The Sever as a Shell: The Bounce's Free Sign as a Material Fact

The Einstein–Cartan bounce frame I work in carries one undetermined bit: the sign 𝒞 of the seam's extrinsic-curvature jump, which the smooth bounce surface cannot supply — at any C¹ bounce both outward traces vanish identically, so the surface the seam was identified with carries no jump to inherit (the flank theorem). This paper constructs the one species that can carry a jump: the sever's cut taken to be a thin shell, its surface stress-energy the sever's own deposited energy, σ = E_dump/A_seam. The construction is sound, and its sign content is derived exactly, with the sign checked twice against independent known cases: [K] = 4πGσ(2w_s − 1), so 𝒞 = sign(σ − 2p) exactly, where w_s = p/σ is the dump's surface equation of state. The record I own constrains the dump only as the rectangle (m, E_dump) ∈ [1, 205] × [0, ∞): σ ≥ 0 follows, σ > 0 does not, and no statement fixes w_s. The bit is therefore not paid; it is reduced — to a named remainder, R-P10D (the dump-trace bit): which side of w_s = 1/2 the dump's surface equation of state lies on, granted the dump does not vanish. One binary distinction, no discount against premise O's one bit — but re-denominated from a bare geometric sign into a physical property of a named material object, at one construction sentence, one fewer than the two-sentence flank package it supersedes, and with no dominated half. The magnitude is unfenced and printed so: at the record's own energy scale E_L = 4.4933e+27 J the dimensionless jump reads q = −0.021873 for a dust dump (w_s = 0) and −0.065619 for a tension dump (w_s = −1), and |q| reaches 1 only at 45.72 E_L and 15.24 E_L respectively; the rectangle forces no magnitude. The construction's disagreement with the stand-off sum S(δ) < 0 is filed as an object difference with its joint-spend contradiction printed, not smoothed. Grade for this construction, printed at full size: (b) 𝒞 REDUCED — construction sound, sign formula derived, remainder named. The program headline stands unmoved: vacuum catastrophe NOT SOLVED / PARTIAL, producing-count 0. This is a construction and computation paper. It reports no measurement.