Triple

T1484055
Position Surface form Disambiguated ID Type / Status
Subject Conway’s topograph E29423 entity
Predicate relatedTo P37 FINISHED
Object Farey tessellation
The Farey tessellation is a geometric partition of the hyperbolic plane into ideal triangles whose vertices correspond to rational numbers, closely linked to number theory and modular group actions.
E169192 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: Farey tessellation | Statement: [Conway’s topograph, relatedTo, Farey tessellation]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Farey tessellation
Context triple: [Conway’s topograph, relatedTo, Farey tessellation]
  • A. 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.
  • B. 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.
  • C. Ulam spiral
    The Ulam spiral is a graphical arrangement of the positive integers in a spiral pattern that reveals striking diagonal alignments of prime numbers, suggesting unexpected structure in their distribution.
  • D. Fermat polygonal number theorem
    The Fermat polygonal number theorem is a result in number theory stating that every positive integer can be expressed as a sum of a fixed number of polygonal numbers of a given order.
  • E. 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.
  • 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: Farey tessellation
Triple: [Conway’s topograph, relatedTo, Farey tessellation]
Generated description
The Farey tessellation is a geometric partition of the hyperbolic plane into ideal triangles whose vertices correspond to rational numbers, closely linked to number theory and modular group actions.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Farey tessellation
Target entity description: The Farey tessellation is a geometric partition of the hyperbolic plane into ideal triangles whose vertices correspond to rational numbers, closely linked to number theory and modular group actions.
  • A. 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.
  • B. 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.
  • C. Ulam spiral
    The Ulam spiral is a graphical arrangement of the positive integers in a spiral pattern that reveals striking diagonal alignments of prime numbers, suggesting unexpected structure in their distribution.
  • D. Fermat polygonal number theorem
    The Fermat polygonal number theorem is a result in number theory stating that every positive integer can be expressed as a sum of a fixed number of polygonal numbers of a given order.
  • E. 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.
  • 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.