Intriguing. LiFePO4 (Lithium Iron Phosphate) prismatic "pouch" cells normally deliver 3.2V per unit, so a 12S pack would provide the required 38.4V nominal voltage for a typical 36V pack, and based on what you are saying each cell has a capacity of 4Ah (unusual, as I've only seen 5Ah and 10Ah cells). My Li Ping cells measure 150x105mm (and about 6.25mm thick), for a 5Ah battery (12S) the whole pack is 75mm deep. My 10Ah (2P12S) battery is 150mm deep.Ours is a 4AH Lithium Iron Phosphate - using 5c rated prismatic cells (x 12) to give up to 20A discharge. Looks like the ping battery with blue heatshrink and includes BMS. Will take and post a picture - but fits perfectly in brompton rear pocket.
So I'm looking forward to seeing photos of your battery in the rear pocket of the Brompton luggage
Cheers, Dan