"""Reproduce the exact85.17–85.26 finite partition diagram.""" from pathlib import Path SVG='\n Finite central partition extraction: repair all cells and select one for every target\n A schematic of Theorem 85.7, not a numerical core realization. An actual finite projection is cut by represented smaller-center projections. The exact pinching identity measures its added commutator cost. A common matrix deletion multiplies traces by n squared. Feasible trimming gives integer dimensions on each positive cell. The total trace-weighted bound chooses one cell for all ambient unitary targets. The simultaneous small pinching estimate remains an input.\n \n Repair every central cell, then select one cell for all targets\n Actual core S in R; A = <N,e> in B = <M,e>. Physical center Z(S) and its represented lift are distinct.\n \n 1. Finite projection and a scalar step from below\n zeta = C_A(p), c = Tr(p) > 0; h = sum_i theta_i z_i <= zeta\n t = tau(h) > 0; rho = (c - t)/t\n Finite central partition z_0 + z_1 + ... + z_r = 1; p_i = p z-hat_i. (85.18)\n \n z_0\n \n z_1\n ...\n \n z_r\n Zero cell includes discarded tails.\n \n \n \n 2. Exact pinching identity, before selecting a cell\n sum_i ||[p_i,u_j]||_2^2 = ||[p,u_j]||_2^2 + 2 sum_(i != l) ||p_i u_j p_l||_2^2\n The off-diagonal blocks are orthogonal in L2. This is (85.17), for each j.\n Lambda = sum_j sum_(i != l) ||p_i u_j p_l||_2^2; mu = 2 Lambda/c\n Sum all targets first: sum_(i,j) ||[p_i,u_j]||_2^2 = c (delta^2 + mu). (85.19)\n \n \n \n 3. Actual common M_n deletion and feasible integer trimming\n Old traces and squared L2 norms multiply by n^2. Centers are preserved. (52.3)\n k_i = floor(n^2 theta_i) >= k_0; q_i <= p_i; C_(A-tilde)(q_i) = k_i z_i; q_0 = 0\n T_n = sum_(i >= 1) k_i tau(z_i); s = tau(sum_(i >= 1) z_i); b = s/(n^2 t) < 1\n Total trim cost = n^2 c - T_n <= n^2 rho t + s\n T_n >= (1 - b)n^2 t > 0. Prescription and cost: (85.20), (85.22).\n \n \n \n 4. One nonzero q_i works for every u_1, ..., u_m\n max_j ||[q_i,u_j]||_(2,new) / sqrt(Tr_new(q_i)) <= Gamma\n Gamma = sqrt((1 + rho)/(1 - b)) sqrt(delta^2 + mu)\n + 2 sqrt(m(rho + b)/(1 - b)). Trace-weighted selection: (85.21), (85.23).\n q_i splits into k_i pieces equivalent to the new Jones corner e_new z-hat_i. (52.4)\n Automatic: finite scalar approximation, (85.25)-(85.26). Missing: simultaneous small actual Lambda and profile loss.\n\n' Path(__file__).with_suffix(".svg").write_text(SVG,encoding="utf-8")