The curing bound: when is a bar of soap actually ready?

Fresh soap is routinely judged ready by feel: it no longer feels slippery, and a touch to the tongue no longer produces a sharp sensation. This paper models the three processes curing must complete, water loss, decline of free alkali, and development of hardness, and tests those signs against the resulting timetable. For a stated 120.0 g bar measuring 80 by 55 by 25 mm, starting at 28.0% water and curing at 20 °C and 50% relative humidity, water falls to 20.2% at day 7, 15.6% at day 14 and 11.3% at day 28. Free alkali in a zero-superfat batch falls from 2.40% at demoulding to 0.43% at day 7 and reaches 0.1% only at day 22.9. The minimum cure satisfying all three criteria is 23 days for a zero-superfat batch and 21 days with a 5% lye discount. The traditional signs clear far earlier: the tongue-test proxy clears at day 9.2 for the zero-superfat batch and day 2.1 for the superfatted batch, and the slippery-feel proxy at day 5.1, a gap of 13.7 days between the tongue test clearing and the zero-superfat minimum. A hardness index from saturated fatty-acid content, H = 12 + 0.92 times the saturated percentage, gives 87.4 for coconut oil, 58.0 for tallow and 24.9 for olive oil, and shows that no cure duration compensates for a low-saturation blend.