Derivation of the Coherence Stress-Energy Tensor from the PDL Axioms: Explicit Form of C_coh and Resolution of OP2 (D35)

This document derives the explicit tensorial form of the coherence stress-energy tensor C_coh appearing in the PDL Einstein field equation G[g_eff] = κ_PDL(N)·C_coh, established in D35, from axioms C1–C4 of the Projective Dynamic Logo (PDL) programme. Prior to this document, C_coh was identified schematically but not derived from first principles (OP2 of D35). The central result is a new structural theorem: the PDL coherence volume V_C = (4/3)π[ħ/(m_p c)]³ is doubly forced — by the proper-time counting theorem of D10a and by the S² topology theorem of D23. The two independent chains converge to the same expression, verified numerically to machine precision (ratio = 1.00000000). From this, four components of C_coh are derived. The mass component C^(mass)_μν = ρ_coh(N)·c²·u_μu_ν, where ρ_coh(N) = σ(N)·R_surf·m_p/(V_C·R_tot), is an unconditional theorem of C1–C4. The spin component C^(spin)_μν is derived as a correction of order ħ² from the SL(2,ℂ) pulsation of K₄ (D33) and the U(1) structure (D46), suppressed by a factor ~10⁻¹² relative to the mass component. The orbital component C^(orb)_μν is derived from the PDL probability current of D32. The leakage component C^(leak)_μν = −C·η_L^18·(m_p c/ħ)²·g_μν is partially derived: the factor η_L^18 is an unconditional theorem (D17, D30), while the proportionality constant C remains open (OP1 of D35), bounded observationally at C ≈ 8.16×10⁻⁴⁶. The complete PDL Einstein field equation with explicit source is stated as a corollary. In the pressureless large-N limit, it reduces to the standard Einstein equation with G_PDL and a PDL-induced cosmological constant Λ_PDL ∝ η_L^18. Three open problems are identified: the derivation of C from C1–C4 (equivalent in structure to the cosmological constant problem), the equation of state of the PDL coherence fluid, and the London equation for the superconducting phase of D46. This document depends on D01, D05, D10a, D11, D17, D23, D24, D27, D29, D30, D32, D33, D35, D40, D42, D46, and D47, and resolves OP2 of D35 and OP5 of DM v17 (partially).