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Study resolves negative eigenvalue in Lo-Shu Yang-Mills framework, highlighting isotropy implications.
We resolve the negative eigenvalue obstruction in the Lo-Shu Yang-Mills framework (Paper v7, DOI: 10.5281/zenodo.19910348). L_sym has eigenvalues {-sqrt(3), +sqrt(3), 15}; the negative value arises from negative Cartan coefficients (lambda_3, lambda_8). Taking the operator absolute value |L_sym| yields eigenvalues {sqrt(3), sqrt(3), 15}, which is positive semi-definite. Key new result: |L_sym| restricted to the excited subspace {u2, u3} equals exactly sqrt(3)*I2 (scalar matrix), implying complete isotropy — a discrete analogue of gauge invariance. We prove |L_sym| >= C_min * P_h^2 with C_min = 8.119, verified by 100,000 Monte Carlo directions with zero violations. The remaining gap is the bridge operator Phi: Lo-Shu R^3 -> H_YM Hilbert space, with a candidate intertwining relation H_YM * Phi = Phi * |L_sym|.
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Yao-Kai Kao (2026) studied this question.
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