Hypergraph framework for irreducible noncontextuality inequalities from logical proofs of the Kochen-Specker theorem
Bibliographic record
Abstract
Kochen-Specker (KS) theorem reveals the inconsistency between quantum theory and any putative underlying model of it satisfying the constraint of KS-noncontextuality. A logical proof of the KS theorem is one that relies only on the compatibility relations amongst a set of projectors (a KS set) to witness this inconsistency. These compatibility relations can be represented by a hypergraph, referred to as a contextuality scenario. Here we consider contextuality scenarios that we term KS-uncolourable, e.g., those which appear in logical proofs of the KS theorem. We introduce a hypergraph framework to obtain noise-robust witnesses of contextuality from such scenarios. Our approach builds on the results of R. Kunjwal and R. W. Spekkens, Phys. Rev. Lett. 115, 110403 (2015), by providing new insights into the relationship between the structure of a contextuality scenario and the associated noise-robust noncontextuality inequalities that witness contextuality. The present work also forms a necessary counterpart to the framework presented in R. Kunjwal, Quantum 3, 184 (2019), which only applies to KS-colourable contextuality scenarios, i.e., those which do not admit logical proofs of the KS theorem but do admit statistical proofs. We rely on a single hypergraph invariant, defined in R. Kunjwal, Quantum 3, 184 (2019), that appears in our contextuality witnesses, namely, the weighted max-predictability. The present work can also be viewed as a study of this invariant. Significantly, unlike the case of R. Kunjwal, Quantum 3, 184 (2019), none of the graph invariants from the graph-theoretic framework for KS-contextuality due to Cabello, Severini, and Winter (the ``CSW framework", Phys. Rev. Lett. 112, 040401 (2014)) are relevant for our noise-robust noncontextuality inequalities.
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How this classification was reachedexpand
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) | 0.000 | 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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".