Complex Chiral Rapidity, Hidden Memory, and Causal Gravitational-Wave Parity Transport

This preprint develops a causal framework for gravitational-wave parity transport in which circular polarization is treated as the projection of a larger helicity-coherency and response structure. It establishes exact criteria for when reduced helicity dynamics are local or acquire projection-induced memory, identifies the minimal auxiliary-state cost required to recover locality, and derives a state–operation Lorentz-cone structure governing passive helicity transport. Within a closed isotropic sector, the paper introduces chiral rapidity as the natural additive coordinate for helicity asymmetry and extends it to a complex causal transfer variable combining amplitude and phase parity. This leads to exact minimum-opacity and parity–intensity bounds, a causal dispersion relation for helicity transfer, and a no-go result showing that a real helicity-odd Berry-like quadratic term is phase-only unless accompanied by a retarded absorptive sector. The microscopic analysis constructs the leading finite-density parity-odd transverse-traceless response of an anomaly-free two-left-Weyl contact effective field theory at O(ℏ)O(\\hbar), including the complete Born O(G2)O(G^2) collision family, curved-space Wigner source and stress, CTP self-energy corrections, collision-gradient contributions, and the gravitational contact term. A contact-gauge equivalence is established between Wigner and explicit-seagull representations, and the resulting response is Ward complete within the stated leading-hard-loop/Born-collision TT scope. The paper also discusses the connection to open gravitational dynamics, quantum-noise constraints, anomaly-induced parity transport, and conditional cosmological, detector, and CMB stress tests, while explicitly separating these downstream applications from the proved microscopic response.