We analyze a discrete substrate model consisting of 6-port unitary scattering nodes on a simple cubic lattice at the site-percolation threshold pc = 0. 3116. Within this framework, two independently constructed geometric strands, coupled through the lattice function nc (R) (mean outward-bond count per surface node at sphere radius R), define a self-consistency condition with a unique solution near the inverse fine-structure constant ^-1. Strand A is a structured effective ansatz for a dimensionless substrate impedance scale, ^-1 = 266. 22/nc (R) ; Strand B is a soliton-equilibrium condition, R = 40. 63\, a/ (6 - nc (R) ), obtained from the model's energy balance. Their intersection at R^* = 10. 019\, a gives a base value 136. 89 (-0. 11\, \% from ^-1 = 137. 036). A small, closure-conditional refinement - including weak next-nearest-neighbor (NNN) secondary couplings already implicit in the local unitary update - then improves the internal consistency: within the adopted closure scheme it induces a multiplicative correction 1 + 3/2800, fixed by lattice topology and the six-port algebra with no continuous fit parameter (the ingredients are detailed in the text). This brings the value to 137. 037, a residual of +0. 0005\, \%. The construction contains no continuous fit parameter and no calibration to ; the only empirical numerical input is pc. The principal result is the existence of a unique fixed point near ^-1 on a constrained discrete choice space, not the third-decimal agreement: the +0. 0005\, \% residual lies well below the framework's own control of nc (R^*) (an uncertainty nc = 0. 001 already shifts ^-1 by 0. 05\, \%), so it is reported as an internal consistency result, not a precision prediction. Sensitivity checks confirm the output stays in the same neighborhood under variations of lattice type, mixing rule, and sphere center, the baseline giving the closest agreement; all assumptions are stated explicitly. This manuscript was drafted and uploaded here in June 2026 as Version 2. 0 of the preprint.
Oliver Marc Wittwer (Sun,) studied this question.