CCCT IV: Collapse Without Annihilation - Recursive Survivability Compression and Conditional Projection in Quantum Computing

This paper presents the fourth installment of the Coherence-Constrained Computation Theory (CCCT) series and documents a major architectural transition in the CCCT quantum-computational framework. Under high reconciliation pressure, the system no longer exhibits binary collapse or annihilation. Instead, it enters recursive inward survivability compression, producing deep-state persistence, conditional projection, and graded manifestation across multiple admissibility strata. The work formalizes how unresolved reconciliation pressure drives systems into DEPTHDIVE regimes, where external projection weakens while internal survivability continues through recursive admissibility structures on the Allen Orbital Lattice (AOL). Projection is reframed as externally stabilized survivability, distinct from existence itself. The paper introduces the operational hierarchy SUBSTRATE → COST → RECONCILIATION → PERSISTENCE → PROJECTION and derives the mathematical conditions governing phase alignment, cost accumulation, reconciliation flow, persistence counters, and conditional manifestation. High-disturbance survivability runs demonstrate that collapse corresponds to degraded projection rather than termination of the underlying structure. Survivability continues internally through compressed deep-state chains, enabling continuity-aware computation even after external coherence fails. This marks a shift from earlier lateral branching regimes toward recursive survivability computation, establishing CCCT as a persistence-oriented architecture with implications for quantum persistence, fault-tolerant computation, and non-destructive observational systems.