The paper, 11 pages · dated September 28, 2026
Approximate Antiunitary Symmetry as a Matching Problem
In brief: For commuting Hermitian matrices H_1, ..., H_d with joint eigenvalue vectors lambda_1, ..., lambda_n counted with multiplicity, and any penalty weight tau >= 0, the least value over unitary U of the sum of ||H_r U - U conj(H_r)||_F^2 plus tau ||U conj(U) + I||_F^2 equals the least, over all matchings M of {1, ..., n}, of 2 times the sum over matched pairs of ||lambda_i - lambda_j||^2 plus 4 tau (n - 2|M|): the least combined error in antiunitary commutation and in the relation T^2 = -I is an exact matching value, attained by signed swaps on the matched pairs. The single-observable case and the parity facts are classical; the paper claims the reduction for commuting tuples of two or more observables.
Its text was revised through October 2, 2026. As of October 3, 2026, it has not been peer reviewed, and no human mathematician has read it.
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