"""Reproduce the exact compatible-state proof schematic.""" from pathlib import Path SVG='\n One actual compatible state: compact selection and finite quadratic tests\n A compact actual constrained state space has a minimum cost, with an exact dual operator order floor. Joint-center projection reweightings have explicit compatibility, centrality and physical trace errors. Low-cost positive-mass cuts with vanishing relative finite-basis errors yield one actual annihilating cluster state. In the abelian GNS representation the larger expectation changes from P to P_alpha(t)=P(t/theta); its new normalized weight is ell, so normalizing a singular state does not itself prove zero original cost.\n \n Select one actual state while preserving every constraint\n b = d^2 sqrt(1-4/d) Q(|E_D0(f-E_C(f))|); a = b_hat in Z(A). (AS.1)-(AS.5)\n \n The one-state variational goal is exact. (AS.6)-(AS.7)\n m_e = min sigma(a), sigma compatible, M-central, sigma|M = tau, sigma(J_e) = 0.\n m_e = sup {lambda : a + L >= lambda 1 for some L in the actual constraint span}.\n Nonemptiness is known; excluding a positive order floor remains a substantive operator problem.\n \n A bounded joint-center weight has finite preservation tests. (AS.8)-(AS.11)\n psi_h(x) = psi(h x)/psi(h); h in D_+, psi(h) > 0. All D lies in psi\'s centralizer.\n Compatibility: psi((h-E_A(h))^2) = 0. Centrality: psi([h,a_i]*[h,a_i]) = 0 for all i.\n Smaller-center weights pass compatibility; larger-center weights pass centrality.\n A low-cost cut in Z(A) still needs the actual basis commutator tests; marginals do not supply them.\n \n \n \n Approximate quadratic tests suffice for one exact limiting state. (AS.12)-(AS.15)\n q in D is a projection; c = psi(q) > 0; V = psi((q-E_A(q))^2); W_i = psi([q,a_i]*[q,a_i]).\n eta = 2 V/c; uniform M-conjugation error <= delta = 2 sum ||a_i|| sqrt(W_i/c).\n q <= 1_[0,epsilon](a), eta and delta tend to zero: compactness gives sigma(a) = 0.\n For q in Z(A), compatibility and sigma_q|M = tau are exact. No separability is required.\n \n Normalizing the singular state changes the larger expectation. (AS.16)\n theta = ell/w; gamma = theta alpha. Q preserves alpha; original P preserves gamma.\n New GNS only: P_alpha(t) = P(t/theta); Q(ell) = P_alpha(ell) = 1.\n P_alpha(ell t) = P(w t). Original P(ell) = 1 and new P_alpha(w) = 1 are unproved.\n alpha((P-P_alpha)(log theta)) = nu(b_log). Its required zero value remains open.\n General amenability has not yet supplied the low-cost finite-basis selection tests.\n Full common-support BF, exact full partition, alignment and generation remain assigned.\n Schematic operator proof maps, no encoded trace areas. Exact hypotheses and complete proofs: AS.1-AS.16.\n' Path(__file__).with_suffix(".svg").write_bytes(SVG.encode("utf-8"))