Triple

T9171568
Position Surface form Disambiguated ID Type / Status
Subject Hilbert’s twenty-second problem E220091 entity
Predicate relatedConcept P37 FINISHED
Object uniformization theorem E259768 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: uniformization theorem | Statement: [Hilbert’s twenty-second problem, relatedConcept, uniformization theorem]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: uniformization theorem
Context triple: [Hilbert’s twenty-second problem, relatedConcept, uniformization theorem]
  • A. uniformization theorem chosen
    The uniformization theorem is a fundamental result in complex analysis stating that every simply connected Riemann surface is conformally equivalent to either the Riemann sphere, the complex plane, or the unit disk.
  • B. Riemann mapping theorem
    The Riemann mapping theorem is a fundamental result in complex analysis stating that any non-empty simply connected open subset of the complex plane (other than the whole plane) can be conformally mapped onto the open unit disk.
  • C. 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.
  • D. 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.
  • 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.
  • 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_69ca83e467108190abcae6a33b3d4dad completed March 30, 2026, 2:08 p.m.
NER Named-entity recognition batch_69ccaae38ee48190bf783477bc37913d completed April 1, 2026, 5:19 a.m.
NED1 Entity disambiguation (via context triple) batch_69d0549746b0819099c2a591900f9c8c completed April 4, 2026, midnight
Created at: March 30, 2026, 7:22 p.m.