Triple

T11098652
Position Surface form Disambiguated ID Type / Status
Subject (2,3,7) triangle group E262443 entity
Predicate isAssociatedWith P2830 FINISHED
Object Hurwitz surfaces
Hurwitz surfaces are compact Riemann surfaces of maximal possible automorphism group size for their genus, achieving the Hurwitz bound of 84(g−1) symmetries.
E907201 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 surfaces | Statement: [(2,3,7) triangle group, isAssociatedWith, Hurwitz surfaces]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Hurwitz surfaces
Context triple: [(2,3,7) triangle group, isAssociatedWith, Hurwitz surfaces]
  • 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. Kummer surfaces
    Kummer surfaces are special quartic algebraic surfaces in projective three-space characterized by having 16 ordinary double points, extensively studied in the context of complex geometry and abelian varieties.
  • E. 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.
  • 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 surfaces
Triple: [(2,3,7) triangle group, isAssociatedWith, Hurwitz surfaces]
Generated description
Hurwitz surfaces are compact Riemann surfaces of maximal possible automorphism group size for their genus, achieving the Hurwitz bound of 84(g−1) symmetries.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Hurwitz surfaces
Target entity description: Hurwitz surfaces are compact Riemann surfaces of maximal possible automorphism group size for their genus, achieving the Hurwitz bound of 84(g−1) symmetries.
  • 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. Kummer surfaces
    Kummer surfaces are special quartic algebraic surfaces in projective three-space characterized by having 16 ordinary double points, extensively studied in the context of complex geometry and abelian varieties.
  • E. 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.
  • 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_69d6aa9a40d88190a373e2c7e48285db completed April 8, 2026, 7:20 p.m.
NER Named-entity recognition batch_69d79a0c46308190889b94c23ebaca62 completed April 9, 2026, 12:22 p.m.
NED1 Entity disambiguation (via context triple) batch_69e441bb14d08190ac01bf3daa34ae43 completed April 19, 2026, 2:45 a.m.
NEDg Description generation batch_69e44c0606408190819b9d3fd58f818f completed April 19, 2026, 3:29 a.m.
NED2 Entity disambiguation (via description) batch_69e4510dc55081908f89aab15726b2a8 completed April 19, 2026, 3:50 a.m.
Created at: April 8, 2026, 9:27 p.m.