Increasing cones, recession cones and global cones
Why this work is in the frame
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Bibliographic record
Abstract
In this paper, we discuss and compare various cones used in the economics literature to analyze arbitrage in general equilibrium models with short seling. Our main result is that under certain conditions on an economic model, the closure of the increasing cone and the closure of the global cone are both equal to the arbitrage cone, the recession cone of the preferred set. It is known that in general, the Page-Wooders increasing cone may be strictly contained in the recession cone. We demonstrate that in general – for example, under the conditions of Werner (1987) or Page and Wooders (1996a, b) – the increasing cone is larger than the global cone; in fact the closure of the global cone may be strictlycontained in the increasing cone. This shows that, except under special assumptions on the economic model, conditions based on the global cone are inadequate to ensure existence of equilibrium
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Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.002 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from it