Diagonal reduction for generalized doubly nonnegative matrix powers

A generalized doubly nonnegative matrix is entrywise nonnegative and diagonalizable over the reals with nonnegative eigenvalues. We prove that any strictly negative entry of a conventional power at time s > 0 can be transferred to a negative diagonal entry in one higher dimension at time s + 2. Thus the full-entry and diagonal critical exponents satisfy CE_n + 2 ≤ DCE_(n+1) ≤ CE_(n+1) for n ≥ 3. The sharp upper-bound question in every dimension is equivalent to its diagonal-only version, and excess above the benchmark 2n − 4 persists under dimension increase. A one-state feedback construction and spectral residues give the transfer, including repeated semisimple eigenvalues and singular starting matrices. An explicit three-state seed gives an independent proof of the known lower bound. Rational witnesses approach 2n − 4 using a fixed oriented three-cycle and a bidirectional pendant path. No universal upper-bound improvement is claimed. The principal results retain candidate-theorem status. Complete proofs, editable sources, exact illustrative certificates and reproduction instructions accompany the article.