Triple

T1762711
Position Surface form Disambiguated ID Type / Status
Subject Harold Hotelling E38691 entity
Predicate hasConceptNamedAfter P3325 FINISHED
Object Hotelling’s lemma E196774 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: Hotelling’s lemma | Statement: [Harold Hotelling, hasConceptNamedAfter, Hotelling’s lemma]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Hotelling’s lemma
Context triple: [Harold Hotelling, hasConceptNamedAfter, Hotelling’s lemma]
  • A. Hotelling’s lemma chosen
    Hotelling’s lemma is a result in microeconomics that links a firm’s profit function to its supply and factor demand functions via partial derivatives.
  • B. Hotelling’s law
    Hotelling’s law is an economic principle that explains why competing businesses or political candidates tend to cluster together by choosing similar locations or positions to maximize their share of consumers or voters.
  • C. Karush–Kuhn–Tucker conditions
    The Karush–Kuhn–Tucker conditions are fundamental optimality criteria in nonlinear programming that generalize Lagrange multipliers to handle inequality constraints.
  • D. Pareto efficiency
    Pareto efficiency is an economic concept describing an allocation of resources where no individual can be made better off without making someone else worse off.
  • E. Coase theorem
    The Coase theorem is an economic theory stating that if property rights are well-defined and transaction costs are negligible, private bargaining will lead to an efficient allocation of resources regardless of the initial assignment of rights.
  • 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_69a8862d562481908d7025a1c1f67c0d completed March 4, 2026, 7:21 p.m.
NER Named-entity recognition batch_69aa6465245c8190b1ee84628c62c529 completed March 6, 2026, 5:21 a.m.
NED1 Entity disambiguation (via context triple) batch_69ada98eb0348190a44e05393a2c6eff completed March 8, 2026, 4:53 p.m.
Created at: March 4, 2026, 7:31 p.m.