Nested Coherence in the Deep Ocean: Independent Physical Evidence for Scale-Invariant Constraint Fields (Paper 3, V1)

We present independent physical evidence for nested coherence dynamics in the deep ocean using daily mean temperature fields from the ECCO v4r4 state estimate. The deep ocean provides a critical falsification domain: it is weakly coupled to direct solar forcing, evolves slowly, and is governed by strong physical constraints. By analyzing rolling correlations between temperature fluctuations at multiple depths at fixed geographic locations, we construct a dimensionless measure of internal coherence that is insensitive to absolute scale or mean state. Across multiple years and spatially separated quiet- ocean sites, we observe a robust, non-monotonic coherence pattern: internal coupling between depth layers rises sharply, reaches a pronounced maximum, and subsequently collapses, even as variability within individual layers persists. This behavior is absent in global spatial averages and cannot be reproduced by time-shuffled null models, which fail to generate comparable coherence amplitudes. The coherence transition therefore reflects a localized reorganization of internal dynamics rather than a basin-wide driver or statistical artifact. Taken together with prior geophysical and biological results, these findings support the ex- istence of nested constraint fields that regulate how complexity is integrated within physical systems. Progression into larger constraint domains is marked not by new timescales, but by transient increases in internal coherence, followed by collapse when organizational capacity is exceeded.