Triple

T2665891
Position Surface form Disambiguated ID Type / Status
Subject Friedrich Bernhard Riemann E55633 entity
Predicate notableConcept P201 FINISHED
Object Riemann mapping theorem E47349 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 mapping theorem | Statement: [Friedrich Bernhard Riemann, notableConcept, Riemann mapping theorem]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Riemann mapping theorem
Context triple: [Friedrich Bernhard Riemann, notableConcept, Riemann mapping theorem]
  • A. Riemann mapping theorem chosen
    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.
  • B. Montel theorem
    Montel's theorem is a fundamental result in complex analysis stating that a family of holomorphic functions that is uniformly bounded on every compact subset of a domain is a normal family, meaning every sequence in it has a subsequence that converges uniformly on compact sets.
  • C. uniformization theorem
    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.
  • D. Schwarz lemma
    Schwarz lemma is a fundamental result in complex analysis that constrains holomorphic self-maps of the unit disk, particularly bounding their magnitude and derivative at the origin.
  • E. Koebe quarter theorem
    The Koebe quarter theorem is a fundamental result in complex analysis stating that any univalent holomorphic function on the unit disk maps it onto a domain containing a disk of radius one quarter, providing a sharp bound on the size of the image.
  • 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_69ab49e54de48190be708cd1cf8be073 completed March 6, 2026, 9:40 p.m.
NER Named-entity recognition batch_69abd96ed2748190a4feae98199b459d completed March 7, 2026, 7:53 a.m.
NED1 Entity disambiguation (via context triple) batch_69afa058fdd08190a355fc8131cd6695 completed March 10, 2026, 4:38 a.m.
Created at: March 6, 2026, 9:54 p.m.