Closure & Non-Closure

1. Closure Is an Imposed Condition

Closure is often treated as a natural outcome: paths return to their starting point, cycles repeat, orbits complete. In reality, closure is a constraint applied by the observer.

A transported frame does not guarantee return. It only guarantees continuity.

2. Transport Around a Loop

Consider transporting a frame continuously while tracing a loop. Position may return to its origin while orientation, phase, or timing does not.

This mismatch is non-closure. It is not error. It is memory.

3. π as a Closure Constant

In flat rotational transport, enforcing closure requires accounting for accumulated orientation. π quantifies the linear-to-rotational overrun required to complete a loop.

π does not describe curvature of space. It describes the cost of enforced closure in Euclidean transport.

4. Orbits and Secular Drift

Real orbital motion does not close. Each cycle accumulates drift: precession, timing offsets, and frame misalignment. Closure is imposed retroactively by redefining the frame.

Ellipses persist only when transport history is periodically erased.

5. Tides as Non-Closure

Tidal cycles do not repeat perfectly. Spring and neap modulation arises from accumulated phase mismatch between transported frames, not instantaneous attraction.

What is observed as periodic forcing is, in fact, long-horizon non-closure.

6. Why Physics Forces Closure

Closed solutions are algebraically cheap. They allow conservation laws to be written without memory terms.

When non-closure is ignored, corrective terms are introduced. These terms are called forces.

7. The Inertia Encyclopedia Position

Closure is optional. Non-closure is physical. Memory accumulates under transport whether it is tracked or not.

Physics that demands closure will always invent causes to explain its loss.