Rate Compatibility and Commutator Obstructions for Projected-Channel BBGKY Bridge Estimates

This preprint gives a rate-compatibility and obstruction certificate for a projected-channel finite-depth BBGKY bridge. The main result identifies the channel-exponent compatibility window qγ − θ < ν < a required for simultaneous trace-sector harmlessness and commutator decay. For the canonical cutoff scaling in the finite-depth s = 2,3,4 regimes, this window is empty, showing that the bridge cannot be upgraded to an unconditional closure theorem under the current rates. The manuscript records the source-budget ledger, the commutator obstruction, parameter-sensitivity tables, and the precise assumptions that future E1/E2/E3 escape routes would need to improve.