# Clarifications to the retained v1 mathematics

The `legacy/` directory preserves the original release for provenance. The current standalone manuscript tightens two assumptions that were not explicit enough in that text.

1. **P1, predictive quotient:** measurability and regular conditional prediction kernels are made explicit. A formal set-theoretic quotient is not by itself an efficient or even appropriately measurable neural statistic for an unrestricted experiment family.
2. **P2, Gaussian moment sufficiency:** the initial state must be Gaussian (possibly singular) for exact filtering by only its mean and covariance. Linear dynamics with Gaussian process/measurement noise do not turn an arbitrary initial prior into an exactly Gaussian posterior. The geometric unobservable-subspace quotient remains a separate statement; it does not imply Gaussian moment sufficiency for a non-Gaussian prior.

These clarifications do not change the recorded numerical experiments, which use the declared finite Gaussian models or explicit deterministic physical oracle. They restrict the interpretation of the general claims. The current manuscript, not the archived v1 wording, is authoritative for this release.