The Amplitude Law: six mechanisms, no survivor, and why the obstruction is arm-level rather than mechanism-level

v2 CORRECTS v1. v1 reported that one of six candidate mechanisms survived adversarial verification. That is withdrawn: the mechanism carried a third referee, on the theoretical-health lens, which refuted it on a parallel-mode ghost. No mechanism survived. (That refutation is itself contested on a stated ground — it covariantised the mediator as a gauge vector where the aether-scalar-tensor vector is Lagrange-multiplier-constrained and unit-timelike — and the deciding recomputation has not been done.) Three further corrections, all against the framework. (1) The deflation: integrating ρ = √(GMba0)/(4πGr2) gives vc4 = GMba0 with vc exactly r-independent, so the ‘amplitude law’ and ‘flat rotation curves at the BTFR value’ are one statement. Four mechanisms ‘derived’ it and all four return the identical Bekenstein–Milgrom phantom density; the coefficient 1.000000 is returned by μ=x/(1+x) and μ=x/√(1+x²) too, so it measures the deep-MOND normalisation and nothing else. (2) The obstruction is arm-level, and proved: all four mechanisms reduce to the same modified-Poisson baryon sector for a general Φ(x,y,z) with no symmetry assumed, so which field carries the halo cannot move the Cassini quadrupole — only the interpolation function can. (3) An ephemeris correction of ~27× in the adverse direction: the stated interpolation exceeds the Mars budget by 3.3–4.0×104, not the ~1.3×103 previously recorded in this programme; two independent derivations agree. What survives, and it is a genuine theorem: the AQUAL functional is strictly convex, so the halo is a unique functional of ρb with zero free data and an attractor in radius — forward integration from a 10× spurious dark point mass converges to the same coefficient by 100 rM. Also established: the equation-of-state route is not the binding constraint (pr-pt is unobservable in the weak field); every static single k-essence scalar has pt = -ρ for any kinetic function; the general khronon cannot produce the amplitude law by a scaling theorem; and identifying the scalar with the condensate does not remove the double count, because the cancelling cross term is capped at κ²/(192π) while cancellation needs s* = 6.71 against a hard cap of 1/2. The paper now names the calculation that decides the programme: does an interpolation ν(y) exist that simultaneously fits the SPARC RAR at ≤0.06 dex, gives Q2 ≤ 5.2×10-27 s-2, and keeps the 1-AU monopole inside per-planet ephemeris budgets? If yes the arm survives; if no it is closed by a no-go and only constructions escaping the modified-Poisson framing remain. κ = 1/2 remains fitted. All numbers on both footings. All load-bearing claims backed by committed scripts that exit zero, produced under adversarial verification in which manufacturing a deficit was penalised as heavily as manufacturing a win.