Finite-Count Power for Target-Centered Instrument Certification

RTCG-P5, version 1.0, establishes finite-count passing guarantees for a target-centered certificate of a prescribed quantum instrument on a specified family of imperfect preparations. Six rank-two states share one signed, support-preserving parameter epsilon in [-10^(-6),10^(-6)]. The diagnostic instrument is fixed; actual readouts and trusted references remain nominal. Both the new rule and the old scalar rule use the same acquired preparation allowances. An explicit doubled fixed allocation of 636776064000000000000 attempted trials yields the upward-reported sufficient upper 0.000098454319447, strictly below 10^(-4). For every fixed parameter in the family and every allowed coupling between settings, the new rule passes with probability at least 1 - 873 exp(-12), approximately 0.994636102615544. Trials are iid within each setting; independence across settings is not assumed. The original allocation's sufficient envelope is 0.000108332505187 and does not close. This does not establish failure of the actual rule or a necessary acquisition cost. A separate single-analyzer argument proves an actual-output obstruction for the unchanged scalar preparation-penalty rule. At either signed endpoint, its reported upper is at least 0.00672 except on an event of probability at most 2 exp(-12), for every fixed valid allocation retaining that conversion. The obstruction is specific to this rule. It is not an information-theoretic lower bound or a lower bound on the physical instrument error. The universal false-certification bound, 889 exp(-12), remains a separate inherited guarantee for complete complex CP competitors under the stated trusted-reference and shared-world contract. The family-specific power guarantee does not restrict that competitor class, and the two probability statements are not combined into one 99-percent event or a posterior correctness assertion. The manuscript and mathematical supplement provide the physical construction, concentration proofs, all signed response coefficients, whole-interval argument and exact arithmetic. The companion provides editable sources, byte-preserved numerical programs and data, supporting Lean sources, actual execution/type/axiom evidence and reader instructions. The retained Lean 4.19.0 execution supports the stated deterministic and conditional probability implications. Physical-source realization, concentration/Holder arguments, inherited unrestricted physical coverage, complete raw-count linkage and general Python refinement retain their explicit formal boundaries. Packaging the public release is not a new Lean execution. This is a new finite-count extension of RTCG-P4, Target-Centered Preparation Calibration for Outcome-Resolved Instrument Certification (10.5281/zenodo.23789860). No experimental acquisition, practical sample efficiency, fewer-shot result or optimal acquisition cost is claimed. Manuscript, supplement, documentation and author-owned mathematical data use CC BY 4.0; original numerical, checking, build and Lean code use MIT. Inherited and third-party notices remain authoritative for their material.