Two Spin Papers, One Density: Ising's Two-Valued Spin and the Aldred Limit's Spin-Density Bound, Priced Jointly

My corpus contains exactly two papers whose load-bearing object is a spin, and they have never been read together. CC-129 priced the Ising model: a magnet replaced, by postulation, with two-valued variables σ = ±1 on a lattice, interacting only as nearest neighbours through a single coupling J that no step in 1920 or 1925 sets from the material — 1 postulated Hamiltonian, carrying 1 fitted coupling and 2 deletion classes, against 0 derivations. My Aldred Limit paper pinned a bound of a different kind: in the dust spin-fluid reading of Einstein–Cartan gravity, the effective density ρ_eff = ρ(1 − ρ/ρ_A) crosses zero at a single density, ρ_A = 9.7×10⁵⁴ g/cm³ at the incoherent coefficient 1/8 for neutron matter, and the same paper printed its own domain limit at full size — the bound is a formal extrapolation, since the carriers' wave packets begin to overlap at a spacing of one neutron Compton wavelength, at a density of about 1.8×10¹⁷ g/cm³, some 38 orders of magnitude below the pinned value. This paper reads the two spin papers against each other and prices the one quantity they share: a density of two-valued spins. If each neutron at the bound carries one two-valued spin, the spin density at ρ_A is 5.791295e+84 m⁻³, the interparticle spacing is 5.568541e-29 m, and the ratio of the bound's density to the domain-expiry density is 5.388889e+37 — 37.731499 orders of magnitude — with 5.363319e+37 lattice sites inside a single Compton cube at the bound's density. The Ising side of the bench reproduces CC-129 exactly: the two-dimensional critical temperature t_c = 2.269185 with sinh(2/t_c) = 1.000000, the mean-field overstatement of 76.274717 per cent, and the one-dimensional correlation lengths 27.296022, 3.671861, 1.295443 and 0.710818 lattice spacings. The joint finding is a fence, not a bridge: the discrete spin that the Ising postulation makes exactly soluble is a semiclassical carrier's spin, and the Aldred paper's own domain limit says the carriers stop existing as particles 37.731499 orders of magnitude before the bound's density is reached — so the two-valued spin cannot be spent at the bound's address, and the bound cannot borrow the Ising model's exactness. Each paper, read alone, prints its own fence; read together, the fences are the same fence seen from two sides, and this paper prices the distance between them. Grade for this joint entry, printed at full size: REASON FOUND / STILL TURNING — PREMISE-ONLY, explicitly not a kill and not a falsification of either parent. The program headline stands unmoved: vacuum catastrophe NOT SOLVED / PARTIAL, producing-count 0.