What is the thinnest insulation with the highest R-value?

The thinnest insulation with the highest R-value per inch is rigid foam boards made from polyisocyanurate and vacuum insulated panels, and among spray foams, closed-cell spray foam. If you rank common insulations by R-value per inch, vacuum insulated panels are the absolute highest at R25 to R50 per inch, but they are expensive, fragile, and used mainly in commercial freezers, not typical home construction. For practical home construction, polyisocyanurate rigid foam, sold as Polyiso, offers about R6.0 to R6.5 per inch and is the highest R per inch board you can buy at Home Depot or Lowe's. Brands like Rmax and GAF EnergyGuard are common. Next is extruded polystyrene XPS like Owens Corning FOAMULAR at R5 per inch. Closed-cell spray foam gives about R6.5 to R7 per inch in perfect lab conditions, typically rated at R6 per inch in the field, and also acts as an air and vapor barrier. Aerogel blankets like Thermablok offer about R10 per inch and are only about 0.4 inches thick, making them the thinnest high-performance option for windows and thin walls, but they cost $3 to $7 per square foot. For comparison, standard fiberglass batt is only R3.2 per inch, cellulose is R3.5 per inch, and mineral wool is R4.2 per inch. So if you have only 2 inches of space and need maximum R-value, 2 inches of closed-cell spray foam or polyiso gives you R12 to R13, while fiberglass would give only R6.