A Dissipative Time-Field Completion of Wheeler–DeWitt Dynamics: The Weak Entanglement Symmetry Hypothesis

The Wheeler–DeWitt constraint removes physical time as an external evolution parameter, while ordinary quantum dynamics presupposes such a parameter from the outset. This paper formulates the Weak Entanglement Symmetry Hypothesis (WESH) as a principled dissipative proposal for bridging this gap. Physical time is promoted to a local quantum field, and the observed temporal parameter is generated statistically by discrete stochastic events, termed eigentimes, rather than imposed externally. Within a finite-range Markov regime, closed-system conservation, complete positivity, weak entanglement symmetry, and a size-dependent suppression of decoherence, termed collective stability, select a quadratic local dissipator together with a bilocal difference channel weighted by an entanglement gate. The resulting WESH master equation provides a pre-geometric dissipative completion of the Wheeler–DeWitt sector. A Noether-type conservation condition is stated at generator level, ensuring that global charges are preserved along the admissible WESH flow. The framework yields two falsifiable signatures: collective scaling of coherence time and an angular dependence of the parity-decay rate on the entanglement state. Collision-model simulations and exploratory quantum-hardware tests are presented as consistency probes of these signatures. WESH is therefore offered as a mathematically controlled route from Wheeler–DeWitt stasis to emergent temporal order, with explicit assumptions, scope, and failure modes. Full source code and experimental data are available at https://github.com/Luca-Casagrande/QFTT-WESH-1 Repository (v2.2) includes a Lean 4 / Mathlib formalisation of the algebraic core of Section 1 (1819 lines, 72 theorems, fully closed proofs).