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We synthesized a two-dimensional (2D) crystalline covalent organic framework (sp2c-COF) that was designed to be fully π-conjugated and constructed from all sp2 carbons by C=C condensation reactions of tetrakis(4-formylphenyl)pyrene and 1,4-phenylenediacetonitrile. The C=C linkages topologically connect pyrene knots at regular intervals into a 2D lattice with π conjugations extended along both x and y directions and develop an eclipsed layer framework rather than the more conventionally obtained disordered structures. The sp2c-COF is a semiconductor with a discrete band gap of 1.9 electron volts and can be chemically oxidized to enhance conductivity by 12 orders of magnitude. The generated radicals are confined on the pyrene knots, enabling the formation of a paramagnetic carbon structure with high spin density. The sp2 carbon framework induces ferromagnetic phase transition to develop spin-spin coherence and align spins unidirectionally across the material.