Triple

T10991783
Position Surface form Disambiguated ID Type / Status
Subject uniformization theorem E259768 entity
Predicate usesConcept P531 FINISHED
Object Riemann surface E47348 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: Riemann surface | Statement: [uniformization theorem, usesConcept, Riemann surface]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Riemann surface
Context triple: [uniformization theorem, usesConcept, Riemann surface]
  • A. Riemann surfaces chosen
    Riemann surfaces are one-dimensional complex manifolds that provide the natural geometric setting for studying complex analytic functions and their multi-valued behavior.
  • B. Riemann sphere
    The Riemann sphere is the complex plane plus a point at infinity, forming a one-dimensional complex manifold topologically equivalent to a sphere and used to study meromorphic functions and complex analysis.
  • C. Liouville surface
    A Liouville surface is a type of Riemannian surface on which the geodesic flow is integrable, typically characterized by a metric that can be written in separable (Liouville) form in suitable coordinates.
  • D. 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.
  • E. Teichmüller theory
    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.
  • 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_69e3a9644ff08190a3005e4f6a8243fe completed April 18, 2026, 3:55 p.m.
Created at: April 8, 2026, 9:24 p.m.