Histone demethylase that specifically demethylates 'Lys-4' of histone H3, thereby playing a central role in histone code (PubMed:28262558). Does not demethylate histone H3 'Lys-9', H3 'Lys-27', H3 'Lys-36', H3 'Lys-79' or H4 'Lys-20'. Demethylates trimethylated and dimethylated but not monomethylated H3 'Lys-4'. Participates in transcriptional repression of neuronal genes by recruiting histone deacetylases and REST at neuron-restrictive silencer elements. Represses the CLOCK-ARNTL/BMAL1 heterodimer-mediated transcriptional activation of the core clock component PER2 (By similarity). 3 2-oxoglutarate + N(6),N(6),N(6)-trimethyl-L-lysyl(4)-[histone H3] + 3 O2 = 3 CO2 + 3 formaldehyde + L-lysyl(4)-[histone H3] + 3 succinate Binds 1 Fe(2+) ion per subunit. The inhibitor KDOAM-25 and others inhibit its demethylase activity, resulting to cell cycle arrest in myeloma cells. kcat is 1.92 min(-1) and 2.71 min(-1) for 2-oxoglutarate and histone H3K4me3, respectively. Part of two distinct complexes, one containing E2F6, and the other containing REST. Expressed in all tissues examined. Highest levels found in brain and skeletal muscle. The first PHD-type zinc finger domain recognizes and binds H3-K9Me3. Both the JmjC domain and the JmjN domain are required for enzymatic activity. The disease is caused by variants affecting the gene represented in this entry. Escapes X-inactivation. Belongs to the JARID1 histone demethylase family.