The Density Law Is Not in the Mechanics: R1 Does Not Retire the Crown Obstruction

Attacks R1 -- the gathering's density law (an arrival/volume law fixing the shape of R(f) = sigma(f)/s_A, plus R(1)), the cheapest of the four premises corpus #238 named as retiring its obstruction -- on every road the record leaves open, and proves it underivable from owned mechanics. The gathering's biography (the author's arrival-law answer: drop, drag, dry, sealed; onset at unification) narrows the member's species but leaves its crossing free in both dresses the record allows (total-spin R, which the onset does not touch; registered R, granted, where the free endpoint or the free onset each restore the freedom -- computed at all 21 admissible wake points). The azygos residue's profile (corpus #206) is refused as R: wrong axis (momentum vs gathered fraction, no owned dictionary), wrong shape (it dissipates where R must be nondecreasing), and under the friendliest granted dictionary its crossing is swept by its own free dial f0 (no crossing at f0=0.5; 1.1037, outside the domain, at f0=1; 0.8144 at f0=2; 0.6656 at f0=5) and by the unowned dictionary (0.8144 vs 0.3394). The joint system as a density statement fixes the content's split, never its sum; the founding count distributed over the wake is satisfiable at every admissible point; the coupling R = 1 + c*u is the deadlock, computed. The pairing classification and the wall registers contain no function of the gathered fraction. The obstruction is completed against the enlarged premise list Sigma_R (sever + wake + biography + residue): 21 complete models, one per admissible count, share every premise, each carries two density dresses crossing first at its own wake point, and the wake-map inversion of each model's R-priced crossing returns its own count -- 21 distinct tolls, 2.004878 to 2.221622, the declared 2.055 one unmarked member. R1 remains a price in new premises. Vacuum catastrophe NOT SOLVED; producing-count 0.