M10 additional primary-source comparison,21October2026 local time.
1303.4701v2 proves the conventional-power critical exponent n-2 for doubly
nonnegative matrices. Its known negative-entry mechanism is explicitly
credited in our path construction; we do not claim that matrix theorem as new.
The research step here is realizing a negative off-diagonal derivative by
one classical state and its actual partial trace, followed by a rigorous
reflected-entropy gap.

2302.10208v2 supplies the earlier alpha<2 counterexamples.2307.12247 Section2.4
proves Lifshitz-field violations only for0<n<4/3 in its displayed family;
the derivative is positive for n>=4/3 there. Neither supplies the finite
nonintegeralpha>2 counterexample checked here.

A newly located August2026 source2608.28897v1 proves a real-exponent scalar
monotonicity in AppendixD, but its Lemma1 is explicitly TWO-BY-TWO. In that
dimension every increasing scalar power has an off-diagonal divided difference
with the required sign. Our alpha5/2 reflected matrices are4-by-4, so this
lemma neither contradicts nor covers our construction. Its main topic is
entanglement-of-purification additivity, distinct from subsystem monotonicity.
Do not cite a secondary summary as claiming positivity in arbitrary dimension.

2502.18433v1 treats the infinity limit and cites finite monotonicity for
integer orders. Targeted current primary-source searches have not found a
covering result. This is bounded source comparison, not a proof of global
novelty or a publication acceptance prediction. No external report was sent.
