Triple
T11085867
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Hurwitz space |
E262118
|
entity |
| Predicate | relatedTo |
P37
|
FINISHED |
| Object |
Hurwitz numbers
Hurwitz numbers are algebraic invariants that count branched coverings of the Riemann sphere (or other curves) with specified ramification data, playing a key role in enumerative geometry and mathematical physics.
|
E904001
|
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 numbers | Statement: [Hurwitz space, relatedTo, Hurwitz numbers]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Hurwitz numbers Context triple: [Hurwitz space, relatedTo, Hurwitz numbers]
-
A.
Hurwitz space
A Hurwitz space is a moduli space that parametrizes branched covers of Riemann surfaces (or algebraic curves) with specified branching data.
-
B.
Hurwitz bound on automorphism groups of curves
The Hurwitz bound on automorphism groups of curves is a classical result in algebraic geometry stating that a compact Riemann surface of genus at least 2 has at most 84(g − 1) automorphisms.
-
C.
Hurwitz determinants
Hurwitz determinants are specific determinants constructed from a polynomial’s coefficients that are used to test whether all roots of the polynomial lie in the left half of the complex plane, thereby assessing system stability.
-
D.
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.
-
E.
Grothendieck–Ogg–Shafarevich formula
The Grothendieck–Ogg–Shafarevich formula is a result in arithmetic geometry that relates the Euler characteristic of an ℓ-adic sheaf on a curve over a finite field to local invariants such as conductors and ramification data.
- 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 numbers Triple: [Hurwitz space, relatedTo, Hurwitz numbers]
Generated description
Hurwitz numbers are algebraic invariants that count branched coverings of the Riemann sphere (or other curves) with specified ramification data, playing a key role in enumerative geometry and mathematical physics.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Hurwitz numbers Target entity description: Hurwitz numbers are algebraic invariants that count branched coverings of the Riemann sphere (or other curves) with specified ramification data, playing a key role in enumerative geometry and mathematical physics.
-
A.
Hurwitz space
A Hurwitz space is a moduli space that parametrizes branched covers of Riemann surfaces (or algebraic curves) with specified branching data.
-
B.
Hurwitz bound on automorphism groups of curves
The Hurwitz bound on automorphism groups of curves is a classical result in algebraic geometry stating that a compact Riemann surface of genus at least 2 has at most 84(g − 1) automorphisms.
-
C.
Hurwitz determinants
Hurwitz determinants are specific determinants constructed from a polynomial’s coefficients that are used to test whether all roots of the polynomial lie in the left half of the complex plane, thereby assessing system stability.
-
D.
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.
-
E.
Grothendieck–Ogg–Shafarevich formula
The Grothendieck–Ogg–Shafarevich formula is a result in arithmetic geometry that relates the Euler characteristic of an ℓ-adic sheaf on a curve over a finite field to local invariants such as conductors and ramification data.
- 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_69d6aa9983c08190b0ef61603b69feac |
completed | April 8, 2026, 7:20 p.m. |
| NER | Named-entity recognition | batch_69d799c2c7d4819087ac793153340178 |
completed | April 9, 2026, 12:21 p.m. |
| NED1 | Entity disambiguation (via context triple) | batch_69e3e7a6dfa8819096f822294eb64dd1 |
completed | April 18, 2026, 8:20 p.m. |
| NEDg | Description generation | batch_69e3f2cafc008190a3504999297f1e4e |
completed | April 18, 2026, 9:08 p.m. |
| NED2 | Entity disambiguation (via description) | batch_69e3f488819081908f9a4225279cde6b |
completed | April 18, 2026, 9:15 p.m. |
Created at: April 8, 2026, 9:27 p.m.