  In 2012, inspired by developments in group theory and complexity, Jockusch
and Schupp introduced generic computability, capturing the idea that an
algorithm might work correctly except for a vanishing fraction of cases.
However, we observe that their definition of a negligible set is not computably
invariant (and thus not well-defined on the 1-degrees), resulting in some
failures of intuition and a break with standard expectations in computability
theory.
  To strengthen their approach, we introduce a new notion of intrinsic
asymptotic density, with rich relations to both randomness and classical
computability theory. We then apply these ideas to propose alternative
foundations for further development in (intrinsic) generic computability.
  Toward these goals, we classify intrinsic density 0 as a new immunity
property, specifying its position in the standard hierarchy from immune to
cohesive for both general and $\Delta^0_2$ sets, and identify intrinsic density
$\frac{1}{2}$ as the stochasticity corresponding to permutation randomness. We
also prove that Rice's Theorem extends to all intrinsic variations of generic
computability, demonstrating in particular that no such notion considers
$\emptyset'$ to be "computable".
