Research proof index

Finite density of a scaled packing.

Hidden-bit decomposition at the SPMF level: the bias of a coin-flip guessing game equals the distinguishing advantage between the two branches, assuming the coin is fair and both branches have full mass (no failure). This is the SPMF analogue of ProbComp.boolBiasAdvantage_eq_boolDistAdvantage_uniformBool_branch. The ProbComp version holds unconditionall...

withStateOracle commutes with <$>: mapping a function over the surface computation is the same as mapping it over the observed SPMF. This holds because interpret is the bundled monad morphism simulateQ', and the StateT observer fun mx => toSPMF (StateT.run' mx s) preserves <$> even though it is not a full monad morphism: <$> does not thr...

Two conditionally independent executions dominate the square of the corresponding single-execution output probability.

The central ℤ₆ subgroup acts trivially on (3, 1)_{-2}.

Characterizes the full-group elements acting trivially on the down-type singlet.