4 A Combinatorial Approach to Nonlocality and Contextuality
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Bibliographic record
Abstract
So far, most of the literature on (quantum) contextuality and the Kochen–\n\t\t\t\t Specker theorem seems either to concern particular examples of contextuality, or be\n\t\t\t\t considered as quantum logic. Here, we develop a general formalism for contextuality\n\t\t\t\t scenarios based on the combinatorics of hypergraphs, which significantly refines a similar\n\t\t\t\t recent approach by Cabello, Severini and Winter (CSW). In contrast to CSW, we\n\t\t\t\t explicitly include the normalization of probabilities, which gives us a much finer control\n\t\t\t\t over the various sets of probabilistic models like classical, quantum and generalized\n\t\t\t\t probabilistic. In particular, our framework specializes to (quantum) nonlocality in the\n\t\t\t\t case of Bell scenarios, which arise very naturally from a certain product of contextuality\n\t\t\t\t scenarios due to Foulis and Randall. In the spirit of CSW, we find close relationships to\n\t\t\t\t several graph invariants. The recently proposed Local Orthogonality principle turns out\n\t\t\t\t to be a special case of a general principle for contextuality scenarios related to the Shannon\n\t\t\t\t capacity of graphs. Our results imply that it is strictly dominated by a low level of\n\t\t\t\t the Navascués–Pironio–Acín hierarchy of semidefinite programs, which we also apply\n\t\t\t\t to contextuality scenarios.\n\t\t\t\t We derive a wealth of results in our framework, many of these relating to quantum\n\t\t\t\t and supraquantum contextuality and nonlocality, and state numerous open problems.\n\t\t\t\t For example, we show that the set of quantum models on a con
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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 | 0.001 | 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) | 0.000 | 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