Length Bridge Definition
The EOTU lattice is expressed internally using the primitive lattice quantum \(L_0\). Radial quantities within the theory are therefore represented as integer or fractional counts of \(L_0\). Version 3.46 defines one King coherence interval as one sixty-fourth of that native unit:
Consequently a native distance of \(N_{L_0}\) lattice units contains \(64N_{L_0}\) King coherence intervals. Its measured-distance projection is \(r_{\mathrm{SI}}=N_{L_0}(1L_0)=64N_{L_0}\lambda_k\).
Measured Length Bridge
The measured proton radius is used to assign an SI scale to native geometry. The proton triad radius \(a_z=467.6952L_0\) is a native count, so the SI length of one \(L_0\) is the proton radius divided by that count:
This is an SI bridge value, not a separate derivation. The coherence interval follows from it as \(\lambda_k=L_0/64\), with no \(\sqrt{3}\) and no further factor. The bridge value used throughout the framework is \(1\,L_0=0.001797965855\,\mathrm{fm}\), which corresponds to \(r_p=a_z(1\,L_0)\approx0.8409\,\mathrm{fm}\).
Derived Coherence Length
The currently published measured bridge gives the King coherence interval:
This is one sixty-fourth of the measured SI length assigned to \(L_0\). Both SI quantities therefore inherit the proton-scale calibration; neither is an independent prediction.
Native \(L_0\) Conversion
The primitive lattice quantum \(L_0\) is the native radial counting unit used throughout CPP, Region, shell, bonding, and curvature geometry. The corresponding SI conversion is:
These conversions allow native EOTU distances to be compared with measured nuclear, atomic, and molecular scales without changing the underlying lattice construction.
Use Across the Framework
The measured \(L_0\) bridge appears wherever native lattice distances are projected into measured units, while \(\lambda_k=L_0/64\) describes a single coherence interval. They support radius comparisons, shell radii, bonding lengths, corridor spacings, curvature coefficients, and time-step conversion.
The recurrence framework remains native to \(L_0\). The SI bridge enters only when the derived lattice value is expressed in meters, femtometers, angstroms, or other measured comparison units.
Summary
The King coherence length is \(\lambda_k=2.809321648\times10^{-20}\,\mathrm{m}=L_0/64\). Native \(L_0\) counts must therefore be multiplied by \(64\lambda_k\), not \(\lambda_k\), for the stated SI conversion.
The associated conversion is \(1\,L_0=0.001797965855\,\mathrm{fm}\), \(1\,\mathrm{fm}=556.1837316\,L_0\), and \(1\,\text{\AA}=55{,}618{,}373.16\,L_0\). These values allow the native EOTU geometry to be compared against nuclear, atomic, bonding, and curvature scales.