Triple
T1762690
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Harold Hotelling |
E38691
|
entity |
| Predicate | notableWork |
P4
|
FINISHED |
| Object |
Hotelling’s lemma
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.
|
E196774
|
NE FINISHED |
How this triple was built (4 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, notableWork, Hotelling’s lemma]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Hotelling’s lemma Context triple: [Harold Hotelling, notableWork, Hotelling’s lemma]
-
A.
Karush–Kuhn–Tucker conditions
The Karush–Kuhn–Tucker conditions are fundamental optimality criteria in nonlinear programming that generalize Lagrange multipliers to handle inequality constraints.
-
B.
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.
-
C.
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.
-
D.
Hamiltonian economic program
The Hamiltonian economic program was Alexander Hamilton’s comprehensive plan to strengthen the early United States’ financial system through federal assumption of state debts, creation of a national bank, and support for manufacturing and commerce.
-
E.
Frisch–Waugh–Lovell theorem
The Frisch–Waugh–Lovell theorem is a fundamental result in econometrics that shows how the coefficients of a multiple linear regression can be obtained by first partialling out (regressing out) other explanatory variables.
- F. None of above. chosen
- G. Unsure - the case is ambiguous/there is not enough information to decide.
NEDg
Description generation
gpt-5.1
Instruction
Generate a one-sentence description of the target entity. You are given a context triple in the form (subject, predicate, object), where the object is the target entity. # Instructions Use the triple to infer relevant information about the entity. Describe the entity based on what is most defining, well-known. Avoid repeating the information from the triple, unless really essential. # Response Format Return only the sentence: "Description: [one-sentence description of the target entity]"
Input
Entity: Hotelling’s lemma Triple: [Harold Hotelling, notableWork, Hotelling’s lemma]
Generated description
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.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Hotelling’s lemma Target entity description: 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.
-
A.
Karush–Kuhn–Tucker conditions
The Karush–Kuhn–Tucker conditions are fundamental optimality criteria in nonlinear programming that generalize Lagrange multipliers to handle inequality constraints.
-
B.
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.
-
C.
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.
-
D.
Hamiltonian economic program
The Hamiltonian economic program was Alexander Hamilton’s comprehensive plan to strengthen the early United States’ financial system through federal assumption of state debts, creation of a national bank, and support for manufacturing and commerce.
-
E.
Frisch–Waugh–Lovell theorem
The Frisch–Waugh–Lovell theorem is a fundamental result in econometrics that shows how the coefficients of a multiple linear regression can be obtained by first partialling out (regressing out) other explanatory variables.
- F. None of above. chosen
Provenance (5 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_69ada0f12fd8819099759ebcdfc19494 |
completed | March 8, 2026, 4:16 p.m. |
| NEDg | Description generation | batch_69ada1e3587c8190bca329c68ff31c41 |
completed | March 8, 2026, 4:20 p.m. |
| NED2 | Entity disambiguation (via description) | batch_69ada2977bfc8190ad028e17184fccaa |
completed | March 8, 2026, 4:23 p.m. |
Created at: March 4, 2026, 7:31 p.m.