A Stove-Left-On Witness With a Priced Warning Lead Time: Hob Temperature and Room-Presence Reasoning for Older People Living Alone

SIMULATED, NOT MEASURED. Unattended cooking is a leading cause of house fires, with risk concentrated in older people living alone. This paper specifies a cheap camera-free witness (infrared pan-temperature sensing, a hob-plate thermistor, and room-presence reasoning, bill of materials 75 USD) and computes its performance from stated assumptions under a lumped thermal model. It alerts 12.40 minutes before an empty pan on full power reaches 400 C, 9.06 minutes before an oil pan reaches its 320 C flash region, 13.24 minutes before a pan boiled dry reaches 400 C, and 5.21 minutes before a cloth/paper item near the hob reaches 233 C. A temperature-plus-duration-plus-absence decision rule does not trigger on a long stock simmer, a slow oven roast, or a kettle boiled and left warm, and implies 0.571 false alarms per week of normal cooking (20,000 simulated weeks). Blind spots are stated in full, including a low-temperature smoulder the design cannot see and a cook present but incapacitated in the kitchen itself. No device has been built, installed, or tested in an occupied home.