§2.4 — SI Energy Bridge

Intrinsic Energy Measure

The EOTU recurrence equations are written in intrinsic variables. These variables are native to the lattice and do not require SI dimensions until a measured comparison is made.

Let \(m_f\) denote the EOTU mass factor derived from geometry and coherence rules. The intrinsic energy measure is written as a squared closure quantity:

\[ E_{\mathrm{intrinsic}} \equiv \left(m_f\right)^2 \]

This quantity is dimensionless inside the native framework. It receives measured energy units only when projected through the energy bridge.

Bridge Definition

The bridge constant \(\Gamma\) assigns SI energy units to the intrinsic closure measure. It does not alter the native derivation. It only defines how the intrinsic result is displayed in measured energy units.

\[ E_{\mathrm{SI}} \equiv \Gamma E_{\mathrm{intrinsic}} \] \[ E_{\mathrm{SI}} = \Gamma\left(m_f\right)^2 \]

In this form, the geometry determines \(m_f\), the recurrence framework determines the intrinsic closure measure, and \(\Gamma\) supplies the measured energy projection.

Electron-Volt Projection

The electron-volt is adopted as the energy projection unit. Its SI definition is exact:

\[ 1\,\mathrm{eV} \equiv 1.602176634\times10^{-19}\,\mathrm{J} \]

Accordingly, the bridge is set to one electron-volt:

\[ \Gamma \equiv 1\,\mathrm{eV} \]

This means intrinsic squared closure values may be read directly as electron-volts when the eV projection is selected.

Projected Energy Forms

With \(\Gamma=1\,\mathrm{eV}\), the measured energy expressions become:

\[ E(\mathrm{eV}) = \left(m_f\right)^2 \] \[ E(\mathrm{MeV}) = 10^{-6}\left(m_f\right)^2 \] \[ E(\mathrm{GeV}) = 10^{-9}\left(m_f\right)^2 \]

Decimal scaling changes only the displayed unit. The intrinsic closure measure remains the same.

Photon Energy Projection

The same bridge applies to resolved curvature-packet transport. A photon begins as an emitted curvature-transfer value \(\Delta\mu\). Its measured energy is the projected value of that native transport quantity.

\[ E_{\gamma} = \Gamma\left(\Delta\mu\right)^2 \]

This preserves the distinction between native curvature transport and measured energy. The photon is the resolved transport packet; the eV value is the bridge projection assigned to the emitted \(\Delta\mu\).

Local Projection Boundary

The energy bridge applies within a single formation-coordinate mapping. Comparisons between unlike formation-coordinate mappings require the recurrence-scale relation carried by Constellus and the redshift framework.

\[ E_{\mathrm{SI}} = \Gamma E_{\mathrm{intrinsic}} \]

\(\Gamma\) projects the local ledger-event energy. Cross-epoch comparison applies the recurrence-scale mapping between Constellus snapshots.

Summary

The SI energy bridge \(\Gamma\) projects intrinsic EOTU closure measures into measured energy units. The native energy measure is \(E_{\mathrm{intrinsic}}=(m_f)^2\), and the projected energy is \(E_{\mathrm{SI}}=\Gamma(m_f)^2\).

With \(\Gamma\equiv1\,\mathrm{eV}\), intrinsic squared closure values are expressed directly in electron-volts, with MeV and GeV obtained by decimal scaling. Photon energy follows the same projection rule through \(E_{\gamma}=\Gamma(\Delta\mu)^2\).