# Output of: python3 attack11.py (run 2026-09-25, numpy 2.0.2 / scipy 1.13.1, macOS, BLAS threads capped at 1, on a machine shared with other jobs) ====================================================================================================================== ATTACK 11 REPRODUCTION -- 2x3 strip, live shared boundary. Baseline beta J=.6, g=.3, nu=1, kappa=.8, J=1 ====================================================================================================================== <++|tau_D^+|++> 0.9830849616 pkg 0.9830849620 diff -4.04e-10 ~ 9.4 digits [1] Model / channel sanity checks frozen 2-spin cell: K nnz = 0 (h_D = Z_other + 3 is never 0), max|L_R1 - L_R2| = 0.0e+00 R1: nnz(L)= 18816 K nnz=112 |[K,H0]|=0e+00 |Tr L(.)|=2e-16 |L(pi)|=1e-16 Choi: herm 2e-19, TP 1e-15, min eig 6.02e-04, finite True (4.9s) R2: nnz(L)= 20992 K nnz=112 |[K,H0]|=0e+00 |Tr L(.)|=2e-16 |L(pi)|=1e-16 Choi: herm 2e-18, TP 2e-15, min eig 6.03e-04, finite True (4.6s) [2] Headline coefficients vs package (digits = -log10 |rel. diff|) --- thermal jumps R1 (fully resolved rank-one flips |sigma^i> R1 T=2: Schur 0.672906551980 | 1/lmax(P J^-1 P) 0.672906551980 | bisection 0.672906551980 | product 0.672906551980 (r-prod +2e-16) | weight of min-eigvec on I(x)|++> 1.000000000000 R1 T=4: Schur 0.912705995891 | 1/lmax(P J^-1 P) 0.912705995891 | bisection 0.912705995891 | product 0.912705995891 (r-prod +1e-16) | weight of min-eigvec on I(x)|++> 1.000000000000 R1 T=6: Schur 0.966108522465 | 1/lmax(P J^-1 P) 0.966108522465 | bisection 0.966108522465 | product 0.966108522465 (r-prod -6e-16) | weight of min-eigvec on I(x)|++> 1.000000000000 R1 T=8: Schur 0.977956300995 | 1/lmax(P J^-1 P) 0.977956300995 | bisection 0.977956300995 | product 0.977956300995 (r-prod +4e-16) | weight of min-eigvec on I(x)|++> 1.000000000000 R2 T=2: Schur 0.673252827106 | 1/lmax(P J^-1 P) 0.673252827106 | bisection 0.673252827106 | product 0.673252827106 (r-prod +0e+00) | weight of min-eigvec on I(x)|++> 1.000000000000 R2 T=4: Schur 0.913042686403 | 1/lmax(P J^-1 P) 0.913042686403 | bisection 0.913042686403 | product 0.913042686403 (r-prod +1e-16) | weight of min-eigvec on I(x)|++> 1.000000000000 R2 T=6: Schur 0.966256916235 | 1/lmax(P J^-1 P) 0.966256916235 | bisection 0.966256916235 | product 0.966256916235 (r-prod +0e+00) | weight of min-eigvec on I(x)|++> 1.000000000000 R2 T=8: Schur 0.978006474307 | 1/lmax(P J^-1 P) 0.978006474307 | bisection 0.978006474307 | product 0.978006474307 (r-prod +1e-16) | weight of min-eigvec on I(x)|++> 1.000000000000 [4] Independent propagation route at T=4: Schroedinger picture, 256 input matrix units R1: max|J_schr - J_heis| = 1.2e-15 p_live(schr) - p_live(heis) = -7.8e-16 (68.5s) R2: max|J_schr - J_heis| = 1.7e-15 p_live(schr) - p_live(heis) = -4.4e-16 (82.5s) (dense Pade expm cross-check available with --dense) [5] Classical deep-upstream diagnostics (u = basis state of U0,U2; U1=U3=+ at entrance) R1 T=4: min_u p(Phi_u -> tau) = 0.9284100882 vs complete p_live 0.9284100882 (diff -1.1e-16) max pairwise ||J(Phi_u - Phi_u')||_1 bracket [0.021269, 0.085075] package [0.02127, 0.08507] max_u P(interface != ++ at time T): D init ++: 0.03766 D init tau_D^+: 0.03812 worst D basis: 0.09528 package 0.03812 R1 T=8: min_u p(Phi_u -> tau) = 0.9947830953 vs complete p_live 0.9947830953 (diff +6.7e-16) max pairwise ||J(Phi_u - Phi_u')||_1 bracket [0.001988, 0.007951] package [0.001988, 0.007951] max_u P(interface != ++ at time T): D init ++: 0.02142 D init tau_D^+: 0.02145 worst D basis: 0.02507 package 0.02145 R2 T=4: min_u p(Phi_u -> tau) = 0.9287525718 vs complete p_live 0.9287525718 (diff +4.4e-16) max pairwise ||J(Phi_u - Phi_u')||_1 bracket [0.020031, 0.080122] package [0.02127, 0.08507] max_u P(interface != ++ at time T): D init ++: 0.03766 D init tau_D^+: 0.03812 worst D basis: 0.09549 package 0.03812 R2 T=8: min_u p(Phi_u -> tau) = 0.9948341319 vs complete p_live 0.9948341319 (diff -1.0e-15) max pairwise ||J(Phi_u - Phi_u')||_1 bracket [0.001959, 0.007837] package [0.001988, 0.007951] max_u P(interface != ++ at time T): D init ++: 0.02142 D init tau_D^+: 0.02144 worst D basis: 0.02500 package 0.02145 [6] Exterior-defect stress tests, T=4 (target tau_D^+ unchanged, entrance U1=U3=+) Interpretation: one flipped frozen exterior neighbour lowers that spin's e_i by 2. 'far' = one exterior neighbour of U0 (left column); 'interface-adjacent' = the exterior neighbour of U1; 'both interface' = exterior neighbours of U1 and U3; 'far+interface both rows' = one flip at each of U0, U1, U2, U3. (Top/bottom mirror symmetry makes the U0-vs-U2 choice immaterial.) all plus exterior e=(2, 1, 2, 1, 2, 2) R1 0.9284101 ( 7.9d) R2 0.9287526 ( 3.4d) pkg 0.9284101 one far upstream exterior defect e=(0, 1, 2, 1, 2, 2) R1 0.9219624 ( 7.9d) R2 0.9223378 ( 3.4d) pkg 0.9219624 one interface-adjacent exterior defect e=(2, -1, 2, 1, 2, 2) R1 0.8959041 ( 7.5d) R2 0.8966578 ( 3.1d) pkg 0.8959041 both interface external neighbours flipped e=(2, -1, 2, -1, 2, 2) R1 0.8495878 ( 7.3d) R2 0.8508240 ( 2.8d) pkg 0.8495878 far+interface defects on both rows e=(0, -1, 0, -1, 2, 2) R1 0.8143947 ( 7.7d) R2 0.8152872 ( 3.0d) pkg 0.8143947 mirror check, far defect on bottom row (e=(2,1,0,1,2,2)), R1: 0.9219624 [7] Parameter spot checks at T=4 (nu=1; tau_D^+ recomputed at each beta) betaJ=0.4 g=0.3 kappa=0.8 | R1 p=0.8912585886 (10.3d) r=0.8178528933 (10.8d) | R2 p=0.8915774650 ( 3.4d) r=0.8181455064 ( 3.4d) | package p=0.8912585886 r=0.8178528933 betaJ=0.6 g=0.3 kappa=0.8 | R1 p=0.9284100882 (10.9d) r=0.9127059959 (11.0d) | R2 p=0.9287525718 ( 3.4d) r=0.9130426864 ( 3.4d) | package p=0.9284100882 r=0.9127059959 betaJ=1.0 g=1.0 kappa=0.8 | R1 p=0.9516407118 (10.7d) r=0.9509968209 (11.1d) | R2 p=0.9528191560 ( 2.9d) r=0.9521744677 ( 2.9d) | package p=0.9516407118 r=0.9509968209 [8] Convention sensitivity, baseline, T=4 (all rows R1 thermal jumps unless labelled R2) p_live T=4 R1 baseline 0.9284100882 pkg 0.9284100882 diff -1.29e-11 ~10.9 digits p_live T=4 R2 baseline 0.9287525718 pkg 0.9284100882 diff +3.42e-04 ~ 3.4 digits p_live T=4 monitoring coherence decay 2*kappa (L=sqrt(kappa) Z) 0.9283198998 pkg 0.9284100882 diff -9.02e-05 ~ 4.0 digits p_live T=4 monitoring coherence decay kappa/2 0.9284732580 pkg 0.9284100882 diff +6.32e-05 ~ 4.2 digits p_live T=4 rates with flipped field sign (anti-detailed-balance) 0.0050983274 pkg 0.9284100882 diff -9.23e-01 ~ 0.0 digits p_live T=4 no tie Hamiltonian, g=0 0.9280040510 pkg 0.9284100882 diff -4.06e-04 ~ 3.4 digits [9] Verdict R1: 12 ten-digit package values (p_live x4, r_clean x2, spot p/r x6): worst agreement ~10.3 sig. digits, max |diff| 4.5e-11; stress tests (7-digit values): worst ~7.3 digits R2: 12 ten-digit package values (p_live x4, r_clean x2, spot p/r x6): worst agreement ~2.9 sig. digits, max |diff| 1.2e-03; stress tests (7-digit values): worst ~2.8 digits p_frozen (T=4,8; convention-independent): ~10.5 sig. digits total wall time 230.0s