The derived four-outcome law

For fixed known $\eta$, the probability $q_{\eta }$ determines the model parameter:

This is population-level identification, not exact acquisition of a probability from one record.

The deterministic specialization

has $u={\sin }^2\varphi ,v=u^2$ and reproduces the finite likelihood of En10-A. The construction above derives that specialization from the named pilot generators.