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.