Cache an immutable occupancy per placements map and derive a candidate's
time-off period groups, holiday-week completeness and placement tie key
from its parent when one date is added or removed. The from-scratch
computation stays as the test oracle and an opt-in shadow mode. A
fast-check property test compares both after every operation.
The loaded year drops from 66.5 s to 48.5 s and the protocol from 262.0 s
to 193.7 s. Outcomes, explanations and final states stay identical.
Refs #283
Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
