Triple

T11534418
Position Surface form Disambiguated ID Type / Status
Subject Adolf Hurwitz E273508 entity
Predicate knownFor P22 FINISHED
Object Hurwitz's automorphisms theorem E262119 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: Hurwitz's automorphisms theorem | Statement: [Adolf Hurwitz, knownFor, Hurwitz's automorphisms theorem]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Hurwitz's automorphisms theorem
Context triple: [Adolf Hurwitz, knownFor, Hurwitz's automorphisms theorem]
  • A. Hurwitz bound on automorphism groups of curves chosen
    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 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. 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.
  • D. Hurwitz theorem
    Hurwitz theorem is a fundamental result in Diophantine approximation that gives an optimal bound on how well any irrational real number can be approximated by infinitely many rational numbers.
  • 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.
  • 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_69d6aae3fbec8190a14632a5df2538b6 completed April 8, 2026, 7:22 p.m.
NER Named-entity recognition batch_69d8839b4bb48190b748ec4119f36c11 completed April 10, 2026, 4:59 a.m.
NED1 Entity disambiguation (via context triple) batch_69e6858af0d081909078d5862ec3d469 completed April 20, 2026, 7:59 p.m.
Created at: April 8, 2026, 9:37 p.m.