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

The PDL Einstein field equation Ggₑff = kappaPDL (N) Ccoh, established in D35, contains a coherence stress-energy tensor Ccoh whose derivation from first principleswas left as OP2 of D35. This document derives the explicit tensorial form of Ccoh fromaxioms C1–C4, corrects four dimensional errors present in versions 1 and 2, and resolvesOP-spin as a new result. The coherence volume VC = (4/3) pi hbar/ (mₚ c) ³ is established as an unconditionaltheorem via the proper-time counting chain (D10a) and the three-dimensional topology (D23). The coherence density rhocoh (N) = sigma (N) Rₛurf mₚ / (VC Rₜot) followsdirectly. The mass component C^ (mass) ₌ₔ ₍ₔ = rhocoh (N) c² uₘu uₙu is an unconditionaltheorem, verified numerically to 0. 013%. The spin component C^ (spin) ₌ₔ ₍ₔ is derived by explicit computation over all 8coherent configurations of K₄ and the 4 pulsation states Tᵏ|+>. The results = 0 and = (1/4) deltaⁱj are exact theorems from C1–C4, from whichthe Weyssenhoff–Raabe formalism gives C^ (spin) ₌ₔ ₍ₔ = 0 in the homogeneous groundstate. This resolves OP-spin. The orbital component C^ (orb) ₌ₔ ₍ₔ = mₚ² / rhocoh 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) ₌ₔ ₍ₔ = - (LambdaPDL c⁴) / (8 pi GPDL sigma (N) ) g₌ₔ ₍ₔis given in uniform units J/m³, so that the full PDL Einstein equation is dimensionallyconsistent throughout. The factor etaL¹8 entering LambdaPDL 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 VC 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 factormₚ 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.