Finite Theta Packets Are Reachable and Jointly Observable Before Mellin Selection
On any finite divisor-closed integer packet, prime multiplication from reaches every labelled basis state. The Gaussian observation family
is jointly faithful because distinct exponential trajectories are linearly independent. The finite theta multiport is therefore reachable and observable.
A dark Mellin-selected output is not loss of the full state, failure of integrality, or an unobservable internal mode. It is an intrinsic selected- channel transmission zero with complementary Gaussian ports still bright.
The remaining RH law must establish a source-derived minimum-phase or outer property for the completed Mellin selector. Generic minimality, reciprocity, and full-output losslessness are insufficient.
Research packet:
research/grothendieck/finite-theta-packets-are-reachable-and-jointly-observable-before-mellin-selection.md
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