= Solution
\b[Test geological associations and their chronology.] The most persuasive hypothetical record would combine rigid-block relative motion, creation of <oceanic lithosphere>, its destruction at a coherent margin, and repeated assembly and dispersal of continents. I would compile independently dated rock and structural occurrences in age bins, map their associations, and distinguish primary formation from later emplacement. The aim is to evaluate alternative tectonic regimes, not simply to collect the oldest example of a familiar name.
\b[Oceanic lithosphere and sutures.] An <ophiolite> association containing residual <peridotite>, <gabbro>, sheeted dikes and submarine <basalt> could demonstrate construction of an oceanic section. Its case for <plate tectonics> strengthens if it is associated with an oceanward <sedimentary succession>, a <metamorphic sole>, an <accretionary prism> or <mélange>, and eventual emplacement along a <suture zone> between formerly distinct blocks. Date construction, metamorphic heating and emplacement separately. A dismembered collection of ultramafic and mafic rocks need not be a complete <ophiolite>; an isolated volcanic pile or <greenstone belt> can also arise in a plateau or vertical-overturn setting. Hotter early <mantle> may produce oceanic sections unlike a modern template.
\b[Cold burial beside a hot arc.] <Blueschist> and <eclogite> with well-constrained low <temperature>/<pressure> ratios would support unusually deep burial before substantial heating. <Coesite> or metamorphic <diamond> in a suitable <continental crust> protolith could establish <ultrahigh-pressure metamorphism>, consistent with deep continental burial and return. Reconstruct <pressure-temperature-time paths> using mineral assemblages, zoning, reaction textures and <radiometric dating>; a peak <pressure> without its timing and burial geometry gives a weaker constraint. <Eclogite> alone only indicates appropriate <pressure>-<temperature>-composition conditions and may also form at the base of thick <crust>.
An approximately coeval, spatially organized pair of low thermal-gradient and high thermal-gradient <metamorphic belts> would be stronger evidence for juxtaposition of a cold descending plate and a hotter <volcanic arc> or hinterland. Test the original spatial relation rather than pairing unrelated rocks brought together much later. A statistical study of metamorphic <temperature>/<pressure> distributions illustrates how gradual widening and bimodality can be used to evaluate changing tectonic behavior. The ratio is an apparent metamorphic thermal gradient, not necessarily a directly measured steady <geothermal gradient>.<Metamorphism and the evolution of plate tectonics by Robert M. Holder and others>[2019, statistical analysis of metamorphic thermal-gradient distributions]{ref}
The absence of old <blueschist> is not a decisive absence of old <subduction>. A hotter thermal regime may suppress its production, and later heating can transform it. The test should therefore include the distribution of <pressure-temperature-time paths> predicted by early-planet models, rather than demanding the youngest modern mineral assemblages at all ages.
\b[Kinematic structures and basin evolution.] Long, coherent <thrust belts>, imbricated <sediments>, <folds>, regionally consistent <shear sense>, major <strike-slip faults>, and <suture zones> can identify lateral shortening and relative displacement. A reconstructed ocean-facing <volcanic arc>, <forearc basin> and <accretionary prism> with a common polarity is more compelling than isolated shortening. <Mountain building> alone is not exclusive to <plate tectonics>: vertical instabilities and impacts can also deform rock. The length scale, sequence, strain partitioning and linkage between structures matter.
For repeated opening and closing, seek a dated progression from <continental rifting>, through a subsiding <passive margin> and an intervening oceanic assemblage, to convergence, <continental collision> and renewed <rifting>. Matching stratigraphy, <sedimentary provenance> and structural restoration on opposing blocks can test whether a reconstructed <Wilson cycle> is geometrically possible. <Paleomagnetism> from independently dated, demonstrably primary magnetizations could show differential latitudinal motion and rotation of separate blocks. Relative motion between blocks is more useful than motion of one block, which could include <true polar wander>. Remagnetization, inclination shallowing and longitude ambiguity must be assessed.
\b[Secular changes require an archive model.] Compile the incidence, spatial scale and recurrence of these associations through time, normalized where possible by exposed rock area, sampling effort and dating opportunities. Include <detrital zircon> and <sedimentary provenance> where they preserve information from eroded source rocks, while recognizing zircon fertility and sedimentary sorting biases. Increased abundance of plate-like associations in several independent regions could support their transition from local episodes to a widespread regime. A sharp break is only one possible outcome; a progressive increase in persistence or geographical coverage would support gradual establishment.
A useful conceptual accounting is
$$
N_{\rm observed}(t)\sim N_{\rm formed}(t)\,
p_{\rm survive}(t)\,p_{\rm expose}(t)\,p_{\rm detect}(t),
$$
with additional redistribution between age bins if ages are reset or misassigned. This is not a calibrated dating law: it shows why an observed first appearance need not equal a true first formation. <Subduction> consumes <oceanic lithosphere>; <erosion>, <metamorphism>, <tectonic reworking> and burial selectively remove or obscure evidence. The oldest archive is especially incomplete, and some apparently diagnostic assemblages only become likely as the planet cools. An age peak may measure enhanced preservation during <continental collision> rather than an increased production rate.
\b[State the chronological inference precisely.] If an unambiguous assemblage forms at time $t_e$, then the required process was operating by $t_e$; an onset time measured forward from planetary formation obeys $t_{\rm onset}\leq t_e$. If both are expressed as ages before present, the inequality reverses: the onset age is at least as old as the assemblage age. Constraining how much earlier onset could have occurred requires well-sampled older records and a credible prediction that the sought evidence would have formed and survived. Several coeval, independent records consistent with sustained horizontal recycling give a stronger inference of widespread <plate tectonics> than the oldest ambiguous occurrence of any single rock type. Combined with <geodynamic modelling> and <geochemistry>, the defensible answer would report a range for first local activity and a potentially different range for establishment of a persistent global system.
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