Triple
T18044581
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | First Welfare Theorem |
E431737
|
entity |
| Predicate | formalizedBy |
P8407
|
FINISHED |
| Object | Arrow–Debreu 1954 existence theorem |
—
|
NE NERFINISHED |
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: Arrow–Debreu 1954 existence theorem | Statement: [First Welfare Theorem, formalizedBy, Arrow–Debreu 1954 existence theorem]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Arrow–Debreu 1954 existence theorem Context triple: [First Welfare Theorem, formalizedBy, Arrow–Debreu 1954 existence theorem]
-
A.
Arrow–Debreu model
chosen
The Arrow–Debreu model is a foundational general equilibrium framework in economics that rigorously characterizes how competitive markets can allocate resources efficiently across time and under uncertainty.
-
B.
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.
-
C.
Walrasian market-clearing framework
The Walrasian market-clearing framework is a general equilibrium model in which perfectly competitive markets continuously adjust prices so that supply equals demand in all markets simultaneously.
-
D.
The Computation of Economic Equilibria
"The Computation of Economic Equilibria" is a seminal book in mathematical economics that develops algorithmic and computational methods for finding general equilibrium solutions in economic models.
-
E.
fundamental theorems of welfare economics
The fundamental theorems of welfare economics are core results in microeconomic theory that formally link competitive market equilibria with Pareto efficiency and the conditions under which any efficient allocation can be supported as a market equilibrium.
- F. None of above.
- G. Unsure - the case is ambiguous/there is not enough information to decide.
Provenance (2 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_69d8b906482481908183315b9ecf9994 |
completed | April 10, 2026, 8:47 a.m. |
| NER | Named-entity recognition | batch_69e4bff13f488190993445769551c9c2 |
completed | April 19, 2026, 11:43 a.m. |
Created at: April 10, 2026, 10:25 a.m.