Derivation of the Coherence Stress-Energy Tensor from the PDL Axioms: Explicit Form of C_coh, Resolution of OP2 (D35) and OP-spin (PDL Framework, D48 — Version 3, Corrected)

The PDL Einstein field equation G[g_eff] = kappa_PDL(N) C_coh, established in D35,contains a coherence stress-energy tensor C_coh whose derivation from first principleswas left as OP2 of D35. This document derives the explicit tensorial form of C_coh fromaxioms C1–C4, corrects four dimensional errors present in versions 1 and 2, and resolvesOP-spin as a new result. The coherence volume V_C = (4/3)pi [hbar/(m_p c)]^3 is established as an unconditionaltheorem via the proper-time counting chain (D10a) and the three-dimensional topology(D23). The coherence density rho_coh(N) = sigma(N) R_surf m_p / (V_C R_tot) followsdirectly. The mass component C^(mass)mu nu = rho_coh(N) c^2 u_mu u_nu is an unconditionaltheorem, verified numerically to 0.013%. The spin component C^(spin)mu nu is derived by explicit computation over all 8coherent configurations of K_4 and the 4 pulsation states T^k|+>. The results<S^i> = 0 and <S^i S^j> = (1/4) delta^ij are exact theorems from C1–C4, from whichthe Weyssenhoff–Raabe formalism gives C^(spin)mu nu = 0 in the homogeneous groundstate. This resolves OP-spin. The orbital component C^(orb)mu nu = m_p^2 <j_mu j_nu> / rho_coh is derived fromthe Madelung decomposition of the PDL wave function (D32), with the wave functionnormalised as a probability amplitude ([psi] = m-3/2). It vanishes in the groundstate by the London gauge theorem of D49. The leakage component C^(leak)mu nu = -(Lambda_PDL c^4)/(8 pi G_PDL sigma(N)) gmu nuis given in uniform units J/m^3, so that the full PDL Einstein equation is dimensionallyconsistent throughout. The factor eta_L^18 entering Lambda_PDL is an unconditional theorem(D17, D30); the constant C is derived in D51–D53. Version 3 corrects four errors from versions 1 and 2: (C1) Chain 2 for V_C was atautology, not an independent proof; (C2) the v1/v2 formula for C^(spin) wasdimensionally incorrect and its claimed magnitude 1e-12 was unverified; (C3) a factorm_p was missing in the formula for C^(orb); (C4) the formula for C^(leak) had unitsm⁻², rendering the Einstein equation dimensionally inconsistent. All corrections areverified numerically to machine precision. This document supersedes D48v1 (10.5281/zenodo.19969831) and D48v2.