Fixed-Threshold Admissibility for Windowed σ-Band Extraction

This paper proves fixed-threshold admissibility for the local windowed σ-band extraction observable used in the main RH implication. For any fixed threshold M>0M>0M>0, exceedances occur on a set of vanishing density. The proof uses Plancherel control of windowed Fourier projections, explicit-formula truncation, and uniform zero-counting in moving temporal windows. All estimates are unconditional and do not assume the Riemann Hypothesis. This result discharges the admissibility hypothesis required by the coercive implication proved in Spectral Admissibility and the Riemann Hypothesis, in exactly the form it is used there.