17 problems

Let $\delta$ and $\epsilon$ be functions producing arbitrary real-valued outputs, and write … Variant Task 2 accepts a pair when $|S-T|<c$ for a fixed constant $c$, rather than con…

Two-story space-time hypothesis. The weaker and more stochastic communication between the various lumps, beneath the macroscopic or quasiclassical surface structure, is responsible…

Let a contextuality model be evaluated in the hierarchy of $n$-contextuality, where increasing $n$ permits inclusion of larger simplices in the underlying simplicial complex, and l…

State-extension conjecture. If state $\nu$ of $A$ satisfies PEP, then there is a state $\hat{\nu}$ of $A[\perp]$ such that

LEP--PEP converse conjecture. If PEP holds, then LEP holds:

Let $|\Psi\rangle$ be a quantum state, let $\hat{P}$ be the operator associated with an experimental proposition, and let $v$ be the function assigning images to truth values. Valu…

Let $P$ be an experimental atomic proposition referring to a quantum system in a pure state. Let the cost of a computation be the time required to solve the relevant computational…

Extension conjecture. Every theory with a “well-behaved” thermodynamics can be extended to a sharp theory with purification.

A physical theory is said to have a well-behaved thermodynamics when its thermodynamic structure satisfies the relevant well-behavedness requirements. Subtheory conjecture. Every t…

Let $H_1,\ldots,H_n$ be contextuality scenarios, let $\overline{H_1\otimes\ldots\otimes H_n}$ denote the completion of their $n$-fold product scenario, let $\bar H_i$ denote the co…

Let $H$ be a contextuality scenario and let $C^*(H)$ denote its universal unital $C^*$-algebra. The decision problem $\mathtt{ALLOWS\_QUANTUM}$ asks whether a given contextuality s…

Let $cmathcal{V}(cmathcal{H})$ be the context category of the Hilbert space $cmathcal{H}$, let $cmathcal{V}_f(cmathcal{H})$ be the same category with the group action forgotten, le…

Let $cmathcal{V}(cmathcal{H})$ be the poset of contexts of the Hilbert space $cmathcal{H}$, let $cmathcal{V}_f(cmathcal{H})$ denote the corresponding context category with the grou…

Ontological single pure state conjecture. A quantized system is in a state corresponding to a two-valued measure on a single definite context; ontologically, there does not exist a…

Disjoint classical purifications conjecture. The sets $A$ and $B$ have neither pure nor mixed states in common.

Classical pure-state cardinality conjecture. The set of pure states of the classical system cannot have lower cardinality than the set of pure states of the generic system. In the…

Minimal classical pure-state model conjecture. The simplest classical physical system capable of reproducing the statistical phenomenology of a generic physical statistical system,…