Three Counts from the Recognition Lattice: Eight Fermion Doublers, a Golden String Tension and the Argon Closing

Three counts on the cubic lattice, for the recognition cost J(x) = ½(x + 1/x) − 1. First, every odd-hopping spin step annihilates every spinor on the eight sign waves. A step with finitely many Hermitian hoppings, a self-adjoint energy and the free square is the central step: exactly eight Pauli corners, four of each handedness, permuted as the cube's vertices are by its 48 symmetries. The forward step is not self-adjoint, vanishes only at momentum 0, and has Jordan, unstable zero modes elsewhere. Second, with link flux in whole steps s ≠ 0, a charge pair costs at least the cheapest charged link per step, exactly J(es) = cosh s − 1 for that link's charge. A cluster separates at bounded cost exactly when its total charge is zero. For a carrier realizing this model on the record orbit, the tension is J(φ) = √5/2 − 1 ≈ 0.118. Third, given exactly 1s below 2s, exactly 1s, 2s, 2p below 3s, and 1s, 2s, 2p, 3s, 3p below 4s with every other subshell but 3d at or above it, the closings are 2, 10, and 18 or 28, with 18 when 4s lies below 3d. Potassium's constrained 4s level lies below every 3d state for a frozen core with the nucleus's own exponents. Preprint of the Recognition Physics Research Institute, 37 pages.