Triple

T17549849
Position Surface form Disambiguated ID Type / Status
Subject Wirtinger presentation of knot groups E427429 entity
Predicate basedOn P98 FINISHED
Object Wirtinger generators NE NERFINISHED

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: Wirtinger generators | Statement: [Wirtinger presentation of knot groups, basedOn, Wirtinger generators]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Wirtinger generators
Context triple: [Wirtinger presentation of knot groups, basedOn, Wirtinger generators]
  • 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. Wirtinger
    Wirtinger is a surname most notably associated with Austrian mathematician Wilhelm Wirtinger, known for his contributions to complex analysis and knot theory.
  • C. Hurwitz determinants
    Hurwitz determinants are specific determinants constructed from a polynomial’s coefficients that are used to test whether all roots of the polynomial lie in the left half of the complex plane, thereby assessing system stability.
  • D. Wirtinger presentation of knot groups chosen
    The Wirtinger presentation of knot groups is a classical method in knot theory that describes the fundamental group of a knot complement using generators and relations derived from a knot diagram.
  • E. Symanzik polynomials
    Symanzik polynomials are graph-based polynomials that arise in the parametric representation of Feynman integrals in quantum field theory, encoding the topology and kinematic dependence of Feynman diagrams.
  • F. None of above.
  • G. Unsure - the case is ambiguous/there is not enough information to decide.

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.