HII-CHI-mistry for active galactic nuclei: optical sulphur abundances without empirical ionisation correction factors

The determination of sulphur abundances in active galactic nuclei (AGN) is uncertain because ionisation correction factors (ICFs) are commonly calibrated for HII regions. We extend the HII-CHI-mistry methodology to derive total S/H in AGN from optical emission lines through comparison with photoionisation models. Tests against Seyfert galaxies with direct-method ionic abundances favour models with alpha_ox=-1.2 and a 98% free-electron stopping criterion. While O/H agrees with previous determinations, HCm yields systematically larger S/H than direct-method analyses using classical ICFs, suggesting that these prescriptions underestimate higher sulphur ionisation stages in AGN. Applied to MaNGA Seyfert and LINER-like regions, the method reveals a common positive S/O-metallicity relation. Seyferts show slightly larger median S/O than star-forming regions at high O/H, while LINERs occupy an intermediate position. These differences become weaker when S/H rather than O/H is used as the metallicity tracer, although Seyferts still tend to populate the upper envelope. Sulphur may therefore provide a robust tracer of gas-phase metallicity, while the differences between Seyferts and LINERs may reflect differences in their ionisation conditions and ionising SEDs.