The Chirality-Matched Receiver of the Aether Fabric: Invariant Boundary Action, One-Moment Spectral Selection, and the Triadic Capture Matrix

This paper derives the receiver-boundary mechanism that selects the six-dimensional material-compatible sector of the twelve-dimensional free phtn representation. It extends the occupied-channel construction by replacing the previously stated chirality-matching seat law with the minimum-work condition of an invariant binary boundary action. The transported scan chirality is $$s_\gamma=b\eta_\gamma,$$ where $b=\pm1$ is antipodal port parity and $\eta_\gamma=\pm1$ is the transported temporal-handed component. The occupied Ligamen chirality is $$s_L=q_E\eta_L,$$ where $q_E=\pm1$ denotes electrostatic-sphere polarity and $\eta_L=\pm1$ denotes the temporal-torque handedness of the occupied Ligamen Circulatus. The only relative binary scalar is $$\chi=s_\gamma s_L\in{-1,+1}.$$ Requiring the receiver work to depend only on relative chirality, remain invariant under simultaneous sign reversal, vanish for complete agreement, and attain the occupied material scale $mc^2$ for complete disagreement uniquely gives $$E_{\mathrm{seat}}(\chi)=\frac{mc^2}{2}(1-\chi).$$ The minimum-work condition is therefore $$s_\gamma=s_L,$$ or equivalently, $$b\eta_\gamma=q_E\eta_L.$$ Thus the chirality-matching seat law is recovered as the zero-mismatch condition of the lowest-order unbiased occupied boundary work rather than introduced as an independent fitted rule. For a fixed occupied sign $s=q_E\eta_L$, define $$K=B\otimes\sigma_{3,\gamma},$$ $$P_s=\frac{1}{2}(I_{12}+sK),$$ and $$Q_s=\frac{1}{2}(I_{12}-sK).$$ The occupied receiver-boundary operator is $$E_{\mathrm{seat},s}=mc^2Q_s.$$ The projectors $P_s$ and $Q_s$ are Hermitian, idempotent, mutually orthogonal, and each has rank six. The compatible sector selected by $P_s$ has zero mismatch work. The rejected sector selected by $Q_s$ carries the complete occupied mismatch scale $mc^2$. The free twelve-dimensional representation is therefore not continuously deformed into the locked representation. Instead, the receiver boundary spectrally selects one six-dimensional compatibility sector while separating its six-dimensional complement. The species angm scale is $$\mathrm{angm}_m=m{\lambda_C}^2{F_q}.$$ Since $$mc^2=m{\lambda_C}^2{F_q}^2=\mathrm{angm}_mF_q,$$ the receiver-boundary operator may be written $$E_{\mathrm{seat},s}=\mathrm{angm}_mF_qQ_s.$$ Over one quantum moment, $$t_q=F_q^{-1},$$ the accumulated mismatch action is $$\mathcal A_{\mathrm{seat},s}=t_qE_{\mathrm{seat},s}=\mathrm{angm}_mQ_s.$$ A compatible component accumulates no mismatch action, while a rejected component accumulates exactly one species angm during the primitive interval. The associated mismatch freq operator is $$\mathrm{freq}_{\mathrm{seat},s}=F_qQ_s,$$ with spectrum $$\operatorname{spec}(\mathrm{freq}_{\mathrm{seat},s})={0,F_q},$$ where each value has multiplicity six. The corresponding squared scale is ${F_q}^2=\mathrm{rson}$, although no second-order restoring equation is assumed. Frequency and resonance remain distinct QMU quantities. The complete $4\pi$ Stage 11D chronogeometry produces three antipodally paired temporal-registration classes. For transported and occupied classes $q_\gamma,q_L\in\mathbb Z_3$, define $$\Delta_q=\frac{2\pi}{3}(q_\gamma-q_L).$$ The normalized three-register coherence kernel is $$\mathcal H_3(\Delta)=\left|\frac{1+e^{i\Delta}+e^{i2\Delta}}{3}\right|^2,$$ or equivalently, $$\mathcal H_3(\Delta)=\frac{(1+2\cos\Delta)^2}{9}.$$ At the allowed registration differences, $$\mathcal H_3(0)=1,$$ and $$\mathcal H_3\left(\pm\frac{2\pi}{3}\right)=0.$$ The nine ordered source–receiver registration combinations therefore divide exactly into $$9=3_{\mathrm{matched}}+6_{\mathrm{mismatched}}.$$ The resulting ideal registration matrix is the $3\times3$ identity matrix. The three diagonal source–seat combinations are admitted, while all six off-diagonal combinations are rejected. The complete ideal receiver gate factors into three logically independent conditions: $$\mathcal G_{s,q}=a_{\mathrm{seat}}\mathcal C_s(\Psi)\mathcal H_3(\Delta_q),$$ where $a_{\mathrm{seat}}\in{0,1}$ records receiver-seat availability, $$\mathcal C_s(\Psi)=\langle\Psi,P_s\Psi\rangle$$ measures chirality compatibility, and $\mathcal H_3(\Delta_q)$ measures temporal-registration compatibility. This factorization distinguishes seat availability, chirality match, and registration match. None can be substituted for another, and no continuous rank-changing interpolation parameter is introduced. The derivation also separates the primitive compatibility decision from the subsequent material response. Spectral selection has the natural quantum-moment action scale, whereas observable receiver filling remains controlled by compatible ligt throughput. The normalized fill interval is $$T_{\mathrm{fill}}^*=\frac{cE_{\mathrm{thr}}}{\mathrm{ligt}_L\,\mathcal{G}_{s,q}}.$$ Defining $$\Theta_{\mathrm{seat}}=\frac{E_{\mathrm{thr}}}{m_ec^2}$$ and using $$\mathrm{ligt}_L=\mathrm{phtn},f_L,$$ gives $$T_{\mathrm{fill}}^*=\frac{\Theta_{\mathrm{seat}}}{\mathcal G_{s,q}}\frac{F_q}{f_L}.$$ The physical fill time is $$T_{\mathrm{fill}}=\frac{\Theta_{\mathrm{seat}}}{f_L\mathcal G_{s,q}}.$$ The accumulated fill phase is $$\Delta\phi_{\mathrm{fill}}=\frac{2\pi\Theta_{\mathrm{seat}}}{\mathcal G_{s,q}}.$$ The receiver may therefore make a primitive topological compatibility distinction on the $t_q$ action scale while requiring a much longer ligt-controlled interval to produce an observable material response. Earlier photoelectric and coherence-window constructions are revised through this exact gate. Their seat-availability, threshold, and throughput relations remain valid after spectral admission. Previously unspecified geometry factors are replaced by the coefficient-free chirality and triadic-registration gate. Receiver-specific coherence-window quantities remain phenomenological descriptors of post-selection material evolution rather than the source of the rank-six projector. The paper supplies experimentally testable diagnostics: a binary mismatch spectrum, an exact three-accepted and six-rejected registration matrix, predictable changes under single-factor chirality reversal, invariance under simultaneous charge-conjugation reversal, and a factorized latency dependence on ligt and receiver compatibility. The Stage 41–46 derivation and validation package verifies the boundary-action uniqueness, projector algebra, one-moment action scale, triadic capture matrix, gate factorization, and receiver-latency relations. The remaining open problem is the receiver-specific material evolution that begins after the transported scan has passed the exact spectral gate.