Triple
T15741862
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Ramsey pricing |
E381619
|
entity |
| Predicate | usesTool |
P98
|
FINISHED |
| Object | Lagrange multipliers |
E156182
|
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: Lagrange multipliers | Statement: [Ramsey pricing, usesTool, Lagrange multipliers]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Lagrange multipliers Context triple: [Ramsey pricing, usesTool, Lagrange multipliers]
-
A.
Lagrange multipliers
chosen
Lagrange multipliers are a mathematical optimization technique used to find the extrema of functions subject to equality constraints.
-
B.
Karush–Kuhn–Tucker conditions
The Karush–Kuhn–Tucker conditions are fundamental optimality criteria in nonlinear programming that generalize Lagrange multipliers to handle inequality constraints.
-
C.
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.
-
D.
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.
-
E.
Lagrangian function
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.
- 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_69d86d9cdb648190bf3171be0bd7d872 |
completed | April 10, 2026, 3:25 a.m. |
| NER | Named-entity recognition | batch_69e04fd97d6c8190b2fa6ca422bfe512 |
completed | April 16, 2026, 2:56 a.m. |
| NED1 | Entity disambiguation (via context triple) | batch_69ff83056aa0819098b757ed125e61fe |
completed | May 9, 2026, 6:55 p.m. |
Created at: April 10, 2026, 4:46 a.m.