One Wall, Two Registers: The Dust Density Is a Truncation Artifact

My obstruction census of vacuum-energy mechanisms in Einstein–Cartan cosmology (The Crossing Charges Nothing) carries one debt I declared in the open and never paid. The census works at a bounce density — the "plateau," $\rho_b = 4.4992\times10^{113}\ \mathrm{eV}^4$ — obtained from the exact Fermi-gas equation of state. But the corpus also carries a second, much older bounce density, the Kopczyński–Trautman dust-register value $\rho_{KT} = m_n^2/\alpha = 1.675\times10^{74}\ \mathrm{eV}^4$, which sits $39.4$ orders of magnitude below the plateau. Inside the census I wrote that "the two registers are not reconciled inside the corpus," and I flagged the disagreement wherever it mattered. This paper pays that debt, and the answer is clean: there are not two bounce densities. There is one wall condition, and the two registers are what you get when you feed it two different truncations of the same equation of state. The plateau comes from the ultra-relativistic limit of the Fermi gas; the dust density comes from the rest-mass-only limit, $\varepsilon = mn$. Fed the exact Fermi-gas energy density $\varepsilon(n;m)$ — the equation of state the census states it uses for every wall computation — the wall condition has exactly one solution, for every carrier mass, and that solution is the plateau. The dust density is not a solution at all: at the number density where the dust formula claims the bounce, the exact energy density exceeds the torsion term by a factor of $1.39\times10^{13}$, so the effective density there is positive and nothing bounces. The dust root is self-inconsistent by construction — it sits at a Fermi momentum $1.85\times10^{13}$ times the neutron mass, deep in the ultra-relativistic regime where the dust equation of state that produced it is not valid. The exact relation between the two registers is one line: $\rho_b / \rho_{KT}(m) = (m_/m)^2$, where $m_ = \sqrt{\alpha\rho_b} = 4.869\times10^{28}$ eV is a mass the census already contains. The registers agree only for a carrier of mass $m_$ — about four Planck masses, a void mass, outside every physical range — and even there both truncations fail and the exact root sits $0.38$ dex above their common value. What survives of the dust register is what it always was: a correct theorem inside the dust spin-fluid model* of the 1972–73 literature, and a historical estimate — not a second density of this frame. No verdict of the census moves: the census's wall computations used the exact equation of state throughout, and the dust density was used only as a comparison, never as an input. The cosmological constant problem is not solved by anything here, and the census's $121.5$-dex gap stands untouched. What is discharged is one internal inconsistency, removed in full.