The Sever, Evolved: The Deposit Layer's Own Dynamics Returns Its Components

The sever's deposit — the layer of material the cut leaves behind — has been carried by this research programme for nine waves as a static object: a shell with a surface density, a thickness chosen from a short list, and an equation of state nobody owned. Three open debts pointed at the same missing object. The composition count of the vacuum derivation needed the interior of the store delineated, or a law for its cells. The per-crossing deposit energy ε_x was unpaid, its price stated exactly: one sentence of sever dynamics. And a standing trigger waited for any sever dynamics that returned the deposit's stress components (σ, p), because two ledgers in the record describe the cut with opposite signs and only the components themselves can say which shell the deposit is. This paper builds the dynamics. The deposit layer is the store's own material — a spin fluid whose bulk pressure at density ρ is −ρ²/ρ_A in units of c², the pressure law of the bounce itself — accumulated at the cut under the density cap, one cell of layer material per crossing. The layer's surface equation of state is then not chosen but derived: w_s(ρ) = −ρ/ρ_A, running from 0 at the layer's birth to −1 at saturation. The settled deposit is the tension shell (σ, p) = (+ρ_A L, −ρ_A L), and the sign of its extrinsic-curvature jump is +1 in the density denomination at every instant of the layer's life. The per-crossing deposit is one cell of the layer's own material — 1.58 in units of the violent bound E_L — which is 6.92 times larger than the largest per-crossing value the programme's exhibit band admits; the band, restated in the deposit's own denomination, demands a deposit of 14.5% of one cell, a sub-cell deposit the layer's granularity cannot make. The composition count is not paid: the dynamics delineates the cut's own boundary layer, not the interior of the assignment book, and the count debt stands at 5.90 counts, unchanged, its species named. What the dynamics does return at that address is the first bound the record owns on the total dump, and a dynamical discriminator on the layer's thickness fork that has stood open since the first shell paper.