Triple

T17035258
Position Surface form Disambiguated ID Type / Status
Subject Albert William Tucker E413305 entity
Predicate knownFor P22 FINISHED
Object Karush–Kuhn–Tucker conditions (naming and dissemination) 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 (naming and dissemination) | Statement: [Albert William Tucker, knownFor, Karush–Kuhn–Tucker conditions (naming and dissemination)]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Karush–Kuhn–Tucker conditions (naming and dissemination)
Context triple: [Albert William Tucker, knownFor, Karush–Kuhn–Tucker conditions (naming and dissemination)]
  • 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. 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.
  • C. 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.
  • D. Gale’s theorem on linear inequalities
    Gale’s theorem on linear inequalities is a fundamental result in convex geometry and linear programming that characterizes the solvability of systems of linear inequalities via an associated alternative system.
  • 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_69d886cd18288190b006abab23f811b7 completed April 10, 2026, 5:12 a.m.
NER Named-entity recognition batch_69e3d8f05824819091d2aa02e5591e26 completed April 18, 2026, 7:18 p.m.
NED1 Entity disambiguation (via context triple) batch_6a011b59ad3c8190914ee6f8c903cbbf completed May 10, 2026, 11:57 p.m.
Created at: April 10, 2026, 5:33 a.m.