Triple

T36468731
Position Surface form Disambiguated ID Type / Status
Subject Möbius transformation E898486 entity
Predicate isBiholomorphism P160143 FINISHED
Object of the Riemann sphere LITERAL 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: of the Riemann sphere | Statement: [Möbius transformation, isBiholomorphism, of the Riemann sphere]
PD Predicate disambiguation gpt-5-mini-2025-08-07
Target predicate: isBiholomorphism
Context triple: [Möbius transformation, isBiholomorphism, of the Riemann sphere]
  • A. isBiholomorphismOf chosen
    Indicates that one complex-analytic map is a biholomorphic equivalence between two complex manifolds, i.e., a holomorphic bijection whose inverse is also holomorphic.
  • B. isHolomorphicOn
    Indicates that a complex-valued function is complex differentiable at every point of a specified domain, i.e., holomorphic throughout that region.
  • C. isHolomorphicallyContractible
    Indicates that a space can be continuously shrunk to a point through holomorphic maps, preserving complex-analytic structure throughout the contraction.
  • D. isDiffeomorphicTo
    Indicates that there exists a smooth, bijective map between two spaces whose inverse is also smooth, so the spaces are equivalent in the sense of differential topology.
  • E. isBijective
    Indicates that a function establishes a one-to-one and onto correspondence between elements of its domain and codomain, with each element in both sets paired uniquely.
  • F. None of above.

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_69f76e58ebd88190b75d9b169b59d793 completed May 3, 2026, 3:48 p.m.
NER Named-entity recognition batch_69f7be9d07ac8190adf796cbef60daf6 completed May 3, 2026, 9:31 p.m.
PD Predicate disambiguation batch_69f7bccf05bc8190b61fdb2b2a315811 completed May 3, 2026, 9:23 p.m.
Created at: May 3, 2026, 4:10 p.m.