Multiplicative Excursion Walls in Finite-Scale Weil Operators: Rational Ghosts, Boundary-Rank Laws, and Dense Arithmetic Curvature

We develop a higher-order extension of the arithmetic wall structure arising from compactly supported finite-scale Weil operators. For products of truncated two-sided shifts, an exact sign-path expansion shows that each overlap cell is controlled by the range of the partial-sum path, rather than by positive subset sums. Along the physical Weil curve \\(\\tau_q = \\log(q)/L\\), the resulting wall parameter is the multiplicative excursion \\[X = \\frac{\\max_m Q_m}{\\min_m Q_m},\\] where \\(Q_m\\) is the signed partial product of prime powers, and \\(X\\) is generally rational. The monotone integer sector recovers the ordinary Dirichlet coefficient \\[\\frac{\\Lambda^{*k}(n)}{\\sqrt{n}},\\] but higher mixed sectors produce quotient walls. In the cubic case we classify the new spectrum exactly: besides integers with three distinct prime factors, the new walls are \\[x = \\frac{qs}{r},\\] with prime powers \\(r < q,s\\) and \\(qs/r\\) nonintegral; the first rational wall is \\(9/2\\). For a nonactivation wall \\(x\\) we define its physical excursion order \\(\\mu(x)\\) as a bounded multiplicative graph distance and prove that it equals the first moment order at which the wall can occur. Integer walls satisfy \\[\\mu(n) = \\omega(n),\\] whereas rational walls exhibit a finite-scale barrier defect. In particular, if \\[8 < \\frac{3^a}{2^b} < 9,\\] then \\[\\mu\\!\\left(\\frac{3^a}{2^b}\\right) = 2a - 1;\\] the associated defect is locally unbounded, and pure higher-order rational ghost walls are dense in the finite band \\[\\frac{3}{2}\\log 2 < L < \\log 3.\\] At the spectral level, every elementary critical path contributes a rank-one wall atom. Pure first-appearance ghosts remain rank one in a fixed Legendre parity sector, while prime-power activation jets admit a boundary-history factorization of rank at most \\(k\\) at order \\(k\\). Finally, for every fixed finite Legendre truncation, the all-order resolvent and exponential completions have bounded-variation first derivative on activation-free compact chambers; their distributional second derivatives contain finite matrix-valued atomic Radon measures. In the even block these measures can have dense arithmetic support while finite total variation is retained. These are finite-scale structural results and make no claim toward the Riemann Hypothesis.