Triple

T17549850
Position Surface form Disambiguated ID Type / Status
Subject Wirtinger presentation of knot groups E427429 entity
Predicate basedOn P98 FINISHED
Object Wirtinger relations — NE NERFINISHED

How this triple was built (3 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: Wirtinger relations | Statement: [Wirtinger presentation of knot groups, basedOn, Wirtinger relations]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Wirtinger relations
Context triple: [Wirtinger presentation of knot groups, basedOn, Wirtinger relations]
  • A. Wirtinger derivatives
    Wirtinger derivatives are complex differential operators that treat a complex variable and its conjugate as independent, providing a convenient formalism for expressing and analyzing holomorphicity and the Cauchy–Riemann equations.
  • B. Cauchy–Riemann equations
    The Cauchy–Riemann equations are fundamental conditions in complex analysis that characterize when a complex-valued function is holomorphic (complex differentiable).
  • C. Cauchy–Pompeiu formula
    The Cauchy–Pompeiu formula is a fundamental result in complex analysis that extends the Cauchy integral formula to functions that are not necessarily holomorphic by expressing them via both boundary and area integrals.
  • D. Bochner–Martinelli formula
    The Bochner–Martinelli formula is a fundamental integral representation in several complex variables that generalizes the Cauchy integral formula to higher dimensions.
  • E. Christoffel–Schwarz formula
    The Christoffel–Schwarz formula is a fundamental result in complex analysis that provides an explicit conformal mapping from the upper half-plane onto polygonal regions in the complex plane.
  • F. None of above. chosen
  • G. Unsure - the case is ambiguous/there is not enough information to decide.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07 
Target entity: Wirtinger relations
Target entity description: Wirtinger relations are algebraic relations among generators in a knot group presentation that encode how strands of a knot interact at each crossing.
  • A. Wirtinger derivatives
    Wirtinger derivatives are complex differential operators that treat a complex variable and its conjugate as independent, providing a convenient formalism for expressing and analyzing holomorphicity and the Cauchy–Riemann equations.
  • B. Cauchy–Riemann equations
    The Cauchy–Riemann equations are fundamental conditions in complex analysis that characterize when a complex-valued function is holomorphic (complex differentiable).
  • C. Cauchy–Pompeiu formula
    The Cauchy–Pompeiu formula is a fundamental result in complex analysis that extends the Cauchy integral formula to functions that are not necessarily holomorphic by expressing them via both boundary and area integrals.
  • D. Bochner–Martinelli formula
    The Bochner–Martinelli formula is a fundamental integral representation in several complex variables that generalizes the Cauchy integral formula to higher dimensions.
  • E. Christoffel–Schwarz formula
    The Christoffel–Schwarz formula is a fundamental result in complex analysis that provides an explicit conformal mapping from the upper half-plane onto polygonal regions in the complex plane.
  • F. None of above. chosen

Provenance (2 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_69d889df6dc081908f67dbadc03c07ee completed April 10, 2026, 5:25 a.m.
NER Named-entity recognition batch_69e45463ddf88190a2c29f3246adcb6e completed April 19, 2026, 4:04 a.m.
Created at: April 10, 2026, 5:50 a.m.