Triple

T11085924
Position Surface form Disambiguated ID Type / Status
Subject Hurwitz bound on automorphism groups of curves E262119 entity
Predicate attainedBy P1518 FINISHED
Object Hurwitz curves E50328 NE FINISHED

Disambiguation candidates (2 decisions)

The exact options the model was shown at each disambiguation step, with the option it chose highlighted — the evidence behind this triple's disambiguated ids.

NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Hurwitz curves
Context triple: [Hurwitz bound on automorphism groups of curves, attainedBy, Hurwitz curves]
  • A. 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.
  • B. Hurwitz space
    A Hurwitz space is a moduli space that parametrizes branched covers of Riemann surfaces (or algebraic curves) with specified branching data.
  • C. 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.
  • D. 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.
  • E. Klein quartic chosen
    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.
  • F. None of above.
  • G. Unsure - the case is ambiguous/there is not enough information to decide.
PD Predicate disambiguation gpt-5-mini-2025-08-07 
Target predicate: attainedBy
Context triple: [Hurwitz bound on automorphism groups of curves, attainedBy, Hurwitz curves]
  • A. achieved chosen
    Indicates that an entity successfully reached, obtained, or accomplished a specified goal, result, or state.
  • B. takenBy
    Indicates that something is captured, acquired, or received by a particular entity.
  • C. gainedBy
    Indicates that something comes to possess, obtain, or receive something else as a result of an action, process, or event.
  • D. achievedOn
    Indicates that a particular result, milestone, or state was successfully reached or completed at a specific time or date.
  • E. attestedBy
    Indicates that the existence, occurrence, or validity of something is supported, confirmed, or documented by a specified source or authority.
  • F. None of above.

Provenance (4 batches)

Stage Batch ID Job type Status
creating batch_69d6aa9983c08190b0ef61603b69feac elicitation completed
NER batch_69d799c2c7d4819087ac793153340178 ner completed
NED1 batch_69e42d66ded88190877a20a10f012d6b ned_source_triple completed
PD batch_69d744185a5881909ba4cf151d1798ec pd completed
Created at: April 8, 2026, 9:27 p.m.