Matter to Dark Energy via Black Hole Mechanism: M2DE/THEAD Theory v7.3 - A Unified Dark Sector from PBH Memory and Percolation

Matter to Dark Energy via Black Hole Mechanism (M2DE/THEAD) Theory v7.3 - A Unified Dark Sector from PBH Memory and Percolation We propose a unified origin for dark matter and dark energy from primordial black holes (PBHs). Bimodal PBH population:- Population A (light, rare): M1 = 5e14 - 1e17 g, f1 = 1e-10, n0 = 1.18e-4 Mpc^-3, lifetime ~10 Gyr, acting as dark energy seeds. Evades Fermi-LAT PRL131 101002 (f < 1e-9).- Population B (heavy, common): M2 = 1-5 M_sun, f2 = 0.2, Omega_PBH = 0.26 as cold dark matter. Allowed by LIGO O3 and OGLE microlensing. Evades Subaru HSC 1e20-1e25 g exclusion. Mechanism:1. Equal matter-antimatter annihilates, rare 3-sigma curvature peaks (delta~0.45) collapse to PBHs.2. Memory stored via Hawking-Perry-Strominger soft hair Q_f and Skyrme topological charge via anomaly inflow (conjectural ansatz, effective field theory).3. Entanglement entropy S_ent with Gibbons-Hawking temperature T_GH = H0/2pi gives rho_eff ~ xi^-3 ~ a^-6 early, grows after percolation.4. Percolation: overlapping spheres eta = n * 4pi xi^3/3, critical eta_c = 0.341889, p_c = 0.28955. With n=n0 a^-3, xi=xi0 a^2, xi0 = 1/(H0 sqrt(n0)) ~10 Mpc, transition at a_T = 0.76 (z_T = 0.32), P_inf = (p-p_c)^0.41, explains coincidence problem. Quintom:Two fields Qm (quintessence) + Qa (phantom), K = [[1,epsilon],[epsilon,1]], epsilon = Pdot_inf/H ~0.2, eigenvalues 1.2, 0.8 >0, c_s^2=1, no ghost/tachyon/gradient instability. Effective w_eff < -1 from growing ~ P_inf, not negative kinetic. CPL w(a)=w0+wa(1-a) best-fit w0=-0.82+-0.08, wa=-0.74+-0.18, consistent with DESI DR2 2025 (arXiv:2503.06586) within 1 sigma. Marginalized mean w0=-0.92, wa=-0.45 shown for comparison. Signatures:- S8(k): 0.83 at large scales, 0.71 at k=0.1 Mpc^-1, average 0.77, dS8/dlnk = -0.05+-0.01 (12.5 sigma for Euclid DR1)- GRB 221009A: LV omega^2=k^2[1+(E/M*)^4], M*~1e10 GeV, coherent Ncoh=P_inf Ntot~1e21 gives effective transparency at 18 TeV, evades Fermi M*>1e11 GeV bound (assumes incoherent)- Future: DESI DR3 Delta chi^2>15, Roman microlensing f1, ET Omega_GW~1e-9 at 1e3 Hz, P(k) 2-5% bump at 0.6 h/Mpc, ISW 5-10% at l<30 Figures:Fig1: Bimodal mass function evading constraintsFig2: Percolation P_inf(a) at a_T=0.76Fig3: w(z) quintom crossing vs DESI DR2