NORTH-STAR · 북극성
Train one system out of two objects: ① a ruler Ec that defines what "correct" means, and ② GRAM, a weight-shared recursion that builds the answer over K=10 steps. Goal — teach ② to obey ① from few examples, no augmentation, and generalize to held-out and OOD.
① Ruler · Ec
the verifier
Hand-written row/col/box conflict count. Exactly 0 only at a valid solution.
② GRAM
the recursion
Weight-shared, K=10 steps. Builds the answer; learns to obey ① from few data.
The law. Energy is consumed as a discrete-state OBSERVATION / verifier — never descended as a continuous −∇E gradient field. Energy-as-gradient died 8× (non-navigable, two-basin, saddle); energy-as-observation lives.
Operator learning lifts held-out exact 0 → 0.09; ①×② verified search takes it to 0.31 / 0.75.
Init-diversification + per-step re-damage breaks the exposure-bias wall (first held-out + OOD liftoff); energy stays a detached no-grad observation (modest but real, +2×). Then C2: the model orders MRV branches, Ec-derived dead-ends prune, sound verification accepts — project record on weakOOD, backtracking wall opened on targetOOD.
The dead "descend the energy" thesis.
Pathwise −∇E into the generator: verifier AUC 1.0, gold E < random, train exact ≈1.0 — yet the method was later falsified as the dead gradient path (vertices-vs-interior). Kept as honest history, not as a live method.
Honest status. Best held-out exact 0.090 is still below the propagation ceiling 0.150 — the learned operator is a soft statistical corrector, not yet a sound propagator. targetOOD exact = 0 (needs guess + backtrack). This list extends as dates grow.