Triple

T13509472
Position Surface form Disambiguated ID Type / Status
Subject KKT conditions E321097 entity
Predicate relatedConcept P37 FINISHED
Object Lagrangian function E321098 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: Lagrangian function | Statement: [KKT conditions, relatedConcept, Lagrangian function]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Lagrangian function
Context triple: [KKT conditions, relatedConcept, Lagrangian function]
  • A. Lagrangian function chosen
    The Lagrangian function is a mathematical construct that combines an objective function with its constraints, widely used in optimization and variational calculus to analyze and solve constrained problems.
  • B. Euler–Lagrange equation
    The Euler–Lagrange equation is a fundamental differential equation in the calculus of variations that provides the condition for a function to make a functional stationary, forming the basis of Lagrangian mechanics and many physical theories.
  • C. Lagrange multipliers
    Lagrange multipliers are a mathematical optimization technique used to find the extrema of functions subject to equality constraints.
  • D. Legendre transformation
    The Legendre transformation is a mathematical operation that converts a function of one set of variables into a function of their conjugate variables, widely used in classical mechanics and thermodynamics to switch between different energy or potential formulations.
  • E. Onsager–Machlup function
    The Onsager–Machlup function is a functional in stochastic process theory that characterizes the most probable paths of fluctuating systems, playing a key role in nonequilibrium statistical mechanics and large deviation theory.
  • 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.