章五・零（Chapter 5.0）
Why Stability Requires Locking

「持続には、自己強化がいる。」
Persistence requires self-reinforcement.

5.0.1 The Problem of Drift

At Chapter 4.0, we achieved memory: collapse structures that reference prior states.

But memory alone does not guarantee persistence.

A structure with memory can still drift. Each new collapse may shift the reference slightly, and over many collapses, the original pattern dissolves.

For structure to survive, it must resist drift.

“Stability” typically implies rigidity: a structure that holds its shape.

But we have no shape. We have no space for shape to occupy.

Stability, in pre-geometric context, means:

Recursive consistency—collapse patterns that reinforce themselves.

A stable structure is one where each collapse makes subsequent collapses more likely to follow the same pattern.

We call this self-reinforcement locking.

A locked structure is not frozen. It is dynamically stable: ongoing collapse continues, but the collapse pattern remains consistent.

Locking occurs when:

Locking is closure without boundary.

In standard mathematics, the Laplacian (∇²) measures how a quantity at a point differs from its surroundings.

Here, we use ∇²Φ to denote recursive consistency.

When ∇²Φ = 0, the collapse structure is in equilibrium: current patterns neither amplify nor diminish.

When ∇²Φ ≠ 0, the structure is unstable: patterns either grow or decay.

Locking corresponds to achieving ∇²Φ ≈ 0 through self-adjustment.

When locking succeeds, a shell forms.

A shell is not a surface. It is not an object. It is:

A self-sustaining region of locked recursion.

Inside the shell: consistent collapse pattern. Outside the shell: different or unstructured collapse.

The “boundary” of a shell is not spatial—it is the limit of pattern influence.

At this stage:

We have achieved persistence without space.

Structures can now survive. But they still cannot coexist. That is the next problem.

「形は無い。だが、殻は在る。」
There is no shape. But there are shells.