Triple

T1484054
Position Surface form Disambiguated ID Type / Status
Subject Conway’s topograph E29423 entity
Predicate relatedTo P37 FINISHED
Object modular group PSL(2,Z)
The modular group PSL(2,ℤ) is a fundamental discrete group of 2×2 integer matrices modulo sign, acting by fractional linear transformations on the upper half-plane and playing a central role in number theory, geometry, and the theory of modular forms.
E169191 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: modular group PSL(2,Z) | Statement: [Conway’s topograph, relatedTo, modular group PSL(2,Z)]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: modular group PSL(2,Z)
Context triple: [Conway’s topograph, relatedTo, modular group PSL(2,Z)]
  • A. 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.
  • B. 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.
  • C. Conway’s topograph
    Conway’s topograph is a geometric visualization tool introduced by mathematician John H. Conway to study binary quadratic forms and their arithmetic properties using a planar graph of curves and regions.
  • D. Conway groups
    Conway groups are a set of three closely related sporadic simple groups discovered by John H. Conway in the study of symmetries of the Leech lattice in group theory.
  • E. Weierstrass elliptic functions
    Weierstrass elliptic functions are a class of doubly periodic meromorphic functions that play a central role in the theory of elliptic curves and complex analysis.
  • 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: modular group PSL(2,Z)
Triple: [Conway’s topograph, relatedTo, modular group PSL(2,Z)]
Generated description
The modular group PSL(2,ℤ) is a fundamental discrete group of 2×2 integer matrices modulo sign, acting by fractional linear transformations on the upper half-plane and playing a central role in number theory, geometry, and the theory of modular forms.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: modular group PSL(2,Z)
Target entity description: The modular group PSL(2,ℤ) is a fundamental discrete group of 2×2 integer matrices modulo sign, acting by fractional linear transformations on the upper half-plane and playing a central role in number theory, geometry, and the theory of modular forms.
  • A. 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.
  • B. 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.
  • C. Conway’s topograph
    Conway’s topograph is a geometric visualization tool introduced by mathematician John H. Conway to study binary quadratic forms and their arithmetic properties using a planar graph of curves and regions.
  • D. Conway groups
    Conway groups are a set of three closely related sporadic simple groups discovered by John H. Conway in the study of symmetries of the Leech lattice in group theory.
  • E. Weierstrass elliptic functions
    Weierstrass elliptic functions are a class of doubly periodic meromorphic functions that play a central role in the theory of elliptic curves and complex analysis.
  • 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_69a498da82e08190ba833330d05f380f completed March 1, 2026, 7:51 p.m.
NER Named-entity recognition batch_69a4c679714c8190ac53630fb49e19c5 completed March 1, 2026, 11:06 p.m.
NED1 Entity disambiguation (via context triple) batch_69ad15b3a8548190b484a15757aee7b1 completed March 8, 2026, 6:22 a.m.
NEDg Description generation batch_69ad16bc23808190ba26aa98764f3186 completed March 8, 2026, 6:27 a.m.
NED2 Entity disambiguation (via description) batch_69ad172912488190b77c77e4e61e0183 completed March 8, 2026, 6:28 a.m.
Created at: March 1, 2026, 8:12 p.m.