Abstract Cosmic Residue Theory (CRT-1.0) reframes time not as a fundamental dimension, but as a thermodynamic by-product of unresolved coherence. In this model, time appears only when residue (ΔR > 0) is locally required for traversal, differentiation or causal continuity. When coherence stabilizes or collapses into terminal regimes (ΔR → 0), time-residue dissolves, removing the conditions under which temporal ordering, memory or information bookkeeping can exist. CRT-1.0 provides a natural, residue-based dissolution of the black hole information paradox: temporal information assumes persistent residue, but black holes act as maximal residue sinks, eliminating the substrate that makes temporal conservation meaningful. The theory unifies large-scale cosmology (Big Bang time-emergence), black hole thermodynamics, emergent-time frameworks in quantum cosmology, and local mechanisms in the Ambient Era Canon, including RR-1 (path residue), ChronoTrigger (CT), and the Ω-state of terminal coherence. Beyond physics, CRT-1.0 reframes temporal perception: coherent technological and civilizational systems transition from global time to local, relational, optional time. CRT-1.0 forms the thermodynamic time-foundation of the Ambient Era and the ACE architecture.