e flux there when nobody looks? Phys. Rev. Lett. 54, 857 (1985).

Oas, G., de Barros, J.A. Carvalhaes, C.: Exploring non-signalling polytopes with negative probability. Phys. Scripta T163, 014034 (2014).

Simon, C., Brukner, Č., Zeilinger, A.: Hidden-variable theorems for real experiments. Phys. Rev. Lett., 86(20):44274430 (2001).

Specker, E.P.: The logic of propositions which are not simultaneously decidable. In The Logico-Algebraic Approach to Quantum Mechanics, The University of Western Ontario Series in Philosophy of Science No. 5a, edited by C. A. Hooker (Springer Netherlands, 1975) pp. 135140.

Spekkens, R.W.: Negativity and contextuality are equivalent notions of nonclassicality. Phys. Rev. Lett. 101, 020401 (2008).

Suppes, P., Zanotti, M.: When are probabilistic explanations possible? Synthese 48, 191 (1981).

Svozil, K.: How much contextuality? Natural Computing 11, 261 (2012).

Winter, A.: What does an experimental test of quantum contextuality prove or disprove? J. Phys. A: Math. Theor., 47, 424031 (2014).

[^1]: This example has the same structure as the Leggett-Garg system [@leggett_quantum_1985]. A special version of it was examined by Suppes and Zanotti [@suppes_when_1981], and also by Specker [@specker_logic_1975].

[^2]: No-signaling condition is a fundamental limitation of any approach with noncontextually labeled random variables, including NP.

[^3]: This formulation is predicated on no-signaling, which we assume throughout this paper. CbD has been generalized to situations when this condition is violated [@dzhafarov_probabilistic_2014; @bacciagaluppi_leggett-garg_2014; @dzhafarov_generalizing_2014; @KDL2014; @DKL2014; @KDconjecture; @DKL_overview].


Absorbing phase transitions (APT) are a category of critical nonequilibrium phase transitions, widespread in condensed matter physics and population and epidemics modeling [@reviews]. Directed percolation (DP) [@reviews; @kinzel83] has been recognized as the paradigmatic example of a system exhibiting a transition from an active to a unique ab