Triple

T18044569
Position Surface form Disambiguated ID Type / Status
Subject First Welfare Theorem E431737 entity
Predicate mathematicalFramework P2450 FINISHED
Object Arrow–Debreu model 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 model | Statement: [First Welfare Theorem, mathematicalFramework, Arrow–Debreu model]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Arrow–Debreu model
Context triple: [First Welfare Theorem, mathematicalFramework, Arrow–Debreu model]
  • 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. 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.
  • C. 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.
  • D. Ramsey–Cass–Koopmans model
    The Ramsey–Cass–Koopmans model is a foundational neoclassical growth model in macroeconomics that analyzes optimal savings, consumption, and capital accumulation over time in a perfectly competitive economy.
  • E. 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.
  • 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.