Single trajectory

In plain terms

Here is the problem. Deterministic accounts of quantum mechanics face a fork: either the world splits, or there are many worlds' worth of possibilities and one actual path. CSD takes the second branch without hedging: a single trajectory, on a single arena, deterministically.

Then where do statistics come from? From repetition. Each run of an experiment re-prepares the system, landing the world at a fresh point of the preparation region. A thousand runs sample the region a thousand times. The frequencies those samples produce is what the volume theorems compute.

What statistics do NOT come from is one run watched forever. Whether a single evolving path eventually visits everywhere fairly -- ergodicity -- is a different and much stronger property, and the programme does not lean on it.

In CSD

CSD is a single-trajectory theory: physical reality is one deterministic path on Sigma. Its typicality is repeated-preparation typicality -- ignorance across runs, priced by the conditioned Liouville measure -- not time-averaging along one path.

The corpus even proves the cautionary half: the projected unitary flow on the sector is not ergodic, so a time-average route to the Born weights is closed at that level. That is a narrow fact about one flow on the projective space, not an objection to the mechanism -- the frequency theorems never invoke ergodicity, which is exactly the point.

Mathematically

The LF1 chain formalises the repetition: i.i.d. draws from the conditioned measure, indicator processes per outcome, and the strong law delivering almost-sure convergence of empirical frequencies to volume weights. The non-ergodicity of the epistemic unitary flow is a proved theorem kept as a boundary marker: the volume route and the time-average route are not the same route, and only the first is claimed.