Gersten's conjecture for integral K-theory of arbitrary regular local rings (Quillen's form), in ramified mixed characteristic

Theorem 1.1 (degree five): with $V$ the integers of the unramified degree-eight extension of $\mathbb Q_5$ and $A=(V[x,y]/(5+x^4+y^4))_{(5,x,y)}$, $A$ is a two-dimensional regular local domain and $\ker(K_5(A)\to K_5(\mathrm{Frac}\,A))\ne0$; the class also gives generic noninjectivity with $\mathbb Z/5$ coefficients. Companion Theorem 1.1 (degree three): the local ring of a cyclotomic quintic model over $\mathbb Z_5[\zeta_5]$ at a special point has a nonzero class in $\ker(K_3(A)\to K_3(\mathrm{Frac}\,A))$ not divisible by 5. Not shown: the order of these classes, whether they survive rationally (the rational Gersten conjecture is untouched), anything about unramified or smooth-over-DVR rings, or the least degree of failure.

S. Mochizuki, Local Gersten's conjecture for regular system of parameters (arXiv:1503.07966v8, 2020), abstract: 'we show local Gersten's conjecture for regular system of parameters. As its consequence we obtain Gersten's conjecture for a commutative regular local ring and smooth over a commutative discrete valuation ring.' The release's degree-five paper says: 'Mochizuki's Theorem 5 in version 8 ... asserts that, for a commutative Noetherian local ring B and a nonzerodivisor g, the inclusion from finitely generated projective B/gB-modules to finitely generated B-modules of projective dimension at most one induces zero on K-theory. This statement reaches the exact support in the present paper', so it 'would annihilate' the class constructed. The release gives a counterexample to Lemma 13(III) used in that proof, and says this 'by itself does not refute its theorem statement'. Mochizuki's headline corollary (rings smooth over a DVR) does not cover the ring used here. Theorem 1.1 (degree five): with $V$ the integers of the unramified degree-eight extension of $\mathbb Q_5$ and $A=(V[x,y]/(5+x^4+y^4))_{(5,x,y)}$, $A$ is a two-dimensional regular local domain and $\ker(K_5(A)\to K_5(\mathrm{Frac}\,A))\ne0$; the class also gives generic noninjectivity with $\mathbb Z/5$ coefficients. Companion Theorem 1.1 (degree three): the local ring of a cyclotomic quintic model over $\mathbb Z_5[\zeta_5]$ at a special point has a nonzero class in $\ker(K_3(A)\to K_3(\mathrm{Frac}\,A))$ not divisible by 5. Not shown: the order of these classes, whether they survive rationally (the rational Gersten conjecture is untouched), anything about unramified or smooth-over-DVR rings, or the least degree of failure.