DERIVED
Open / non-recurrent
Compatible histories that do not return to a finite recurrent class provide the structural basis for propagation-like response.
Derivation map
From Events to Physics
A relational progression from compensated events to open and recurrent dynamical classes.
One event
A single event provides one compensated relational distinction but does not by itself establish a persistent closed structure.
Interaction and recurrence
Multiple events create a relational state. Pure relational combinatorics already allows an irreducible directed cycle with three events:
\[1\rightarrow2\rightarrow3\rightarrow1\]
Therefore three events are sufficient for a first irreducible recurrence. This corrects earlier working statements that associated the first recurrence exclusively with four events.
Complete closure candidates
Four-event complete-neighborhood structures remain important as richer closure candidates and in tested effective network models, but they are not the first recurrence of any kind.
Open vs recurrent classes
DERIVED
Closed / recurrent
Finite recurrent classes provide the structural basis for persistent and bound-like response.
Coarse-graining
UGSD does not identify its deepest relational units with meters, seconds or Planck cells. Continuous fields, coordinates and familiar equations are treated as effective representations obtained after coarse-graining and calibration.