Appendix A — Hop-Count Horizon

Native horizon scale from Dormant-Corridor photon transport.

Dormant-Corridor Hop Rule

Photon transport after Freeze-Out is governed by the Dormant-Corridor hop rule. A photon advances one King-coherence step per update interval.

\[ \tau_0 \]

The number of corridor hops across an elapsed duration \(t\) is:

\[ N_{\mathrm{hop}} = \frac{t}{\tau_0} \]

The hop-count horizon is therefore:

\[ D_{\mathrm{hop}} = N_{\mathrm{hop}} \]

Native \(L_0\) Horizon Scale

Since one hop spans one King-coherence step, the native step length is:

\[ \lambda_k = \frac{1}{64}L_0 \]

The same horizon expressed in \(L_0\) units is:

\[ D_{L_0} = \frac{N_{\mathrm{hop}}}{64} \]

Substituting the hop count gives:

\[ D_{L_0}(t) = \frac{t}{64\tau_0} \]

Native Propagation Coefficient

Using the post Freeze-Out update interval:

\[ \tau_0 = 9.370217606 \times 10^{-29}\,\mathrm{s} \]

the native propagation coefficient is:

\[ c_{L_0} = \frac{1}{64\tau_0} \]
\[ c_{L_0} = 1.667800087 \times 10^{26}\, \frac{L_0}{\mathrm{s}} \]

Thus, the native horizon extent may also be written:

\[ D_{L_0}(t) = c_{L_0}t \]

Interpretation

This appendix defines the native EOTU horizon scale measured by recurrence-cycle photon propagation through Dormant Corridors. It counts transport reach in the lattice itself.

This is not yet the recurrence-scaled comparison horizon. The hop-count horizon records actual transport extent, while the recurrence-scaled horizon compares epochs through Constellus recurrence scaling.

Appendix A Summary

The native transport horizon follows directly from the update interval \(\tau_0\), the King-coherence step, and the fixed Dormant-Corridor photon transport rule.

\[ N_{\mathrm{hop}} = \frac{t}{\tau_0} \]
\[ D_{L_0}(t) = \frac{t}{64\tau_0} = c_{L_0}t \]

This relation gives the native hop-count horizon before any cross-epoch recurrence comparison is applied.