TRIDENT Mini Case Card — Boundary-Driven Instability and Threshold Pattern Formation: Rayleigh–Bénard Convection (PHYS-RBC-001.v1)

This mini case card applies the TRIDENT-Z0 diagnostic framework to Rayleigh–Bénard convection as a clean example of boundary-driven instability and threshold-induced pattern formation. A horizontal fluid layer heated from below develops organized convection rolls once the Rayleigh number exceeds the critical value Ra_c ≈ 1708 (for rigid boundaries). Below this threshold, the system remains in a purely conductive state. The analysis evaluates the phenomenon through four gates (Bulk Lock, Boundary Flow, Constraint Field, Coherence Dependency). G1–G3 pass cleanly: the instability is experimentally robust, mechanistically well-defined via buoyancy-driven flow under thermal gradients, and mathematically constrained by viscosity, diffusivity, geometry, and boundary conditions. G4 receives a CONDITIONAL PASS: pattern coherence is explicitly boundary-dependent and contingent on Ra > Ra_c with maintained DeltaT. Collapse below threshold is predictable and reversible — a defining feature of the instability, not a weakness. This case demonstrates classical emergence without invoking hidden variables or quantum coherence narratives. Ordered structure arises strictly from boundary energy injection interacting with constraint fields once a scalar threshold is crossed. The card includes explicit falsifiers and situates the system within the SHRF band for boundary-driven instability and dynamic pattern selection.Produced under the Sympathetic Harmonic Resonance Framework (SHRF) evidence-bound analysis protocol. KEYWORDS TRIDENTSHRFRayleigh–Bénard convectionRayleigh numbercritical thresholdpattern formationboundary-driven instabilityfluid dynamicsnonlinear systemsemergencefalsifiabilitydynamic coherence