To make assertions about how a collection of atomic objects influence each other requires that no unknown external influences be at work. {The name "integral regime" alludes to the idea of integrity and also to the idea that the set is whole and not, somehow, dependent on something else.}

Correctness proofs for systems built in Gnosis would generally involve a varying set of nodes and pages R called an (_integral regime). {These are the pages and nodes from which the system is built.} The proof will consist of statements about pages and nodes in R and also keys outside R that designate nodes and pages in R but not the location of such keys.

The intent of such assertions about keys outside R is that they are designed for communications between the system and untrusted things outside R. These assertions are part of the proof of the integrity of the integral regime.

Part of the function of the types of integral regimes that we shall be interested in here is the support of discreet key sets.

The discreetness of such key sets will follow from the external specifications of the integral regime and the correctness of the implementation of that regime.

More concretely we intend to provide space banks that cannot be used as communication channels but yet have some of the advantages of dynamic allocation. Since such banks cannot be structurally discreet they must be discreet by virtue of their algorithms and integrated within an integral regime.

A trusted computing base {or "TCB", a DoD term} must consist of the kernel together with an integral regime running under the kernel.

Nature of anticipated integral regimes

Perhaps the most important integral regime is one that includes in its specifications some discreets key sets to provide the functions of space banks, domain creators and meters.

The discreetness of these sets would depend in part on the logic of the code that implements them {in distinction to structurally discreet sets}.