The Signed Jump, Read Geometrically: P7-K Denominated, and P7's Remainder at Its Closed State

P7's remainder after ten waves stood at one real datum — the gate rate law's exponent a, bench band [0.01237, 0.01264] — plus premise O, whose determining object was named as a signed extrinsic-curvature jump [K] read geometrically. This paper is the paper of record for Wave 11's front P7-K, which completed that read, converted whole and stated at the post-Wave-12 state. The read is a trichotomy: every owned identification of the seam returns \mathcal{C} = 0 by a profile-free theorem (smooth identifications), returns nothing (bookkeeping identifications, whose Jacobian vanishes and whose orientation is the premise itself), or returns the sign only as the deposit's material fact, \mathcal{C} = \mathrm{sign}(\sigma - 2p) in the density denomination, exact at threshold w_s = 1/2 and +1 at every owned equation-of-state row (the shell). Bit-B, the seam's bit, is therefore denominated — it is the deposit's (\sigma, p) fact — and the sever-dynamics build that returns those components, graded by the front as a premise-tier input claim, has since been chair-merged in Wave 12: both of the front's cautions dissolved on the filed record, SL-15 graded FIRED AT PREMISE TIER, the merged statement standing for the deposit's components, and \varepsilon_x usable at 1 cell-equivalent per crossing = 1.58\,E_L, premise-tagged. At P7's own address the wave's second result governs: the traversal's direction is the emitter bit Bit-E, which no [K] read can supply by parity — and Wave 12's P7-L has since proved the rate-law sector \mathcal{D}-even at inventory scope, closing P7's premise-O front with Bit-E resting at exactly 1 bit and its conditional determination on file. P7's remainder stands, unchanged in count and closed in structure: one real datum + Bit-E. Program headline, unchanged: NOT SOLVED / PARTIAL · producing-count 0.