(GQR36) Time-Ordered Accessibility as a Constraint on Transport - Why Averaging Fails When Connectivity Is Transient

Transport is commonly modelled using static or time-averaged connectivity, implicitlyassuming that pathways exist continuously. We show that when connectivity itself is tran-sient and enabled sequentially by accessibility constraints, time ordering becomes irreducible:outcomes produced by ordered accessibility schedules cannot, in general, be reproduced byany static or averaged description. Using minimal quantum and Markovian models, we pro-vide explicit counterexamples, robustness results on open parameter sets, and closed-formexpressions demonstrating strict order dependence even under strong dephasing or fullymemoryless dynamics. These results identify a finite-time regime in which equilibrium intu-ition fails and clarify the distinction between tunnelling through static barriers and transportdriven by temporal reorganisation of accessible state space. Full 70 article programme https://github.com/jamessutton600613-png/GQR/blob/main/Programme_Index.md The programme contains both standalone and self referencing articles. These can all be read as notes in proof of GQR1.