The Scanning Mass String and Occupied-Channel Closure of the Aether Fabric: Time-Integrated Exposure, Species Chirality, and the Rank-Six Compatibility Gate

This paper derives the occupied-channel mechanism that converts the twelve-component free phtn representation of the Aether fabric into the six-component locked representation required for material compatibility. It extends the relational, dynamical, contact, and compatibility-bifurcation papers by distinguishing three structures that must not be conflated: the occupied Ligamen Circulatus species geometry, the transported phtn temporal fiber, and antipodal six-port parity. The electron mass-string content is $$\mathcal{S}_e=m_e\lambda_C,$$ Its scanning and transport relations form the exact QMU chain $$\mathrm{angm}=\mathcal{S}_e c,$$ $$\mathrm{phtn}=\mathrm{angm},c=\mathcal{S}_e{\lambda_C}^2{F_q}^2,$$ and $$\mathrm{ligt}_L=\mathrm{phtn},f_L.$$ The first factor of $c=\lambda_C F_q$ describes the internal scan of the one-dimensional mass string through one quantum moment. The second factor describes transfer of the completed scan presentation between neighboring Aether Units. A two-parameter scanning worldsheet with string support length $\lambda_C$ and complete temporal-transfer path length $\lambda_C$ presents the physical quantum area $$A_{\mathrm{scan}}={\lambda_C}^2,$$ while the instantaneous mass geometry remains one-dimensional. An expanding cardioid phtn front containing $n^2$ participating Aether Units is represented as one globally normalized state rather than $n^2$ duplicated photons. Uniform local amplitudes scale as $1/n$, so that $$\sum_{k=1}^{n^2}|a_{n,k}|^2=1.$$ This separates transport participation from material occupation. An Aether Unit traversed by phtn is dynamically engaged for a quantum interval but remains materially unoccupied unless a Ligamen Circulatus capture occurs. The unloaded Stage 11D chronogeometry contains a visible outer $2\pi$ scan followed by a newly generated hidden inward $2\pi$ return, producing a complete $4\pi$ temporal history. Sampling this history at six equal intervals produces phase advances of $$\Delta\Phi=\frac{4\pi}{6}=\frac{2\pi}{3}.$$ Antipodal pairing reduces the six-register shift to the real representation $$1\oplus R_2\left(\frac{2\pi}{3}\right).$$ The $2\pi/3$ temporal-registration rotation of the locked operator is therefore obtained from the established $4\pi$ chronogeometry rather than from a fitted transition parameter. The authoritative occupied electron, proton, positron, and antiproton paths determine the species chirality law $$s_{\mathrm{lox}}=q_E\eta_L,$$ where $q_E=\pm1$ denotes electrostatic-sphere polarity and $\eta_L=\pm1$ denotes temporal-torque handedness. The four species satisfy $$s_e=s_{e^+}=-1,$$ and $$s_p=s_{\bar p}=+1.$$ Charge conjugation reverses both sphere polarity and temporal torque and therefore preserves loxodromic chirality. Reversing either factor alone reverses the chirality sign. The electron and proton reciprocal radii satisfy $$r_x=\frac{\lambda_C\alpha_x}{2\pi},$$ $$R_x=\frac{\lambda_C}{2\pi\alpha_x},$$ and $$4\pi^2r_xR_x={\lambda_C}^2.$$ Using $$\frac{m_p}{m_e}=6\pi^5$$ and $$\alpha_p=\frac{\alpha_e}{6\pi^5},$$ the occupied ledger gives $$\frac{R_p}{R_e}=\frac{r_e}{r_p}=\frac{m_p}{m_e}=6\pi^5,$$ $$q_p-q_e=\ln(6\pi^5),$$ $$m_pr_p=m_er_e,$$ and $$\frac{R_p}{m_p}=\frac{R_e}{m_e}.$$ These relations preserve the common quantum area while scaling the electron and proton reciprocal geometries in exact proportion to their mass ratio. Binary occupation of one Ligamen channel reduces the available temporal state count but does not by itself generate the complete locked port-temporal operator. The required composition law is chirality matching between transported phtn and the occupied receiver seat: $$b\eta_\gamma=q_E\eta_L,$$ where $b=\pm1$ is antipodal port parity and $\eta_\gamma=\pm1$ is the transported temporal-handed component. The corresponding spectral projector is $$P_{q_E\eta_L}=\frac{1}{2}\left[I_{12}+(q_E\eta_L)B\otimes\sigma_{3,\gamma}\right].$$ This projector is Hermitian, idempotent, and rank six. It selects the compatible six-dimensional graph subspace from the twelve-dimensional free representation while leaving the complementary six modes inaccessible to the occupied state. The normalized capture compatibility is $$\mathcal{C}_s=\langle\Psi,P_s\Psi\rangle,$$ and the occupied mismatch work is $$E_{\mathrm{gap},s}=mc^2\left(1-\mathcal{C}_s\right).$$ The scale $mc^2=m{\lambda_C}^2{F_q}^2$ is localized material enrg associated with the occupied receiver boundary. It is not enrg transported as a phtn pellet. Combining the rank-six spectral gate with the inherited tangential registration action gives the species-oriented locked coin $$V_s=P_S+P_0+E_TR_2\left(s\frac{2\pi}{3}\right)E_T^\dagger,$$ where $$s=q_E\eta_L.$$ The complete locked transport operator is $$U_{\mathrm{locked},s}=V_sD^{-1},$$ which recovers the established locked propagation branch $$v_{\mathrm{locked}}=\frac{c}{\sqrt{3}}.$$ The preceding compatibility-bifurcation paper proved that smooth reciprocal strain, packing participation, positive inertia, damping, and additional smooth profile modes cannot change the representation rank. The present paper respects that no-go result. The free-to-locked conversion is not a smooth interpolation of propagation rate; it is a composition-dependent spectral selection followed by constrained six-port transport. The sole composition axiom is the microscopic seat law $$b\eta_\gamma=q_E\eta_L.$$ Once this law is imposed, the species projector, rank-six reduction, mismatch work, and locked-operator compression follow exactly. The remaining open problem is the microscopic receiver kinetics that enforce chirality matching and determine the absolute capture interval. The cumulative Stage 29–40 derivation package validates the mass-string factorization, normalized expanding-front transport, six-register quotient, species chirality ledger, reciprocal electron–proton invariants, rank-six projector algebra, and locked-operator recovery.