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.