Triple

T10991672
Position Surface form Disambiguated ID Type / Status
Subject Kleinian group E259766 entity
Predicate studiedIn P770 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: [Kleinian group, studiedIn, Teichmüller theory]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Teichmüller theory
Context triple: [Kleinian group, studiedIn, 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 metric
    The Teichmüller metric is a natural Finsler metric on Teichmüller space that measures the minimal quasiconformal distortion needed to deform one Riemann surface into another.
  • C. 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.
  • D. 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.
  • E. 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.
  • 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_69d6aa8a6a548190a750f944ccdc8064 completed April 8, 2026, 7:20 p.m.
NER Named-entity recognition batch_69d795d1e918819090c71f5a077fa15a completed April 9, 2026, 12:04 p.m.
NED1 Entity disambiguation (via context triple) batch_69e374639f1481908ea372b81a834f6f completed April 18, 2026, 12:09 p.m.
Created at: April 8, 2026, 9:24 p.m.