The Branch Table of the Einstein-Cartan Spin-Density Bound, and Its Falsifiability Registration Restated

Companion note to 'Pinning the Einstein-Cartan Spin-Density Bound' (concept DOI 10.5281/zenodo.23485324), which pinned rho_A = 9.72 x 10^54 g/cm^3 on one branch: neutron carrier, coefficient 1/8, and a dust balance in which kinetic energy is set to zero. Part 1 collects every branch admitted by that paper into a single table recomputed from one formula by the accompanying script compute.py: current-quark carrier (5 MeV, dust) 2.75 x 10^50 g/cm^3; constituent-quark carrier (~300 MeV, dust) 9.91 x 10^53; aligned net spin f = 1 (coefficient 1/4), neutron, dust, 4.86 x 10^54; neutron, coefficient 1/8, dust, 9.72 x 10^54; npe mixture at Y_p = 0.1, coefficient 1/8, dust, 1.17 x 10^55; net spin f = 0.5, neutron, dust, 1.94 x 10^55; net spin f = 0.1, neutron, dust, 4.86 x 10^56; and the degeneracy-complete (Fermi) reading, whose zero of the effective density is at approximately 1.3 times the Planck density, approximately 6.7 x 10^93 g/cm^3. The total spread across these rows is 43.4 orders of magnitude; the dust-only spread is 6.2 orders; and in the net-spin limit f tends to zero the bound diverges and ceases to exist. A separate paragraph gives the electron-carrier value, 2.87 x 10^48 g/cm^3 (script output 2.874 x 10^48), as the value applying to electron-degenerate matter, and states the discipline the table imposes: outside the derivation the figures 9.72 never appear without '(neutron, coef = 1/8, dust balance)' attached, and the branch-free headline is rho_A ~ 10^55 g/cm^3 on the dust branch. A short section incorporates the companion coefficient computation (DOI 10.5281/zenodo.24113586): coef(u) = (1/24)[1 + 2A(u)^2], falling from 1/8 non-relativistically to 1/24 in the ultra-relativistic limit, so at bounce conditions the neutron dust row moves to 2.92 x 10^55 g/cm^3, a rescaling by a factor of exactly 3 within the branch. Part 2 re-registers the earlier paper's four test conditions honestly: Condition 1 is relabelled a consistency theorem; Condition 2 a discovery search whose adverse clause can fire only on a positive detection, with its five conjuncts stated; Condition 3 is marked unexecutable with current or planned instruments and calibration-dependent over about nineteen orders of magnitude through M_thresh proportional to rho_c^(-1/2) (6.7 x 10^14 g at the dust calibration to approximately 2.9 x 10^-5 g at the Planck calibration), and is stated to test the rho_c = rho_A calibration of the rotating-core ansatz rather than Einstein-Cartan theory itself; Condition 4 is recorded as already demoted to non-independent. The conclusion states plainly that, as of this note, no observation or computation is currently specifiable whose outcome the framework would accept as falsifying its core claim; the core claim is a theorem of a stipulated classical model, and its empirical content runs through the branch choices tabulated in Part 1. Disclosure: this paper was prepared with the assistance of Dave, an AI system; all computations were performed by the archived script compute.py deposited with the paper, and every numerical value reported is an output of that script or is identified in the text as a value quoted from the earlier paper.