Triple

T7338680
Position Surface form Disambiguated ID Type / Status
Subject Farey tessellation E169192 entity
Predicate appearsIn P795 FINISHED
Object Teichmüller theory E259765 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: Teichmüller theory | Statement: [Farey tessellation, appearsIn, Teichmüller theory]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Teichmüller theory
Context triple: [Farey tessellation, appearsIn, Teichmüller theory]
  • A. Teichmüller theory chosen
    Teichmüller theory is a branch of complex analysis and geometry that studies the deformation spaces of Riemann surfaces and their moduli, often via quasiconformal mappings.
  • B. Teichmüller curve
    A Teichmüller curve is a complex geodesic in the moduli space of Riemann surfaces that arises from flat surface structures and has rich connections to dynamics, geometry, and number theory.
  • C. Riemann surfaces
    Riemann surfaces are one-dimensional complex manifolds that provide the natural geometric setting for studying complex analytic functions and their multi-valued behavior.
  • D. Conformal Invariants
    Conformal Invariants is a foundational mathematical work by Lars Ahlfors that systematically develops the theory of quantities preserved under conformal mappings in complex analysis and geometric function theory.
  • E. Dynamics in One Complex Variable
    Dynamics in One Complex Variable is a foundational graduate-level textbook by John Milnor that introduces and develops the theory of complex dynamical systems, particularly the iteration of rational maps on the Riemann sphere.
  • 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_69c68a57710481909f0c1f3c6ebdb6f2 completed March 27, 2026, 1:47 p.m.
NER Named-entity recognition batch_69c6f0d702108190a00a3681ff6e67d4 completed March 27, 2026, 9:04 p.m.
NED1 Entity disambiguation (via context triple) batch_69c7fa82498c8190b1898a8c27cec71d completed March 28, 2026, 3:57 p.m.
Created at: March 27, 2026, 3:04 p.m.