Information-Efficient Shot Budgets for a Compiled Shor-15 Readout: Conditional 4-Shot Analysis, Decision-Preserving Adaptive Stopping, and Phase-Denominator Lifting

We consolidate a previously described IBM Quantum ibm_marrakesh compiled Shor-15 readout comparison (128 shots in a RAW configuration versus 8 shots in a preconfigured configuration) with three local, reproducible algorithmic analyses. First, an independent-binomial model quantifies the probability that a hypothetical 4-shot batch meets the original accepted-peak mass threshold of 0.60: at an assumed per-shot peak probability p=0.90 the pass probability is 0.947700, requiring p≈0.902389 for a 95% pass rate. Second, decision-preserving adaptive stopping of an eight-shot binary acceptance rule is proven pathwise by terminating at five accepted peaks or four failures. Under IID p=0.90 it requires 5.544908 shots on average, a 30.69% expected count reduction while preserving the fixed-eight-shot decision, conditional on per-shot feedback. Third, phase-denominator lifting tests a multiple of the measured phase denominator against modular order and factor constraints. For the period-informed compiled N=15, a=2 example this recovers factors from outcomes 0100, 1000 and 1100, versus two directly informative outcomes under the stricter denominator-only diagnostic. A five-shot intermediate candidate achieves a 0.988443 model probability for the joint peak-mass and lifted-evidence criterion at p=0.90, compared with 0.940581 for four and 0.994877 for eight. No new IBM QPU execution, hardware 32× speedup, independently measured throughput improvement or blind Shor period-finding result is claimed. We supply executable scripts, tests, archived local outputs, limitations, and a proposed matched-hardware validation protocol.