Experiment-specific memory and relaxation structure in graphene transport: a kernel-first state-trajectory analysis

Graphene transport experiments probe relaxation through different observables, timescales and measurement domains, making direct comparison of reported relaxation parameters difficult. Here we develop a kernel-first, provenance-constrained methodology for determining what aspects of relaxation structure can be identified from heterogeneous transport measurements before assigning them a common physical interpretation. The approach distinguishes measured, processed, fitted and theoretically derived quantities, and separates response magnitude, kernel sensitivity and experimentally observed state evolution. The method is applied to three complementary graphene experiments. Frequency-resolved complex conductivity provides identifiable spectral relaxation descriptors and, where an admissible parametrisation is supported, permits explicit kernel-sensitivity and state-trajectory analysis. Ultrafast electronic heat spreading constrains an additional short-time response relative to an independently determined momentum-relaxation interval, but does not identify a unique kernel time. DC electrical and thermal measurements constrain integrated response weights, geometry dependence and a relative relaxation hierarchy without uniquely determining temporal kernel shape. The three experiments therefore occupy different levels of dynamical identifiability rather than providing interchangeable relaxation times. A localized change in an effective-kernel trajectory is not by itself interpreted as a triggered process. The stronger test requires such a change to reproducibly predict an independently measured dynamical response. We propose a same-device, cross-domain experiment implementing this criterion across controlled state trajectories. The principal contribution is a general analysis methodology for determining what relaxation information heterogeneous measurements support and what additional evidence is required before state-dependent response is promoted to a physical mechanism.