§2.2 — Dormant Corridor Mean Amplitude

The dormant corridor mean amplitude \(\bar{A}\) defines the zero-curvature reference state used for curvature departure and transport calculations.

Mean Amplitude Definition

The dormant corridor mean amplitude \(\bar{A}\) is the reference amplitude of the post Freeze-Out dormant fabric. It defines the zero-curvature level against which local amplitude departures are measured.

\[ \Delta A = A-\bar{A} \]

A lattice cell or Region at \(\bar{A}\) contributes no curvature departure. Curvature appears only where a stable Region, transport packet, void, or composite structure departs from this dormant reference level.

Vacuum-Density Mapping

The dormant corridor mean is mapped through the empirical vacuum energy density and the King coherence-cell volume. This provides the measured comparison bridge for the post Freeze-Out background amplitude.

\[ \rho_{\mathrm{vac}} \approx 5.36\times10^{-10}\,\mathrm{J\,m^{-3}} \] \[ \bar{A} \equiv \rho_{\mathrm{vac}}\lambda_k^3 \]

The value \(\rho_{\mathrm{vac}}\) enters as the SI bridge for comparison. The native curvature framework remains expressed through amplitude departure from \(\bar{A}\).

King-Cell Volume

Using the King coherence length from §2.1, the coherence-cell volume is:

\[ \lambda_k = 2.809321648\times10^{-20}\,\mathrm{m} \] \[ \lambda_k^3 = \left(2.809321648\times10^{-20}\right)^3 = 2.217197587\times10^{-59}\,\mathrm{m^3} \]

This volume supplies the SI projection cell used to express the dormant corridor mean amplitude as energy per coherence cell.

Dormant Mean Value

Substituting the vacuum-density bridge and the King-cell volume gives:

\[ \bar{A} = \left(5.36\times10^{-10}\right) \left(2.217197587\times10^{-59}\right) \] \[ \bar{A} = 1.188417907\times10^{-68}\,\mathrm{J\ per\ cell} \]

Converting to electron-volts:

\[ \bar{A} = \frac{1.188417907\times10^{-68}} {1.602176634\times10^{-19}} = 7.417521150\times10^{-50}\,\mathrm{eV\ per\ cell} \]

Expressed in the \(L_0\)-based amplitude ledger:

\[ \bar{A} = 4.747213536\times10^{-48}\,\mathrm{eV}\,L_0 \]

Role in Curvature Accounting

The dormant corridor mean is the baseline from which curvature response is measured. Region curvature, photon transport, compact-body curvature, and large-scale curvature response all depend on departure from this reference.

\[ \bar{A} \rightarrow \Delta A \rightarrow I_{\mu} \rightarrow C(r) \]

This sequence connects the dormant amplitude reference to closed-Region inventory and the distance-sampled curvature response used later in the framework.

Summary

The dormant corridor mean amplitude \(\bar{A}\) defines the zero-curvature reference level of the post Freeze-Out fabric. Curvature is measured as departure from this value through \(\Delta A=A-\bar{A}\).

Using \(\rho_{\mathrm{vac}}\approx5.36\times10^{-10}\,\mathrm{J\,m^{-3}}\) and \(\lambda_k^3=2.217197587\times10^{-59}\,\mathrm{m^3}\), the mapped dormant mean is \(\bar{A}=1.188417907\times10^{-68}\,\mathrm{J}\) per cell, or \(7.417521150\times10^{-50}\,\mathrm{eV}\) per cell.