphic curves is a foundational framework in symplectic geometry that systematically develops the analysis, topology, and applications of pseudoholomorphic curves in symplectic 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: Morse–Bott theory
Triple: [Morse theory, hasVariant, Morse–Bott theory]
Generated description
Morse–Bott theory is a generalization of Morse theory that allows critical points of a smooth function to form non-isolated submanifolds while still yielding powerful topological information about the underlying manifold.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Morse–Bott theory
Target entity description: Morse–Bott theory is a generalization of Morse theory that allows critical points of a smooth function to form non-isolated submanifolds while still yielding powerful topological information about the underlying manifold.
  • A. Morse Theory chosen
    Morse Theory is a branch of differential topology that studies the relationship between the topology of manifolds and the critical points of smooth real-valued functions defined on them.
  • B. Introduction to Symplectic Topology
    Introduction to Symplectic Topology is a foundational graduate-level textbook that systematically develops the theory and applications of symplectic manifolds and symplectic geometry.
  • C. Arnold conjecture
    The Arnold conjecture is a central statement in symplectic geometry predicting a lower bound on the number of fixed points of Hamiltonian diffeomorphisms in terms of the topology of the underlying manifold.
  • D. Floer theory
    Floer theory is a branch of symplectic geometry and low-dimensional topology that extends Morse-theoretic ideas to infinite-dimensional spaces, providing powerful tools for studying periodic orbits, Lagrangian intersections, and invariants such as Floer homology.
  • E. McDuff–Salamon theory of J-holomorphic curves
    The McDuff–Salamon theory of J-holomorphic curves is a foundational framework in symplectic geometry that systematically develops the analysis, topology, and applications of pseudoholomorphic curves in symplectic manifolds.
  • 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_69e4f3c681148190a31c7e7ecb0d9478 completed April 19, 2026, 3:24 p.m.
NEDg Description generation batch_69e4f7dbfafc8190afa1e9fe67f1296e completed April 19, 2026, 3:42 p.m.
NED2 Entity disambiguation (via description) batch_69e4ff4645948190a2bfcc3a4efd8e2a completed April 19, 2026, 4:13 p.m.
Created at: April 8, 2026, 9:30 p.m.