We present a standalone analytic reduction of the Collatz problem to a finite explicitresidual frontier. The argument proceeds through reduction to odd multiples of 3, analyticdescent in the regime e(u) = v2(9u + 1) ≥ 7, reduction of the residual regime e(u) ≤ 6to stable dyadic leaves, passage from depth-3 stable leaves to primitive families, andreorganization of the resulting primitive layer into 64 admissible affine families modulo192. The active branch of each admissible family is reduced to a distinguished terminalfamily associated with 104, whose remaining 34 base cases are finite and explicitly listed.The only configurations not closed analytically in the present paper are the rigid first-exitseeds arising from the admissible active families. These seeds form a finite explicit residualfrontier of cardinal at most 722. No claim is made in the present manuscript that thisresidual frontier is itself closed analytically within the manuscript.
julian redero (Tue,) studied this question.