Uniqueness of the Horizon Bit Count and the Calibration-Free Recognition Length

Recognition Physics (RP) stipulates that stable reality is assembled from mutual-observation
"bit diamonds" of edge length λrec arranged on a golden-ratio lattice. Previous work fixed
all fundamental constants once λrec was matched to a single laboratory number, but a fully
parameter-free anchor remained elusive. Here we prove that consistency of flux neutrality,
phase closure, and minimal prime-shell packing on a de-Sitter recognition horizon forces
the total triangle count to be the unique integer Ntot = 10122. That integer, combined
with the dimensionless spacing Xopt = φ/π, yields λrec = 7.23 ×10−36 m with no empirical
input. The result closes the last calibration gap in RP and renders the framework strictly
parameter-free; experimental channels at the fixed length scale are outlined.