Atmospheric Curvature Gates And Sun–Earth Transport A diagnostic program linking UTLS thresholds, waveguide throats, and L1 separatrix geometry with Z2 Seam Diagnostic: Sun–L1–Earth Pocket Episodes as chapter II

We present a mechanism-neutral, falsifiable diagnostic program for probing Sun–Earth coupling through “curvature gates” in the terrestrial atmosphere. The program is anchored in a well-defined atmospheric threshold: the tropopause/UTLS curvature inversion (lapse-rate inflection) co-located with (i) an ozone-gradient bulge and (ii) a marginal shear-stability boundary expressed by the gradient Richardson number near its canonical instability threshold. These empirical anchors motivate a gate functional that quantifies when vertical transport is suppressed versus intermittently unlocked. We then connect this atmospheric gate to a second boundary layer: the ionospheric D/E-region, whose conductivity and effective height define the Earth–ionosphere waveguide “throat” relevant to global electromagnetic resonance and lightning-driven cavity modes. Solar-wind variability is treated strictly as a boundary-condition driver observed upstream at L1, not as a mechanical forcing of the deep Earth. Finally, we formalize a correspondence between (a) atmospheric gate-crossing and (b) separatrix/turnstile transport near L1 (and conceptually L2) in the circular restricted three-body problem: both are codimension-one boundaries organizing which dynamical regime a trajectory inhabits. The detour named sections defines a Z2-only diagnostic program in Sun–L1–Earth measurement context. The spine is operational and audit-friendly: a fixed sampling grammar is declared; complex band amplitudes are extracted; a unit-modulus phase-closure comparator is formed; an involutive palindromic pairing is declared; a single seam-qualification gate is applied; a Z2 basis tag is emitted only under that gate; local wrap-aware drift and pivot events are defined; an atmospheric curvature proxy defines pocket episodes; and the central claim is tested as a lagged association between upstream pivot/flip structure and downstream curvature pockets under explicit nulls and falsifiers. No ontology, forecasting, or mechanism claims are asserted. Any morphology that survives seam-off and phase-scramble nulls is vetoed from the spine. Scope and non-ontology clause. This manuscript is a separate approach and does not extend or modify any prior RSM Paper I–II invariant grammar. All “gate,” “throat,” “separatrix,” “hinge,” “loxodromic,” and “monodromic” language is used as local modeling shorthand for boundary and transport organization. they are used only as disciplined descriptors for (i) thresholds in observed profiles and (ii) phase-space transport structure. Mechanism claims are restricted to established electromagnetic and thermodynamic pathways; any deeper geodynamic implications are treated, at most, as weak secondary hypotheses requiring significantly stronger evidence and tighter falsifiers. This matches the strict scale-separation posture already laid out in the atmospheric curvature note. Empirical anchor I: the UTLS/tropopause as a curvature threshold. The tropopause is operationally defined in meteorology as a sharp reduction in lapse rate; equivalently, it is the altitude band where the curvature of the temperature profile changes sign, marking a transition from convectively mixed troposphere to stably stratified lower stratosphere. The atmospheric note already frames this as a “curvature inversion gate” and highlights co-location with a jet-shear maximum and an ozone-gradient bulge.