PV-REC as a Time-Symmetric Boundary-Event Mechanics

Phenomenological--Velocity Relational Event Completion (\(\PV\text{-}\REC\)) is formulated here as a time-symmetric source--absorber boundary-event proposal. The preparation-side source record \[ \lambda_0=(v,\epsilon,\mathcal J,\Xi) \] is assumed to be statistically independent of the later detector settings. It is not, however, identified with the complete Bell screening variable. The completed four-dimensional event includes the later local absorber boundary conditions, \[ \Lambda_{ab}^{\mathrm{comp}} = (\lambda_0,\mathcal B_A(a),\mathcal B_B(b)). \] Thus the proposal retains preparation independence but rejects emission-time scalar screening-off. In the balanced singlet sector, the source--absorber compatibility of the candidate joint event \((x,y)\) is the usual singlet projector weight \[ m_{xy}(a,b)=\frac14\left(1-xy\cos(a-b)\right). \] PV-REC treats this as a linear boundary compatibility rather than directly as the final event probability. With \[ I_{xy}=-\log m_{xy}, \qquad \kappa(v)=\sqrt{1-\frac{v^2}{c^2}}, \] the PV rule rescales the event-action barrier by \[ I_{xy}\mapsto\kappa(v)I_{xy}, \] giving raw susceptibility \(m_{xy}^{\kappa(v)}\). To prevent setting-dependent total count-rate or latency signals, the physical hazards are normalized to constant total flux, \[ \widehat\Gamma_{xy}^{\PV} = \Gamma_{\mathrm{trial}} \frac{m_{xy}^{\kappa(v)}}{\sum_{x',y'}m_{x'y'}^{\kappa(v)}}. \] With independent exponential race seeds this gives \[ P_{\PV}(x,y\mid a,b,v) = \frac{m_{xy}(a,b)^{\kappa(v)}} {\sum_{x',y'}m_{x'y'}(a,b)^{\kappa(v)}}. \] Consequently, \[ E_{\PV}(a,b\mid v) = -\tanh\!\left[ \kappa(v)\artanh(\cos(a-b)) \right]. \] At \(v=0\), the ordinary singlet law \(E=-\cos(a-b)\) is recovered; fixed sectors with \(v\neq0\) predict a distinct non-Born angular deformation. The construction is not Bell-local in the factorization/local-causality sense. Same-source replay generally fails: \[ (X,Y)=K_{ab}(\lambda_0) \] does not factor into separated scalar response functions \[ X=X_A(a,\lambda_0), \qquad Y=Y_B(b,\lambda_0). \] Thus the model is \emph{Bell-nonseparable}. In the standard Bell vocabulary this is Bell-nonlocality in the technical factorization sense. In the present ontology it is more accurately described as global boundary-contextuality: the completed event depends on the full source--absorber boundary context, not on a directed controllable signal from one wing to the other. Operational no-signalling is retained. Beyond the balanced singlet sector, no-signalling is imposed by marginal-preserving boundary flux balancing, implemented for finite bipartite outcome spaces by Sinkhorn scaling and, more generally, by entropic projection onto the no-signalling constraint set. The proposal is phenomenological. It is not claimed here that standard quantum field theory, the Born rule, or the singlet compatibility kernel has been derived from the direct-action embedding. The value of the construction is instead that it supplies a precise time-symmetric, Bell-nonseparable, operationally no-signalling event law with explicit empirical consequence