Conformal-Depth Routes to the Electron Mass in Meta-Connective Physics

In the Standard Model, the electron mass is encoded in a Yukawa coupling and is not predicted from first principles.  In Meta-Connective Physics (MCP), the microscopic substrate is modeled as a network of Relational Tension Quanta (RTQ).  The electron is modeled as an acyclic RTQ influence spine carrying a closed internal massive-Dirac holonomy, embedded in a three-dimensional coherent causal carrier.  This paper reframes the electron-mass problem as a metrology problem for the conformal causal depth of the Universe.  Once a conformal causal depth $T$ and a structural angle are supplied, the RTQ/MCP electron readout is fixed:
\[
 m_e^{\rm pred}c^2(T,\Theta_{\rm struct})=
 \Gamma_{e,24}
 \frac{\hbar c}{8\pi\sqrt{8\pi}\,\ell_P\cos\Theta_{\rm struct}}
 \left(\frac{t_P}{T}\right)^{1/3} .
\]
The question is therefore not whether one can tune a lepton mass formula, but which independently auditable route supplies the physically relevant conformal causal depth $T_{\rm conf}^{\rm lock}$.

Three routes are studied.  Route I is a Planck-2024/PR4 NPIPE cosmological-parameter route: $(H_0,\Omega_\Lambda,\Omega_c h^2,h^2)$ fixes $\Lambda_{\rm PR4}^{\rm lock}$, $T_{\rm PR4}^{\rm lock}$, and reconstructs the historical/conformal value $\Theta_{\rm struct}=0.3589887297$, giving $m_e c^2=0.511058662~\mathrm{MeV}$, a relative deviation $1.17\times10^{-4}$ from CODATA.  Route II is the internal MCP structural-susceptibility route: the zero-mode coordinate $X$ supplies a sharper conformal depth $T_{\rm conf}^{\rm lock}\simeq14.19~\mathrm{Gyr}$, giving $m_e c^2=0.511044~\mathrm{MeV}$, a central-value deviation $8.76\times10^{-5}$.  Route III is an external conformal-gravity concordance route: Faria's massive conformal-gravity fit to Pantheon SNIa reports $t_0=14.19\pm0.03~\mathrm{Gyr}$, which is read here not as a proof of MCP but as an external conformal-depth scale compatible with the same RTQ/MCP electron readout.

The result is not a Koide-type charged-lepton relation, nor a fitted Yukawa texture.  It is a three-route conditional cross-sector audit: Planck-2024/PR4 NPIPE cosmological parameters, MCP structural susceptibility, and an independent conformal-gravity cosmology all feed the same causal-depth readout of the electron. The agreement is a central-value structural closure, not yet a full uncertainty-propagated metrological prediction.