The Silence Bound: How Long a Missed Check-In May Last Before It Must Be Treated as an Emergency

A decision model, computed from stated chosen assumptions (SIMULATED, NOT MEASURED), for how long a missed daily check-in from an elder living alone may last before escalation: soft prompt at 1.5 h, telephone/neighbour check at 2.5 h, entry at 3.5 h after a 09:00 deadline, producing 1.17 expected false call-outs per year and average discovery 3.5 h after the deadline. Sensitivity analysis shows the ladder is hostage to the assumed rate at which undiscovered time converts into harm, not to the benign forgetfulness rate; the daily rhythm itself imposes a worst-case undiscovered interval of 27.5 hours.