Triple

T13509501
Position Surface form Disambiguated ID Type / Status
Subject Lagrangian function E321098 entity
Predicate relatedTo P37 FINISHED
Object Karush–Kuhn–Tucker conditions E83405 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: Karush–Kuhn–Tucker conditions | Statement: [Lagrangian function, relatedTo, Karush–Kuhn–Tucker conditions]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Karush–Kuhn–Tucker conditions
Context triple: [Lagrangian function, relatedTo, Karush–Kuhn–Tucker conditions]
  • A. Karush–Kuhn–Tucker conditions chosen
    The Karush–Kuhn–Tucker conditions are fundamental optimality criteria in nonlinear programming that generalize Lagrange multipliers to handle inequality constraints.
  • B. KKT conditions
    KKT conditions are a set of necessary (and under certain conditions, sufficient) optimality conditions used in nonlinear programming to characterize solutions of constrained optimization problems.
  • C. Slater’s condition
    Slater’s condition is a regularity condition in convex optimization that guarantees strong duality and the validity of the Karush–Kuhn–Tucker optimality conditions by requiring the existence of a strictly feasible point.
  • D. Lagrange multipliers
    Lagrange multipliers are a mathematical optimization technique used to find the extrema of functions subject to equality constraints.
  • E. Kantorovich duality
    Kantorovich duality is a fundamental result in optimal transport theory that characterizes the optimal transport cost as the supremum of a dual variational problem over suitable test functions.
  • 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_69d807629d6c8190998f1b9bb12d2ed0 completed April 9, 2026, 8:09 p.m.
NER Named-entity recognition batch_69dbaf85a74081909eb08751fc55ce8f completed April 12, 2026, 2:43 p.m.
NED1 Entity disambiguation (via context triple) batch_69f75d9009688190b8f18bb3525c6afd completed May 3, 2026, 2:37 p.m.
Created at: April 9, 2026, 9:43 p.m.