arXiv:2611.14689v1 Announce Type: new Abstract: We prove that freeness is determined by the intersection lattice for arrangements of seventeen lines in the complex projective plane. The proof reduces a possible counterexample to smaller arrangements whose realisation spaces can be computed. A minimal logarithmic derivation defines a foliation; its inflection divisor and a local singularity count imply that the non-free member of a counterexample is nearly free with exponents $(7,10)$. Deleting four lines then produces a thirteen-line arrangement whose second Chern class is controlled by a combinatorial deficit. When the deficit is four, the remaining arrangement is free with exponents $(6,6)$. An exact covering argument places the necessary thirteen-line cores in four finite classes, containing $3{,}829{,}691$ lattices. We compute their realisation spaces and reconstruct all relevant seventeen-line extensions, including specialisations of positive-dimensional families. Among the candidate lattices, exactly sixteen admit a non-free realisation; they are rigid and have no free realisation. Together with the known cases, this establishes Terao's conjecture for central arrangements of at most seventeen planes in $\mathbb{C}^3$.
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