Triple

T20627346
Position Surface form Disambiguated ID Type / Status
Subject Darboux theorem E506852 entity
Predicate symplecticFormLocalExpression P140827 FINISHED
Object omega = sum_{i=1}^n dq_i wedge dp_i in Darboux coordinates 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: omega = sum_{i=1}^n dq_i wedge dp_i in Darboux coordinates | Statement: [Darboux theorem, symplecticFormLocalExpression, omega = sum_{i=1}^n dq_i wedge dp_i in Darboux coordinates]
PD Predicate disambiguation gpt-5-mini-2025-08-07
Target predicate: symplecticFormLocalExpression
Context triple: [Darboux theorem, symplecticFormLocalExpression, omega = sum_{i=1}^n dq_i wedge dp_i in Darboux coordinates]
  • A. CartanFormula
    Indicates how a derivation or differential operator acts on a product, expressing the result as a graded Leibniz rule that distributes over the product with appropriate signs.
  • B. wirtingerForm
    Indicates a relationship where an object is expressed or analyzed using the Wirtinger (complex differential) form, typically involving derivatives with respect to complex variables and their conjugates.
  • C. hasSymbolicForm
    Indicates that one entity serves as the symbolic representation or abstract form of another entity.
  • D. minimalCouplingForm
    Indicates that one entity is expressed in a form where its interaction or dependence on another entity is reduced to the simplest or least complex coupling necessary.
  • E. associatedQuadraticForm
    Indicates that one mathematical object (such as a bilinear form, matrix, or linear operator) is linked to or determines a specific quadratic form derived from it.
  • F. None of above. chosen

Provenance (4 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_69e0b4bd4a0081908d4e97a590a33fb2 completed April 16, 2026, 10:06 a.m.
NER Named-entity recognition batch_69e6abe645888190b639ebedc5b3041a completed April 20, 2026, 10:42 p.m.
PD Predicate disambiguation batch_69e5a00c43308190b7ea58d559257e07 completed April 20, 2026, 3:39 a.m.
PDg Predicate description generation batch_69e5a6a9f3f88190b961db9aca36f7da completed April 20, 2026, 4:08 a.m.
Created at: April 16, 2026, 11:42 a.m.