"""Reproduce the exact normal-component mechanism JC.3–JC.14.""" from pathlib import Path SVG='\n Actual center transfer preserves the normal hypertrace component\n The finite common basis with first vector one dominates each conjugated smaller-center positive element by a normal positive larger-center transfer. This proves that the maximal centrally normal subfunctional remains compatible and M-central. Its nonzero normalization annihilates the exact canonical cost. The remaining purely singular component satisfies an exact bounded functional balance, with no inherited-trace density asserted.\n \n A normal part survives actual M-conjugation\n A = <N,e> inside B = <M,e>; e = e_R^M. Actual represented centers and common basis.\n \n The operator domination uses a_1 = 1. (JC.3)\n x in Z(A), x >= 0: x <= I(x) = sum a_i x a_i* in Z(B); I(1) = d 1.\n u x u* <= I(x) for every physical u in U(M). I is a normal finite-sum map.\n No normalization of A or its center by M is assumed.\n \n \n \n Take the maximal subfunctional phi_n normal on Z(A). (JC.4)-(JC.6)\n phi_n E_A = phi_n; E_A maps Z(B) normally into Z(A), so phi_n is normal on Z(B).\n phi_n(u x u*) <= phi_n(I(x)) proves normality of the conjugated Z(A) restriction.\n Maximality: phi_n Ad(u) <= phi_n. Equal mass m gives equality: phi_n is M-central.\n Normal-band z lives in the bidual bookkeeping; it is not the physical tail atom f.\n \n \n \n \n \n m > 0 supplies an annihilating state.\n phi_n / m is compatible and M-central.\n 83.5 gives phi_n(b_hat) = 0. (JC.7)\n Corner witness: m >= phi(e) > 0. (JC.9)\n \n Residual singular component\n phi_s remains compatible and M-central.\n Both represented-center restrictions are singular.\n Nonzero m is not supplied by amenability here.\n \n Exact tail atom and the unclosed singular balance, d > 4\n p = (1-sqrt(1-4/d))/2; q = 1-p; k_F = (q/p) f + (p/q)(1-f); tau(f) = p.\n w = E_D0(k_F); ell = E_D0(E_C(k_F)); gamma_s(w t) = alpha_s(ell t). (JC.13)\n b = d^2 sqrt(1-4/d) E_Z(S)(|E_D0(f-E_C(f))|); need nu_s(b) = 0. (JC.14)\n A bounded ratio ell/w compares singular states; it does not produce an L1 trace density.\n Proof-mechanism schematic. All formulas are exact; rectangles encode no trace areas. Full original BF/partition/generation remain assigned.\n' Path(__file__).with_suffix(".svg").write_text(SVG,encoding="utf-8")