The Canonical Local Singular Series on Primorial Lattices: Strict Decrease, Crossing Structure, and the Plateau Conjecture

We develop the structural theory of the canonical local singular series on primorial lattices. The adjacent aggregate ratio R_k(s) = U_{s+1}/U_s is proved strictly decreasing with an explicit three-term slope identity (Theorems 1-2), yielding a unique crossing in an unconditional window (Theorem 11), weak unimodality and peak-set characterization of the aggregate sequence (Theorem 9), and no-plateau bands at both ends (Theorem 14). The channel quantities D_j satisfy the elementary two-sided sandwich j P_{>k}(2) <= D_j <= log(k/(k-j)) (Theorem 15). All proofs of Theorems 1-19 are elementary, telescoping-based, and free of unproved prime-distribution hypotheses. A zero-floating-point certification pipeline gives unconditional finite-domain proofs for k = 122, 218, 1000 (Theorem 20, PROVEN (finite domain)), certifies 305 of 306 scanned points in 2 <= k <= 10^4 under a pessimistic rounding budget (minimal margin-to-bound ratio 1.046e5), and a deterministic sieve verifies pi(2k)-pi(k) >= 0.8 k / ln k throughout 10^6 <= k <= 10^7 (NUMERICAL/CERTIFIED). The Plateau Conjecture (R_k(s) != 1) is stated with twelve further open problems, all graded. Complete manuscript, appendices, references, and the full reproduction toolchain (45 scripts, frozen claims registers, stage ledgers S0-S7) are included. The entire manuscript is rendered in English.