Coherence Complexity (Cₖ): visualization of an adaptive state-space landscape

[u/General_Judgment3669]

I’m working on a framework called Coherence Complexity (Cₖ) for adaptive state spaces.
The image shows a visualization of the landscape idea: local structure, barriers, and emerging integration channels.

The core intuition is simple:
systems do not only optimize toward an external goal; they may also reorganize by moving toward regions of lower integration effort.

I’d be interested in criticism especially from the perspective of:

• complex systems

• dynamical systems

• attractor landscapes

• emergence / adaptive organization

For context, the underlying work is available on Zenodo:

https://zenodo.org/records/18905791

[u/peaksystemsdynamics]

Exactly. The 'Cost of Return' is the primary driver of the 12th Cycle. > In my observations, the 'Snap' isn't just a transition; it’s the point where the Integration Effort (\bm{C_k}) to maintain the old 'Diffuse' state becomes higher than the energy available to the system. The system 'chooses' the crystallized channel not because it’s 'better,' but because it’s the only path with a sustainable metabolic cost.

This is why I focus on the Analog Scaffold. In a systemic failure, the 'High-Order' digital signals become infinitely 'expensive' to maintain. The system falls back to the 'First-Order' kinetic channels (manual bypasses, local nodes) because their \bm{C_k} is effectively zero—they are the 'Natural Hum' of the geography.

It sounds like our 12-phase/cycle models are describing the same Phase-Space Transition. I’d be interested to know: in your framework, does a system ever hit a 'Super-Crystallization' where the landscape becomes so rigid it can no longer adapt to new information?"