Closed Curvature
A closure condition where a route can conserve around a full tiling or loop instead of remaining an open local bend.
What the term means
Closed curvature is ECM’s name for curvature that becomes a completed boundary condition. The book emphasizes that closure may not be obvious inside one local wedge; it becomes visible when the full tiling is considered.
It is not just “curved shape.” It is the point where a route or relation can return, compare, and preserve bookkeeping around a boundary.
How it relates to the ECM
In ECM, closed curvature marks the difference between an unconserved local asymmetry and a stable conservation path. Phase-locked units can create transport rules that are not transient fluctuations.
Closed curvature connects scalar geometry to gravity-like curvature responses, vortex remainder routing, and large-scale tiling behavior.
Why it is important to understand
This term matters because ECM treats conservation as something geometry earns through closure. If the route does not close, the system may disperse, leak, or remain only partially coherent.
It also explains why local observation can miss a global boundary condition: the relevant closure may belong to the larger lattice.
Book context
Book anchors: Chapter 1, Figure 1.8 and Chapter 6/Fractal Math describe closed curvature as a boundary condition visible in the full tiling rather than one local wedge.
Read this as ECM vocabulary: it defines how the book uses the term inside its own conservation-first model. The term can overlap with standard physics or mathematics, but this page is explaining the ECM role first so readers do not lose the model-specific meaning.
Related ECM Diagram
This diagram belongs on the Closed Curvature page because it shows why closure is not always visible in one local wedge and becomes clear only across the full tiling boundary.
The takeaway is that closed curvature is a boundary condition earned by the larger route. ECM uses this distinction to separate local bending from conserved loop closure.