## Abstract (Crystalline / IRIS-Locked Electrodynamics) We present a Maxwell-compatible electrodynamic completion of the IRIS / crystalline bank-phase framework in which a compact, branch-quantized Z\(_{24}\) phase \(\vartheta\) couples to electromagnetism only through a gauge-invariant axion-like operator,\[\mathcal{L}\supset -\frac{\kappa}{4}\,\vartheta\,F_{\mu\nu}\tilde F^{\mu\nu}.\]The design principle is structural: we do **not** replace Maxwell’s theory. Instead, we preserve the Bianchi identity \(\dd F=0\) and gauge invariance exactly, while allowing \(\vartheta\) to appear only through derivatives. The resulting modified Maxwell equation takes the canonical “constitutive completion” form\[\partial_\mu F^{\mu\nu}=J^\nu-\kappa(\partial_\mu\vartheta)\tilde F^{\mu\nu},\qquad\partial_\mu\tilde F^{\mu\nu}=0,\]so constant \(\vartheta\) is invisible to vacuum electrodynamics and observable effects arise solely from \(\dd\vartheta\). Crystallinity enters through discrete Z\(_{24}\) branches,\[\vartheta_k=\frac{k\pi}{12},\qquad k=0,\dots,23,\]so any branch difference is quantized:\[\Delta\vartheta=\Delta k\,\frac{\pi}{12},\qquad \Delta k\in[-12,11]\ \text{(wrapped)}.\]We certify the resulting physics with two *independent* probe geometries that isolate the two derivative channels of the completion: 1) **Road A (Space / IRIS step interface).** A spatial jump \(\Delta\vartheta\) across a planar interface generates a boundary-localized Hall-like response. At normal incidence we derive a closed-form scattering matrix with reflectance and transmittance \[ R=\frac{\lambda^2}{1+\lambda^2},\quad T=\frac{1}{1+\lambda^2},\quad R+T=1, \] and a transmitted polarization rotation described by \[ \alpha_{\rm A,obs}=\arctan(\lambda),\qquad \lambda=\frac{\kappa}{2}\Delta\vartheta=\frac{\kappa\pi}{24}\Delta k. \] The Road A lockpack verifies energy conservation at machine precision (max \(|R+T-1|=2.22\times10^{-16}\)) and exact agreement with analytic identities (max rotation error \(4.89\times10^{-15}\) deg for \(\kappa=0.1\)). Table EM-A reports the quantized rotation and the corresponding \(R,T\) values. 2) **Road B (Time / homogeneous quench).** A time-dependent \(\vartheta(t)\) produces birefringence: helicity modes acquire dispersion \[ \omega_\pm^2(t)=k^2\mp \kappa k\,\dot\vartheta(t), \] and the relative helicity phase rotates linear polarization. In the adiabatic regime the rotation converges to the endpoint law \[ \alpha_{\rm B,obs}\to \alpha_{\rm pred}=\frac{\kappa}{2}\Delta\vartheta=\frac{\kappa\pi}{24}\Delta k. \] Stability is enforced by requiring \(\omega_\pm^2(t)>0\) across the quench. At fixed adiabatic timescale \(\tau=5\) with \((\kappa,k)=(0.1,1)\), a full wrapped \(\Delta k\)-scan achieves **PASS fraction = 1.0**, with max \(|\alpha_{\rm obs}-\alpha_{\rm pred}|=5.65\times10^{-4}\) deg, max relative error \(6.28\times10^{-5}\), and max ellipticity \(2.54\times10^{-5}\) deg (Table EM-B1). **Convention alignment statement.** To ensure sign consistency between the boundary (Road A) and quench (Road B) solvers, we adopt the Road B Stokes-angle definition as the global observable convention. We therefore report the Road A interface rotation as \(\alpha_{\rm A,obs}\equiv-\alpha_t\), where \(\alpha_t\) is the raw transmitted Jones angle extracted from the scattering matrix. With this convention, Road A and Road B rotations agree in sign for identical \(\Delta k\). **The integer-comb.** Because \(\Delta\vartheta=(\Delta k)\pi/12\), the predicted adiabatic rotation is discrete:\[\alpha_{\rm pred}^{(\deg)} = 7.5\,\kappa\,\Delta k.\]For \(\kappa=0.1\) this yields a step size of \(0.75^\circ\) per unit \(\Delta k\), producing an “integer comb” of allowed polarization rotations. This converts an otherwise continuous birefringence signal into a topology-tagged target suitable for matched-filter searches and systematics rejection: the observable is not merely “a small rotation”, but a discrete, branch-labeled pattern. Moreover, the two-road structure provides mechanism discrimination: Road A exhibits mild geometric nonlinearity (\(\arctan\) clipping) characteristic of a hard interface, while Road B exhibits linear adiabatic transport in the bulk. In summary, we provide a self-consistent, reproducible electrodynamic completion that preserves Maxwell’s core structure while making the Z\(_{24}\) crystalline branch data operationally measurable through a quantized polarization signature validated in two independent geometries.