Determinism

In plain terms

Here is the problem. Prepare two systems as identically as any procedure allows, measure them identically, and quantum mechanics happily reports different outcomes -- offering no reason why this one rather than that. Either the world contains genuine chance, or the preparations were not actually identical.

Determinism takes the second answer. The systems agreed on everything the procedure fixed, and differed in what it could not fix. The observed spread is that hidden variation showing through, and probability is bookkeeping for ignorance -- the same move classical statistical mechanics has always made about gases.

Whether that answer is still available after the no-go theorems is not a matter of taste. It survives, at the stated price: contextuality and non-locality. See those entries for the receipts.

In CSD

The substrate's motion is deterministic and volume-preserving; chance appears nowhere in the dynamics. Probability enters exactly once -- as ignorance of the microstate within the region a preparation fixes -- and the forced measure turns that ignorance into unique numbers.

The honest debt is recorded rather than buried, and it is the interesting part. The frequency argument assumes independent trials. A deterministic substrate with memory would violate that, showing up as deviations from ordinary shot noise in high- statistics data. This is one of the very few places CSD could differ measurably from quantum mechanics -- and it needs no Planck-scale machine, just patience and statistics.

Mathematically

Positional. The formal content is the measure-preserving flow and the volume-ratio weights; determinism is the reading of that structure. The nearest formal object is the preservation field itself, carried as an ontic postulate and listed as such in the axiom ledger -- assumed for physical admissibility, not derived.