A Covariant Relational Tension Quanta–to–Infrared Bridge for Meta-Connective Physics: Emergent Metric/Tetrad Sector, Gauge Connections, Chiral Anomaly Closure, and Effective QFT Matching

Meta-Connective Physics (MCP) starts from a pre-metric relational substrate made of Relational Tension Quanta (RTQ), carrying a constrained complex tension variable
\(\Lambda=\Lambda^P+i\Lambda^I=\Lambda_0 e^{i\Theta}\). This paper makes explicit the conditional bridge by which an ordered RTQ regime can support the standard infrared language of metric gravity, tetrads, gauge connections, chiral matter records, and effective field theory.

The bridge is developed as a controlled continuum readout. In a stable long-wavelength regime, RTQ propagation defines a principal symbol; when this symbol is non-degenerate, hyperbolic, and branch ordered, it admits a Lorentzian metric interpretation and a tetrad factorization. Internal RTQ holonomies provide the corresponding gauge-connection slots, while MCP winding records reconstruct a chiral, anomaly-free one-generation electroweak pattern under the stated branch locks. The resulting Einstein-frame layer is treated conservatively as an effective QFT/EFT interface: standard propagators, gauge fixing, BRST identities, running, and threshold matching are kept distinct from the pre-metric substrate.

The scope is deliberately restricted to metricization, tetrad readout, gauge/chiral interfacing, and projector-level branch closure. The angular tension split defines two pre-metric projectors,
\(\Pi_P=\cos^2\Theta\) and \(\Pi_I=\sin^2\Theta\). In the branch-resolved principal symbol, the visible sheet weights the temporal and spatial sectors by \((\Pi_P,\Pi_I)\), while the cross-sheet continuation exchanges these weights. Consequently, the dimensional pivot \(c_0\) cancels in the exact ratio
\[
\frac{|c_-^{\rm cross}|}{c_+}
=
\frac{\Pi_P}{\Pi_I}
=
\cot^2\Theta
=
q_\Theta .
\]
Electroweak-torsion, \((\hbar G)\), and large-root transition-branch closures are recorded separately in the supplementary note \emph{MCP Remarkable Closures v3} and are not used as assumptions in the present bridge construction.