The Price of One Number: The ε_x Hunt and the Remainder of the Dump's Magnitude Law

The vacuum program's junction front factorized the dump's magnitude law exactly: Edump(m) = ε_x · N_x(m), and a predecessor paper owned the count, N_x(m) = m on m ∈ [1, 205], modulo one priced sentence. One factor remained: ε_x, the energy deposited per crossing. This paper is the record of the hunt for its value at every address the program owns — Wave 9's two arms, converted whole. Arm 1 grades every owned per-event energy on two axes, band membership in (0, 0.2286\,E_L] and identification as the crossing deposit: the record owns a crowd of in-band numbers (4.44×10⁻³⁶, 0.0869, 0.0423 E_L, and their kin) and exactly one identified deposit (the cut layer's, at 3.18 / 19.99 / 20.13 E_L by thickness), and the two sets are disjoint — no candidate passes both axes. Arm 2 attacks the identified candidate's thickness dial through eight selection principles: none selects; the dial is binary (thin 3.18 E_L against a pitch cluster at ≈ 20 E_L); and the band-meeting thickness L^* = 0.0719\,_T is owned by no length, so no selection could pay the band anyway. The remainder is therefore priced exactly, and this paper prints the price as its result: ε_x costs one sever-dynamics sentence — a statement of the deposit's per-crossing energy from the crossing flux's own energetics, or a thickness sentence inside the seam's settled tagged premise — and until that sentence exists the magnitude debt rests, declared, beside the SL-15 trigger that waits on the same species from the vacuum side. Program headline, unchanged: NOT SOLVED / PARTIAL · producing-count 0.