Newton's constant from a jammed packing the area-law coefficient is computed and measured, and it measures the Planck length in monad diameters

Require no preferred direction at the fundamental level, and for a structureless constituent everything follows: identical spheres, jammed rather than crystalline, one spin-1/2 each, Heisenberg-coupled. On that substrate Newton's constant is the vacuum's entanglement density, G = 1/(4 eta_A), and the entanglement across a surface returns the black-hole area law with a coefficient the packing computes rather than fits. The model's central identification - monad diameter is Planck length - then becomes a constraint on separately measured quantities. The constrained one is the area-law coefficient a, not the ratio S/c. There are two targets, not one, and which applies is decided by C - so the comparison has to name which it is against. Against the target the model derives, pi/(18 phi_J z) = 0.04545 at C = sqrt3, the measurement a = 0.0474+/-0.0013 statistical sits 1.50 sigma above, with a band systematic an order larger whose direction is unfavourable to the model. Against the target that d = l_P requires, 0.13635, the same measurement is short by a factor of 2.5 to 2.9 - and that is the figure to quote only if C = 1, which the derivation in the Letter gives no room for and the measurement rejects at 30 sigma within the model's own operational definition of C. ==> So a one-line summary of this Letter as "short by a factor of three" states the shortfall against a value the model does not use: the anchor identity a phi_J z = T(3)/C^2 puts the two targets exactly C^2 = 3 apart, and the factor is therefore the content of the result rather than a discrepancy in it. Both numbers are given in every place one of them appears, and the comparison is led by the target the model derives because that is the one the model is committed to - the shortfall against d = l_P follows it and is not withheld anywhere. And the order in which the two arrived is stated rather than left to be reconstructed: d = l_P was the expectation this paper was written with, the measurement refuted it, and the reading that puts the factor at C^2 came afterwards - so C = sqrt3 is post hoc with respect to this measurement, and we label it so. ==> What makes it more than a rescue is that it is not free: C is derived twice without using a, it predicts sqrt2 in two dimensions where a run returns 0.12 sigma, and the test that would break it is registered in the Letter before it is run - a post-hoc reading with an a-priori test attached is a hypothesis, which is what we claim it is. With c = C d/tau and the tick fixed at the Planck time, d/l_P, the shortfall and k_A ~ C^-2 are all functions of C. And C is derived rather than adopted: a monad presents itself as a d x d x d cell of geometry and must connect its most distant points within one tick, so light crosses the diagonal, sqrt3 d = c t_P = l_P. That gives C = sqrt3 = 1.732 against a measured 1.696+/-0.023, agreeing at 1.6 sigma - a purely geometric conversion ratio, one Planck sphere to one Planck cube of geometry. The factor then sits in the ratio rather than the target: T(3)/a phi_J z = C^2 = 3 against 2.9965 measured, and two dimensions predict sqrt2, which a run returns at 0.12 sigma. We give the measurement, the escapes closed, and the one thing not established - convergence.