Balance

Balance is a fundamental Protocol Particle of Level +2 allowing functional system gradients to emerge. Balance requires all other Particles to be realized across any given dimension.

Equilibria

Equilibria are focal points of locally convex¹² permutations, e.g. $f(x)=x^2$, providing relatively stable system states. Entropy dictates that potentially many different equilibria exist within the same system. Transitions between equilibria tend to follow tipping point dynamics, which means that systems rarely shift linearly between states of stability. System states of perceived chaos may dominate any rule set for extended periods of time, as long as the inherent permutations of multidimensional points of gravity remain imbalanced relative to one another.

Thresholds

Thresholds are focal points of locally concave³⁴ permutations, e.g. $f(x)=-x^2$, providing relatively unstable system states. We consider thresholds to be the functional inversions of equilibria. Gravity dictates that the crossing of a threshold requires significant amounts of energy. And once a threshold is reached minimal effort in either direction may be enough to cause gravitropic forces to converge towards their new local minima. Note that there may be many potential local minima beyond the apex of any given threshold, since gravitropic topologies are notoriously multi dimensional.

Footnotes

1. Convex Function ↩

2. $f(x)=x^2$ ↩

3. Concave Function ↩

4. $f(x)=-x^2$ ↩