Causal Memory Gravity XI develops the directed bi-orthogonal continuum limit of the Dynamic Planck Network and studies how chirality can emerge from asymmetric causal transfer. The paper examines non-Hermitian but controlled network dynamics in which left and right modes are treated through a bi-orthogonal structure rather than through a standard symmetric spectral decomposition. In this setting, infrared pseudo-unitarity provides an effective long-wavelength consistency condition, while directed memory flow can generate chiral sector separation under clearly stated assumptions. The document also clarifies the status of the result: emergent chirality is derived within a controlled directed-network construction, but a universal classification over all possible DPN graph families remains open. It serves as the main CMG paper connecting directed Planck-network dynamics, continuum limits, chirality, and infrared consistency of the matter-sector extension. For the full CMG corpus, theory map, and related materials, visit: https://cmg.beogradpc.com