Triple

T2394217
Position Surface form Disambiguated ID Type / Status
Subject Riemann–Hurwitz formula E47610 entity
Predicate relatedTo P37 FINISHED
Object Hurwitz space
A Hurwitz space is a moduli space that parametrizes branched covers of Riemann surfaces (or algebraic curves) with specified branching data.
E262118 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: Hurwitz space | Statement: [Riemann–Hurwitz formula, relatedTo, Hurwitz space]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Hurwitz space
Context triple: [Riemann–Hurwitz formula, relatedTo, Hurwitz space]
  • A. Klein quartic
    The Klein quartic is a highly symmetric algebraic curve of genus 3 that plays a central role in complex geometry, group theory, and the study of Riemann surfaces.
  • B. Riemann–Hurwitz formula
    The Riemann–Hurwitz formula is a fundamental result in algebraic geometry and complex analysis that relates the genera of two Riemann surfaces connected by a branched covering map, accounting for the ramification data.
  • C. Brill–Noether theory
    Brill–Noether theory is a branch of algebraic geometry that studies linear series on algebraic curves, particularly the existence and dimension of spaces of special divisors and maps to projective spaces.
  • D. Riemann surfaces
    Riemann surfaces are one-dimensional complex manifolds that provide the natural geometric setting for studying complex analytic functions and their multi-valued behavior.
  • E. Riemann–Roch theorem
    The Riemann–Roch theorem is a fundamental result in algebraic geometry and complex analysis that relates the dimension of spaces of meromorphic sections of a line bundle on a curve to topological data such as genus and degree.
  • 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: Hurwitz space
Triple: [Riemann–Hurwitz formula, relatedTo, Hurwitz space]
Generated description
A Hurwitz space is a moduli space that parametrizes branched covers of Riemann surfaces (or algebraic curves) with specified branching data.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Hurwitz space
Target entity description: A Hurwitz space is a moduli space that parametrizes branched covers of Riemann surfaces (or algebraic curves) with specified branching data.
  • A. Klein quartic
    The Klein quartic is a highly symmetric algebraic curve of genus 3 that plays a central role in complex geometry, group theory, and the study of Riemann surfaces.
  • B. Riemann–Hurwitz formula
    The Riemann–Hurwitz formula is a fundamental result in algebraic geometry and complex analysis that relates the genera of two Riemann surfaces connected by a branched covering map, accounting for the ramification data.
  • C. Brill–Noether theory
    Brill–Noether theory is a branch of algebraic geometry that studies linear series on algebraic curves, particularly the existence and dimension of spaces of special divisors and maps to projective spaces.
  • D. Riemann surfaces
    Riemann surfaces are one-dimensional complex manifolds that provide the natural geometric setting for studying complex analytic functions and their multi-valued behavior.
  • E. Riemann–Roch theorem
    The Riemann–Roch theorem is a fundamental result in algebraic geometry and complex analysis that relates the dimension of spaces of meromorphic sections of a line bundle on a curve to topological data such as genus and degree.
  • 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_69a88a1c450c81909f61abb8b6863885 completed March 4, 2026, 7:38 p.m.
NER Named-entity recognition batch_69abc87827d88190bb2351a688e6de32 completed March 7, 2026, 6:40 a.m.
NED1 Entity disambiguation (via context triple) batch_69aeb3da0978819094584cb23194fb3a completed March 9, 2026, 11:49 a.m.
NEDg Description generation batch_69aeb46f882881909294a3698ead865e completed March 9, 2026, 11:52 a.m.
NED2 Entity disambiguation (via description) batch_69aeb4c715a88190b1009a2cf1d95441 completed March 9, 2026, 11:53 a.m.
Created at: March 4, 2026, 7:57 p.m.