nx_folkgame_sow_gate.nx

nx_folkgame_sow_gate.nx -- GATE for the sow (mancala) family of nx_folkgame_sow_lib. THE LOAD-BEARING TOOTH IS T8: seed conservation over an EXHAUSTIVE game tree. Sowing moves seeds and never creates or destroys one, so the total must equal perside*2*seeds at EVERY node of the tree, not at a sampled few. A sowing loop that is off by one anywhere -- a wrap that drops a seed, a capture that adds one, a relay that re-sows a pit it already emptied -- breaks it at some node, and no implementation can satisfy it across thousands of positions by accident. HONEST SCOPE, STATED PLAINLY: this is an INVARIANT, not a published constant. Unlike the align family's 255168 there is no cheap external number for these boards. Conservation proves the seeds are handled correctly; it does NOT prove the capture rules match Oware as played. The external anchor for that is OpenSpiel's Oware, graded THOROUGHLY-TESTED in its own table, and cross-checking against it is the named open rung. A green here means the arithmetic is sound and says nothing stronger. T9 CARRIES THE ANTI-VACUITY: the conservation checker is proven able to FAIL by planting a seed into a live position and asserting the total goes wrong. A checker that has only ever agreed has not been shown to check anything. license_tier: ORIGINAL No hw writes (Rule 26).