Triple

T6800853
Position Surface form Disambiguated ID Type / Status
Subject Lagrange multipliers E156182 entity
Predicate generalizedBy P2372 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: [Lagrange multipliers, generalizedBy, Karush–Kuhn–Tucker conditions]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Karush–Kuhn–Tucker conditions
Context triple: [Lagrange multipliers, generalizedBy, 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. Nonlinear programming
    Nonlinear programming is a branch of mathematical optimization focused on finding optimal solutions to problems where the objective function or constraints are nonlinear.
  • E. Gale–Nikaidō–Debreu theorem
    The Gale–Nikaidō–Debreu theorem is a fundamental result in mathematical economics that provides conditions ensuring the existence (and sometimes uniqueness) of equilibrium in certain nonlinear and general equilibrium models.
  • 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_69c68826e6a48190a3d220b541e639de completed March 27, 2026, 1:37 p.m.
NER Named-entity recognition batch_69c6d2e595188190a0bb4b595df3adb2 completed March 27, 2026, 6:56 p.m.
NED1 Entity disambiguation (via context triple) batch_69c71a9b0cc48190819380aeaf0228e7 completed March 28, 2026, 12:02 a.m.
Created at: March 27, 2026, 2:16 p.m.