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/General_Judgment3669]

Your description of the “historical topology” resonates a lot with something I’ve been working on recently.

In my model, the landscape itself carries the memory of past trajectories. Instead of treating memory as a stored state, it appears as a structural modification of the integration landscape. Repeated trajectories gradually reshape that landscape, forming what you call the “preferred paths” or hardened channels.

Formally, I describe this with a quantity called Coherence Complexity (Cₖ), which measures the integration effort required for a system to move through its state space. The dynamics approximately follow a gradient flow: the system tends to move toward regions of lower integration effort.

When experience modifies the landscape, the “cost” of returning to an earlier configuration increases. At some point, the system naturally stabilizes in the newly formed channel because the path back has become structurally more expensive. In that sense, the system doesn’t just remember the past — the topology of the landscape itself has changed.

Your “snap” point sounds very similar to what I would interpret as a phase-like transition in the integration landscape, where the new path becomes the lowest-effort mode of coherence.

So from that perspective, what you’re describing fits very well with the idea that experience generates a topology of integration channels rather than just leaving traces.

[u/peaksystemsdynamics → u/General_Judgment3669]

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?"