Triple

T11085926
Position Surface form Disambiguated ID Type / Status
Subject Hurwitz bound on automorphism groups of curves E262119 entity
Predicate example P1259 FINISHED
Object The Klein quartic has 168 = 84(3 − 1) automorphisms E50328 NE FINISHED

How this triple was built (2 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: The Klein quartic has 168 = 84(3 − 1) automorphisms | Statement: [Hurwitz bound on automorphism groups of curves, example, The Klein quartic has 168 = 84(3 − 1) automorphisms]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: The Klein quartic has 168 = 84(3 − 1) automorphisms
Context triple: [Hurwitz bound on automorphism groups of curves, example, The Klein quartic has 168 = 84(3 − 1) automorphisms]
  • 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 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 quaternions
    Hurwitz quaternions are a specific lattice of quaternions with integer and half-integer components that form a maximal order in the quaternion algebra and provide a natural algebraic framework for understanding representations of integers as sums of four squares.
  • 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. Fuchsian group
    A Fuchsian group is a discrete group of isometries of the hyperbolic plane, fundamental in the study of Riemann surfaces, modular forms, and hyperbolic geometry.
  • F. None of above.
  • G. Unsure - the case is ambiguous/there is not enough information to decide.

Provenance (3 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.
Created at: April 8, 2026, 9:27 p.m.