Triple

T11098644
Position Surface form Disambiguated ID Type / Status
Subject (2,3,7) triangle group E262443 entity
Predicate uniformizes P97243 FINISHED
Object Klein quartic E50328 NE FINISHED

How this triple was built (3 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: Klein quartic | Statement: [(2,3,7) triangle group, uniformizes, Klein quartic]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Klein quartic
Context triple: [(2,3,7) triangle group, uniformizes, Klein quartic]
  • A. 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.
  • B. 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.
  • C. Clebsch
    Clebsch is a German surname most notably associated with mathematician Alfred Clebsch, known for his contributions to algebraic geometry and invariant theory.
  • D. Hurwitz group
    A Hurwitz group is a finite group that attains the maximal possible order of the automorphism group of a compact Riemann surface of given genus, as specified by Hurwitz's bound.
  • E. 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.
  • 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: uniformizes
Context triple: [(2,3,7) triangle group, uniformizes, Klein quartic]
  • A. uniformizedBy
    Indicates that one entity has been made uniform, standardized, or brought into a consistent form or structure by another entity.
  • B. uniformDistinction
    Indicates that a clear and consistent difference is maintained between two or more entities within a given context.
  • C. unites
    Indicates that one entity brings together multiple entities into a single, cohesive whole or shared state.
  • D. usesUniform
    Indicates that one entity regularly wears or employs a standardized set of clothing or equipment designated as a uniform.
  • E. uniformStyle
    Indicates that the related entities share the same or a consistent style, pattern, or formatting.
  • 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_69e462e5c08c8190bba2e3c8ec82051b completed April 19, 2026, 5:06 a.m.
PD Predicate disambiguation batch_69d7441aa3548190b92dbde57841c135 completed April 9, 2026, 6:15 a.m.
PDg Predicate description generation batch_69d750ca52ec8190a559432a5de106fd completed April 9, 2026, 7:10 a.m.
Created at: April 8, 2026, 9:27 p.m.