Triple

T8359601
Position Surface form Disambiguated ID Type / Status
Subject Harold Hotelling E196771 entity
Predicate notableConcept P201 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, notableConcept, Hotelling's lemma]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Hotelling's lemma
Context triple: [Harold Hotelling, notableConcept, 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. 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.
  • D. Hicksian demand
    Hicksian demand is a concept in microeconomics that describes how a consumer’s demand for goods changes when prices vary while holding utility (satisfaction) constant, often used in welfare and consumer theory.
  • E. Karush–Kuhn–Tucker conditions
    The Karush–Kuhn–Tucker conditions are fundamental optimality criteria in nonlinear programming that generalize Lagrange multipliers to handle inequality constraints.
  • 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_69ca82f08b348190bfb7881944bbff6f completed March 30, 2026, 2:04 p.m.
NER Named-entity recognition batch_69cb807134008190b4671326e0414210 completed March 31, 2026, 8:06 a.m.
NED1 Entity disambiguation (via context triple) batch_69cdc775a548819090c83d916b352f41 completed April 2, 2026, 1:33 a.m.
Created at: March 30, 2026, 6 p.m.