The Rectangle Halved: A Crossing Count for the Dump's Magnitude Law

A predecessor paper in this program (The Dump Is Dust, production run 19) earned the sign of the sever junction — the deposit of crossings is dust, w_s = 0, \mathcal{C} = +1 — and left the dump's magnitude open at full size. The campaign's wave-7 record then factorized that magnitude exactly: E_{\mathrm{dump}}(m) = \varepsilon_x \cdot N_x(m), a per-crossing energy times a crossing count, both factors unowned in value — a rectangle of ignorance with two sides. This paper discharges the count side. On one further sentence, (S4) TRANSIT-COUNT — a cell transit is one crossing event — the count is the traversal's own bookkeeping: N_x(m) = m exactly on the whole rectangle m \in [1, 205], and the magnitude law reads E_{\mathrm{dump}}(m) = \varepsilon_x \cdot m. The sentence is evaluated on its face, its falsifier is pre-registered, and the rival counter in the record — a hazard dynamics counting sealing events — is graded as counting a different event: it supplies no N_x and does not falsify (S4). What survives is one factor: \varepsilon_x, a single real number, unowned in value, which the cut layer's own denominations overshoot against the record's sane band by factors of about 14 and about 88 under two unselected thicknesses — the pressure that charges the successor hunt. Campaign headline, unchanged: NOT SOLVED / PARTIAL · producing-count 0.