Version v6. 1 is a layout-corrected edition of CCC V6. The theoretical content remains unchanged. This version adds a Table of Contents for improved navigation. Version V6 of the Causal Cloud Cosmology (CCC) main framework record. It supersedes V5. 3 as the current canonical paradigm edition of CCC while preserving V5. 3 as a citable prior version in the same continuing framework. CCC V6 is written from a simple scientific question: What remains coherent when observation is limited? Starting from this question, the work develops a consolidated structural formulation of accumulated structural persistence, projection-compressed observability, residual coherence, and observable certification. The central CCC object is accumulated realizable structure, C = C (x, T), where x denotes observable-regime position and T denotes structural time as an accumulation parameter of realizable organization. The framework is organized around three root cores: globality, continuity, and realizability constraint. These root cores support the main CCC sequence: Structure → Accumulation → Projection → Observable Residual. Within this sequence, observable weakness does not necessarily imply structural absence. Projection-compressed observability may suppress amplitude while preserving residual coherence. CCC V6 therefore asks whether accumulated structural persistence can leave an observable trace that remains coherent, testable, and distinguishable from projection-disrupted cancellation. A major purpose of V6 is to move CCC from structural interpretation toward observable coherence certification. The manuscript introduces and consolidates curvature-direction persistence, the residual curvature indicator (RCI), the sign-coherence statistic (SCS), and the normalized significance measure Z = SCS sqrt (Nₒbs). These diagnostics are used to test whether projection-compressed residuals preserve coherent curvature direction beyond disrupted or randomized baselines. V6 also clarifies the nonlinear accumulated structural-memory term. The T²-like contribution is interpreted not as an arbitrary fitting correction, but as a natural diagnostic scaling of pairwise accumulated realizability. If the effective accumulated count satisfies Nₑff (T) ∝ T, then the number of pairwise realizable relations scales as Nₑff (T) Nₑff (T) -1/2 ∝ T². This provides a CCC-native structural basis for nonlinear residual accumulation and curvature-direction persistence. The framework does not claim to replace ΛCDM, general relativity, or quantum mechanics. ΛCDM remains the standard reference model for observable expansion and parameter fitting. General relativity describes observable geometry. Quantum mechanics predicts observable manifestation. CCC V6 adds a structural-residual diagnostic layer for testing accumulated structural persistence and residual coherence under projection-compressed observability. Compared with V5. 3, V6 strengthens the CCC main framework by stabilizing the C = C (x, T) backbone, clarifying pairwise accumulated realizability as the source of T²-like nonlinear structural memory, placing practical SCS–Z verification in the main text, adding a ΛCDM diagnostic comparison, and defining a conservative GR/QM compatibility boundary. The result is a canonical V6 formulation in which CCC is not only a language of accumulated structure, but also a self-consistency and observability certification framework. Its scientific task is to test whether its own structural claims can generate falsifiable residual-coherence diagnostics under observable conditions. CCC V6 is offered in a conservative and open spirit. It does not ask the reader to accept a final cosmology. It asks whether a structural idea can become clear enough to meet observation, disruption, criticism, and future verification.
Jimmy Chen (Mon,) studied this question.