Theoretical analysis reveals a critical line in composite domains, suggesting deeper insights into resonance stability.
We give a purely theoretical path to the critical line coming from the composite domain: (1) a zero–free composite explicit formula in windowed cpw (cycles-per-window) coordinates with a Weil–compatible test class; (2) a W–scaling lemma which forces window–stable line shapes precisely at β= 1/2 ; (3) a Mellin–Fourier representation of the transfer T= JMΠW with symbolic derivations of mirror antiphase, ratio2f /1f and ∆AIC invariance. With uniqueness of the test class we identify the composite spectral measure with the zeta–zero measure and obtain an RH conclusion from resonance stability.
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Stephen Steiner (2025) studied this question.
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