§2.3 — Update Time

The update time \(\tau_0\) defines the post Freeze-Out propagation interval for one coherence-length step through the lattice.

Update-Time Definition

The post Freeze-Out update time \(\tau_0\) is the duration associated with one propagation step across the King coherence length. It links the native spatial lattice scale to the measured propagation rate used for comparison.

\[ \tau_0 = \frac{\lambda_k}{c} \]

In this expression, \(\lambda_k\) is the King coherence length and \(c\) is the measured propagation bridge used for SI comparison.

Substitution

Using the coherence length from §2.1:

\[ \lambda_k = 2.809321648\times10^{-20}\,\mathrm{m} \] \[ c = 2.99792458\times10^{8}\,\mathrm{m\,s^{-1}} \]

The update interval is:

\[ \tau_0 = \frac{2.809321648\times10^{-20}} {2.99792458\times10^{8}} = 9.370217606\times10^{-29}\,\mathrm{s} \]

This value defines the measured-time projection of one post Freeze-Out lattice update.

Native Propagation Coefficient

The corresponding native light-propagation coefficient expresses propagation in \(L_0\) units per second:

\[ c_{L_0} \approx 1.667800087\times10^{26}\,L_0\,\mathrm{s^{-1}} \]

This coefficient is used when distances remain in the native lattice ledger rather than being projected directly into meters.

Corridor Hop Count

Photon transport through Dormant Corridors advances by discrete update steps. For an elapsed measured duration \(t\), the number of corridor hops is:

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

The corresponding native horizon extent in \(L_0\) units is:

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

This relation keeps propagation expressed in native lattice distance while allowing measured time to be used as the comparison parameter.

Role in Transport

The update time provides the timing bridge for post Freeze-Out transport. Photon packets, phase-transfer events, horizon comparisons, and curvature-response propagation all require a consistent relation between lattice distance and elapsed measured time.

\[ \lambda_k \rightarrow \tau_0 \rightarrow N_{\mathrm{hop}} \rightarrow D_{L_0}(t) \]

Cross-epoch horizon comparisons require the recurrence-scale relation between Constellus snapshots. The local update time supplies the propagation step; Constellus supplies the comparison between different recurrence-scale frames.

Summary

The post Freeze-Out update time is \(\tau_0=9.370217606\times10^{-29}\,\mathrm{s}\), obtained from \(\tau_0=\lambda_k/c\).

The corresponding native propagation coefficient is \(c_{L_0}\approx1.667800087\times10^{26}\,L_0\,\mathrm{s^{-1}}\). These values define the local timing and distance bridge for transport through Dormant Corridors.