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.