Unified Delay Theory of Entanglement--Consciousness--Time: Fourfold Bridging of Spectral--Scattering--Information--Discounting and Cross-Modal Verifiable Scales

We propose a unified delay theory spanning from quantum scattering to conscious time perception to social delay discounting. First, we establish a scale identity based on spectral shift--phase--group delay, providing regularization via Kontsevich--Vishik (KV) and relative determinants for countable channels and infinite-dimensional cases, with explicit ``almost everywhere'' differentiability and de-singularization schemes in neighborhoods of thresholds and embedded eigenstates. Second, we charac