A two-qubit program without pre-combination

Failure has probability $1/2$ and remains reported. No branch is removed. The invariant boundary is the declared coarse record and unit residual, not an exported log of every raw bit.

The circuit is informative about $\cos \theta$, not globally faithful to $I_{\mathrm{rel}}$: phase periodicity and the evenness of cosine create aliases. Physical informativeness requires admissible invariant values with different cosines. Classical pre-combination avoids those statistical aliases. Neither realization is an exact single-run decoder of a real coefficient.