Triple

T10991623
Position Surface form Disambiguated ID Type / Status
Subject Teichmüller theory E259765 entity
Predicate usesConcept P531 FINISHED
Object Fenchel–Nielsen coordinates
Fenchel–Nielsen coordinates are a system of parameters that describe hyperbolic structures on surfaces by recording lengths and twist angles along a collection of simple closed geodesics.
E898483 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: Fenchel–Nielsen coordinates | Statement: [Teichmüller theory, usesConcept, Fenchel–Nielsen coordinates]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Fenchel–Nielsen coordinates
Context triple: [Teichmüller theory, usesConcept, Fenchel–Nielsen coordinates]
  • A. Milnor–Wood inequality
    The Milnor–Wood inequality is a result in differential geometry and topology that bounds the Euler class of flat circle bundles over surfaces, with important implications for foliations and group actions on the circle.
  • B. Hyperbolic Manifolds and Discrete Groups
    "Hyperbolic Manifolds and Discrete Groups" is a foundational mathematical monograph that develops the theory of hyperbolic geometry and its deep connections with discrete group actions and low-dimensional topology.
  • C. Culler–Vogtmann Outer space
    Culler–Vogtmann Outer space is a topological space that parametrizes marked metric graphs, serving as an analogue of Teichmüller space for studying the outer automorphism group of a free group.
  • D. Teichmüller curve
    A Teichmüller curve is a complex geodesic in the moduli space of Riemann surfaces that arises from flat surface structures and has rich connections to dynamics, geometry, and number theory.
  • E. Dehn surgery
    Dehn surgery is a fundamental operation in 3-manifold topology that modifies a 3-dimensional manifold by cutting out a solid torus and gluing it back in a different way, playing a central role in the classification and study of 3-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: Fenchel–Nielsen coordinates
Triple: [Teichmüller theory, usesConcept, Fenchel–Nielsen coordinates]
Generated description
Fenchel–Nielsen coordinates are a system of parameters that describe hyperbolic structures on surfaces by recording lengths and twist angles along a collection of simple closed geodesics.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Fenchel–Nielsen coordinates
Target entity description: Fenchel–Nielsen coordinates are a system of parameters that describe hyperbolic structures on surfaces by recording lengths and twist angles along a collection of simple closed geodesics.
  • A. Milnor–Wood inequality
    The Milnor–Wood inequality is a result in differential geometry and topology that bounds the Euler class of flat circle bundles over surfaces, with important implications for foliations and group actions on the circle.
  • B. Hyperbolic Manifolds and Discrete Groups
    "Hyperbolic Manifolds and Discrete Groups" is a foundational mathematical monograph that develops the theory of hyperbolic geometry and its deep connections with discrete group actions and low-dimensional topology.
  • C. Culler–Vogtmann Outer space
    Culler–Vogtmann Outer space is a topological space that parametrizes marked metric graphs, serving as an analogue of Teichmüller space for studying the outer automorphism group of a free group.
  • D. Teichmüller curve
    A Teichmüller curve is a complex geodesic in the moduli space of Riemann surfaces that arises from flat surface structures and has rich connections to dynamics, geometry, and number theory.
  • E. Dehn surgery
    Dehn surgery is a fundamental operation in 3-manifold topology that modifies a 3-dimensional manifold by cutting out a solid torus and gluing it back in a different way, playing a central role in the classification and study of 3-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_69d6aa8a6a548190a750f944ccdc8064 completed April 8, 2026, 7:20 p.m.
NER Named-entity recognition batch_69d795d1e918819090c71f5a077fa15a completed April 9, 2026, 12:04 p.m.
NED1 Entity disambiguation (via context triple) batch_69e34504ebec8190a78e4795765b0c24 completed April 18, 2026, 8:47 a.m.
NEDg Description generation batch_69e3556fd3548190a33f04604be947cf completed April 18, 2026, 9:57 a.m.
NED2 Entity disambiguation (via description) batch_69e3593b0f8481909ed7a90f8bb9839d completed April 18, 2026, 10:13 a.m.
Created at: April 8, 2026, 9:24 p.m.