A parsec-scale cm–to–sub-mm SED study of the compact radio jet components in NGC 1068

We present parsec-scale cm–to–sub-mm spectral energy distributions (SEDs) of the compact radio-jet components NE, C, S2, and S3 in the Seyfert 2 galaxy NGC 1068. Matched-uv e-MERLIN, VLA, and ALMA imaging spans 4.5–706 GHz at a common 0.06-arcsec resolution and 15–3300 kλ uv-coverage. Spatial-blending tests show weak inter-component covariance, less than 1 per cent direct neighbour-induced flux transfer, and a maximum S2 perturbation of 8.4 per cent across the 18.9–22.9-GHz turnover region, corresponding to |Δνcl| ≲ 1.6 GHz or |Δfcov| ≲ 0.06. Bayesian MCMC modelling with synchrotron emission, free–free emission, and free–free absorption yields steep intrinsic synchrotron indices, αsy ≃ −0.9 to −1.7. The cut-off is lowest in C, ν c=420⁺¹⁴⁶₋₁₀₃ GHz. NE and S3 have measured cut-offs of 634⁺²⁴⁴₋₂₂₅ and 598⁺²⁶⁴₋₂₃₁ GHz, respectively, whereas S2 yields only the lower limit νc > 418 GHz. A partial-covering absorber is favoured for all four components (ΔAIC = 6.6–30.1; ΔBIC = 4.3–28.0). NE, C, and S3 have comparable clump-opacity scales, νcl ≃ 11–12 GHz, and covering factors, fcov ≃ 0.43–0.53, with C additionally requiring diffuse absorption. S2 is the clear exception, with ν cl=26.0+1.8-2.1 GHz and fcov=0.83+0.05-0.07; its opacity scale differs from those of the other components by approximately 4.8–5.6σ. The results support a sightline-dependent ionised medium in which S2 intersects the densest and most strongly covering absorber, plausibly near the torus–inner-NLR interface. No off-nuclear component requires a significant mm–sub-mm excess above the synchrotron model.