Triple

T13509434
Position Surface form Disambiguated ID Type / Status
Subject KKT conditions E321097 entity
Predicate fullName P16 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: [KKT conditions, fullName, Karush–Kuhn–Tucker conditions]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Karush–Kuhn–Tucker conditions
Context triple: [KKT conditions, fullName, 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. Lagrange multipliers
    Lagrange multipliers are a mathematical optimization technique used to find the extrema of functions subject to equality constraints.
  • D. 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.
  • E. Pontryagin maximum principle
    The Pontryagin maximum principle is a fundamental result in optimal control theory that provides necessary conditions for an optimal control process by characterizing optimal trajectories via a Hamiltonian maximization condition.
  • 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_69f75490291c8190b5985d8c90ef1af6 completed May 3, 2026, 1:58 p.m.
Created at: April 9, 2026, 9:43 p.m.