nx_folkgame_sow_lib.nx

nx_folkgame_sow_lib.nx -- THE SOW (MANCALA) FAMILY: pits, seeds, laps and capture. Seven registry rows run on this one engine: Oware, Kalah, Congkak, Omweso, Tsoro, Pallanguzhi and Bao. It reuses nx_folkgame_lib's image, save/restore and terminal plumbing entirely -- cells are pits and state[c] is a SEED COUNT rather than an occupancy code. There is no second parser and no second position representation. THE INVARIANT THIS FAMILY IS PROVEN BY: sowing MOVES seeds, it never creates or destroys them. Total seeds is conserved across every legal move from every reachable position, and that is arithmetic rather than an opinion -- a sowing loop that is off by one anywhere breaks it, and no implementation can satisfy it by accident. It is the sow family's answer to what the published game-tree constant is for the align family. HONEST DIFFERENCE, STATED NOT HIDDEN: unlike Tic-Tac-Toe's 255168 there is no cheap PUBLISHED constant for these boards -- Oware was solved by Romein and Bal over 889 billion positions and Kalah by Irving, Donkers and Uiterwijk, neither reproducible inside a gate. The external anchor available to us is OpenSpiel's Oware, which its own table grades THOROUGHLY-TESTED, and wiring that cross-check is the named rung. Until it lands, this family is proven by an exhaustive invariant and NOT by an external count, and the gate says so in those words. license_tier: ORIGINAL No hw writes (Rule 26).