TransportPath

The module derives the CKM CP phase $\delta_{\mathrm{CKM}}$ from Berry phases of generation eigenstates transported around the directed eight-tick Gray-code cycle. The fundamental period is one octave of eight ticks ($\tau_0=1$ in RS-native units), forced by the T7 step of the unified forcing chain.

The cycle permutation cyclePerm advances a vertex along the Gray order: if $v$ is visited at tick $t$, the next vertex is the one at tick $t+1$. Explicitly it acts as $0\mapsto 1$, $1\mapsto 3$, $2\mapsto 6$, $3\mapsto 2$, $4\mapsto 0$, $5\mapsto 4$, $6\mapsto 7$, $7\mapsto 5$. A transport path is the discrete trajectory of a state under successive applications of that permutation.

Berry phase for generation $g$ is the sum of overlap arguments $\gamma_{\mathrm{Berry}}(g)=\sum_{t=0}^{7}\arg\langle\psi_g(t)|\psi_g(t+1)\rangle$ along such a path. The CP phase is a signed combination of the three generation Berry phases; chirality of the Gray code and directed traversal make it nonzero, while $\theta_{\mathrm{QCD}}$ is driven to zero by $J$-cost minimization.

Pure definitional abbreviation: the type of transport paths is identified with functions $\mathrm{Fin},8\to\mathrm{Fin},8$. No proof obligations, tactics, or lemmas.

This type is the carrier for all discrete cycle transport in the CP-phase derivation. Downstream, canonicalPath builds the standard path starting at vertex $v$ by iterating the cycle permutation: at tick $k$ the state sits at $\mathrm{cyclePerm}^k(v)$. That path feeds closed-loop lemmas, per-flip and per-cycle Berry phases, generation-dependent phases, and ultimately the nonzero raw CP phase.

In the Recognition framework it sits on the eight-tick octave (T7) and the chiral Gray-code geometry that distinguishes topological $\delta_{\mathrm{CKM}}$ from energetic $\theta_{\mathrm{QCD}}$. Without a uniform path type, the discrete Berry sum and the generation comparison cannot be stated cleanly.