Discrete samples versus completed cone orders

Equation (eq:orderfaithful) prevents a representation from introducing false comparisons among actual events. Equation (eq:generated) prevents enlargement to a convenient ambient cone unsupported by the represented displacements. Neither equation asserts that every point of $V$ is an event, or that every boundary displacement is operationally attained.

In a continuum model one may instead start with an order on all of $V$. Theorem thm:conefromsymmetry, closedness, and nonempty interior then provide the proper cone. With $\iota$ the identity, (eq:generated) is automatic.