The Rungs, Priced: An Amplitude Envelope for the Bounce's Gravitational-Wave Background from the Sever-as-Shell

The sever-as-shell's surface stress-energy (sigma = rho_A * L, w_s = -1 on the cut-layer route) is spent on the amplitude Three Rungs left unclaimed. Totalled over the written block's faces against the pair's division books (SL-5), the shell carries f_shell = 0.0773 (thin layer, m = 200) to 0.5158 (thick layer, m = 211) of the founding content, so the bounce's gravitational-wave background at 2.23 Hz / 445 Hz / 3.45 kHz obeys Omega_GW = Omega_r,0 * f_shell * eps_rad with eps_rad the one named unowned factor (the shell's tensor efficiency). The envelope (eps_rad = 1) is 7.10e-6 to 4.74e-5 and is already excluded by the BBN/CMB Delta N_eff bound, which caps eps_rad < 0.53 (thin) / < 0.079 (thick). DECIGO-class surveys probe eps_rad to ~1e-11 at the sever rung; existing LIGO limits already probe ~1e-3 at the cell rung. On the dump-spread route no amplitude is priced (sigma owns a sign, no magnitude) — printed as ungradeable. Falsifiers pre-registered, including the pincer (F1/F2) and the envelope breach (F3).