A quantum system can have many states close to its lowest energy. A spectral gap asks whether there is a definite energy step between the ground-state space and the first excitation. The difficult question is whether that step can stay positive as the system grows. This research candidate addresses a particular model of spin-two particles arranged on the kagome lattice, a pattern of corner-sharing triangles. Its proposed lower bound is just over zero point zero zero five, in the paper’s chosen energy units. It is a conservative guarantee, not a prediction of the exact excitation energy. The proof does not try to diagonalise an enormous lattice. It studies overlapping local blocks, groups two before comparing them with a third, and uses symmetry to reduce the required calculations. Fifty-four positive-definiteness tests then support a written argument that carries the local bounds to every allowed system size. The computer first constructs exact rational inputs. Approximate matrix factors are only suggestions: a checker bounds every entry of their errors before accepting the result. The largest matrix has eleven thousand five hundred and twenty-four rows. The stated volumes matter. The claim covers rectangular periodic lattices with both periods at least three, and a specified family of open patches. It is not a theorem for arbitrary boundaries, and it does not establish stability under perturbations. The open package includes the proof, code, receipts and deliberately failing tests. Fresh replay passed, but the work remains an unrefereed candidate, with explicit software and arithmetic assumptions. This is Evidence Press, the spin-two kagome AKLT gap, dated the thirtieth of September twenty twenty-six. The paper and evidence are linked on the release page. This synthetic AI voice is explanatory, not additional scientific evidence.