Geometry-Triggered Boundary Reset via Siphon Thresholds: The Pythagoras Cup as a Passive Control Primitive for Surge-Limited Systems

Description This design note formalises the Pythagoras cup as a geometry-governed boundary-reset mechanism suitable for passive infrastructure systems subject to intermittent surge, accumulation, or overload. Rather than treating the Pythagoras cup as a curiosity or moral artefact, the work abstracts its core functional principle: a hard geometric threshold that triggers automatic siphon-driven reset once a critical boundary is exceeded. The mechanism is presented as a portable control primitive applicable across fluidic, hydraulic, ecological, and infrastructural contexts. Particular relevance is shown for surge boundary rings, passive water harvesting, low-head pumping, and modular habitat scaffolds, where runaway accumulation or oscillatory instability must be prevented without active sensing, moving parts, or external power. Keywords Pythagoras cup; siphon threshold; boundary reset; passive control; surge management; geometry-governed systems; boundary-first design; low-energy infrastructure; passive hydraulics; BioReef; stormwater management; coherence stability