Spectral Overlap Phenomenology: Applications of the Cauchy–Schwarz Recognition Formula Across Sixteen Domains (Paper 33 in the Intertwiner Series)

IntroductionPaper 32 derived the spectral equalization effect: the LQC bounce brings spectrally distant perspectives closer while leaving nearby perspectives essentially unchanged. The derivation used only theCauchy–Schwarz formula applied to spectral profiles weighted by the Pöschl–Teller mode amplitudes and the KMS thermal weight. No consciousness-specific content entered the proof; the resultfollowed from the interplay of the spectral window W(κ), the thermal weight w(κ) = coth(βBκ/2),and the mode suppression at the bounce.This raises a structural question: if the equalization effect is a property of the Cauchy–Schwarzformula acting on weighted spectral profiles, does the same structure appear in domains the formulawas not designed for? Specifically, do phenomena involving overlap between spectral territories—fading memories,birthmarks, near-deathexperiences, skillacquisition, contemplativepractice, dreams,immune recognition—follow from the same mathematical objects that produced the cosmologicalequalization?This paper tests that question by applying the Cauchy–Schwarz recognition formula to sixteendomains, in each case using only the mathematical objects already derived in the series:(i) the overlap formula κ(A,B;η) (Paper 32, Eq. 12),(ii) the KMS thermal weight w(κ) = coth(βBκ/2), βB = π√2 (Paper 6),(iii) Gaussian spectral profiles gA(κ) with variable centre and width (Paper 32, §5.1),(iv) the logistic recognition dynamics dχ/dt = 2αχ(1 − χ) (Paper 22, Theorem 2.1),(v) the inverse participation ratio IPRA = |gA|4wdκ/( |gA|2wdκ)2 (Paper 32, §5.2).No additional parameters, domain-specific modifications, or ad hoc assumptions are introduced.