Appendix A — Closed-Region Inventories

Closed-Region inventory ratios expressed relative to the smallest closure-equivalent unit.

Inventory Reference Scale

Closed-Region inventory ratios are expressed relative to the smallest closed compound-Region inventory unit. The electron Region defines the reference inventory scale.

\[ \mu_e \equiv 1 \]

Proton and neutron inventories are then expressed as ratios against this smallest closure-equivalent reference.

Electron Region Inventory

For the electron, the geometric mass factor is derived from the EZZZ closure geometry:

\[ m_f^{EZZZ} = 408\sqrt{3}+8 = 714.6767295 \]

With the SI energy bridge \(\Gamma = 1~\mathrm{eV}\), the corresponding electron energy is:

\[ E_e \equiv E_{EZZZ} = \Gamma \left( m_f^{EZZZ} \right)^2 = \left( 408\sqrt{3}+8 \right)^2 ~\mathrm{eV} \]
\[ E_e \approx 510{,}762.7855~\mathrm{eV} = 0.5107627855~\mathrm{MeV} \]

Proton Region Inventory

For the proton, the geometric mass factor is formed from the UUD mass term and the internal coherence completion term.

\[ m_p = m_p^{UUD} + m_{Z\Delta} + \Delta m_{\mathrm{int}} \]
\[ m_p^{UUD} = \sqrt{ \frac{\pi}{3} } \left( 51 \cdot 9 \right)L_0 = 30{,}061.2454 \]
\[ \Delta m_{\mathrm{int}} = 256g_{UUD} = 256(2.22474488) = 569.5347 \]
\[ m_p = 30{,}061.2454 + 0 + 569.5347 = 30{,}630.7801 \]

The projected proton energy is:

\[ E_p = \Gamma \left( 30{,}630.7801 \right)^2 \approx 938.2446895~\mathrm{MeV} \]

Neutron Region Inventory

For the neutron, the geometric mass factor is treated as a closed proton coupled to a non-terminal Emeon-family closure with an additional internal closure burden.

\[ m_n \equiv m_p + m_{n,\mathrm{int}} \]
\[ m_n = 30{,}650.3113 + 20.8 = 30{,}671.1113 \]
\[ E_n = \Gamma \left( 30{,}671.1113 \right)^2 = 940.7170684~\mathrm{MeV} \]

The Emeon-family component remains structurally present, but it is not counted as an added external mass-factor term. The additional contribution is the residual internal closure burden required to maintain the proton-coupled non-terminal state.

Closed-Region Inventory Units

Using the EOTU-derived energy values, each closed Region can be expressed as an inventory quantity using the native light-propagation coefficient.

\[ E_e = 510{,}762.7855~\mathrm{eV} \]
\[ E_p = 938.2446895~\mathrm{MeV} \]
\[ E_n = 940.7170684~\mathrm{MeV} \]
\[ u_x = \frac{E_x}{c_{L_0}^{\,2}}, \qquad c_{L_0} = 1.667800087 \times 10^{26}~L_0/s \]
\[ u_e = \frac{510{,}762.7855}{c_{L_0}^{\,2}} \approx 1.83625 \times 10^{-47} ~\mathrm{eV\,s^2} \]
\[ u_p = \frac{938{,}244{,}689.5}{c_{L_0}^{\,2}} \approx 3.37309 \times 10^{-44} ~\mathrm{eV\,s^2} \]
\[ u_n = \frac{940{,}717{,}068.4}{c_{L_0}^{\,2}} \approx 3.38198 \times 10^{-44} ~\mathrm{eV\,s^2} \]

EOTU-Derived Inventory Ratios

Using the electron closed-Region inventory as the dimensionless reference scale, the EOTU-derived inventory ratios are:

\[ \mu_e = 1 \]
\[ \mu_p = \frac{938.2446895}{0.5107627855} \approx 1836.9480 \]
\[ \mu_n = \frac{940.7170684}{0.5107627855} \approx 1841.7886 \]
\[ \mu_e = 1, \qquad \mu_p \approx 1836.9480, \qquad \mu_n \approx 1841.7886 \]

Measured Comparison Ratios

For measured comparison, the CODATA/NIST mass-energy values are expressed using the same electron-normalized inventory structure.

\[ m_ec^2 = 0.51099895069~\mathrm{MeV} \]
\[ m_pc^2 = 938.27208943~\mathrm{MeV} \]
\[ m_nc^2 = 939.56542194~\mathrm{MeV} \]

Using the electron mass-energy as the dimensionless comparison scale:

\[ \mu_e = 1, \qquad \mu_p = \frac{m_pc^2}{m_ec^2}, \qquad \mu_n = \frac{m_nc^2}{m_ec^2} \]
\[ \mu_p = \frac{938.27208943}{0.51099895069} \approx 1836.1527 \]
\[ \mu_n = \frac{939.56542194}{0.51099895069} \approx 1838.6837 \]
\[ \mu_e = 1, \qquad \mu_p \approx 1836.15, \qquad \mu_n \approx 1838.68 \]

Inventory Ratio Summary

Region EOTU-Derived Ratio Measured Comparison Ratio Role
Electron \(\mu_e = 1\) \(\mu_e = 1\) Smallest closure-equivalent reference unit.
Proton \(\mu_p \approx 1836.9480\) \(\mu_p \approx 1836.15\) Compact baryonic Region inventory.
Neutron \(\mu_n \approx 1841.7886\) \(\mu_n \approx 1838.68\) Proton-coupled non-terminal Emeon-family composite inventory.