A Explicit evaluation of the mixed \(JT^{0j}\) Kubo correlator This appendix provides the detailed one-loop derivation of the mixed \(J^iT^{0j}\) correlator used in Sect. 3. The fermionic sector and DoS factor are those defined in Sect. 2. App. A.1 decomposes the Belinfante momentum density vertex, App. A.2 isolates the parity-odd rotational structure, and App. A.3 performs the Matsubara sums, vacuum subtraction, analytic continuation, and static long-wavelength limit.