Structured Variance in Conformal Cyclic Cosmology: A Constraint-Based Hypothesis for Non-Uniform CMB Signatures

This paper proposes a constraint-based extension of Conformal Cyclic Cosmology (CCC) in which any putative imprints from previous aeons in the cosmic microwave background (CMB) need not exhibit statistically uniform properties. Instead, we hypothesize that the variance, persistence, and dilution of such signatures may be modulated by an underlying geometric constraint structure, leading to structured (non-uniform) variance rather than homogeneous anomalies. Within this framework, configurations near an optimal channel experience slower deviation and enhanced persistence, while those farther from the optimum are preferentially diluted. A central implication is dimensional stratification: observational probes sensitive to effectively two-dimensional (projected) quantities and three-dimensional (volumetric) quantities should yield systematically different characteristic scales, corresponding to distinct geometric anchors determined by constraint geometry. This perspective is compatible with holographic entropy scaling and does not imply information loss or conflict with standard cosmology. We emphasize that no detection of CCC signatures is claimed. Rather, the contribution is methodological: we identify an expanded hypothesis space in which structured variance signatures could evade searches based on assumptions of statistical uniformity. The framework yields clear, falsifiable predictions involving variance clustering near geometrically distinguished scales, redshift-dependent evolution toward optimal configurations, and probe-dependent characteristic thresholds. These predictions can be tested using map-level CMB analyses and complementary cosmological datasets with current and forthcoming observations.