Hostless GRBs as Technosignature Failures: Kardashev Thresholds and Probe Kinematics

We present a novel, unified astrobiological and physical framework proposing that a sub-class of anomalous, non-debris gamma-ray bursts (GRBs)---specifically ``hostless,'' ``orphan,'' or exceptionally clean short/long GRBs---may represent macroscopic engineering failures of advanced civilizations attempting to cross critical Kardashev thresholds. We mathematically formalize the \textit{Thermodynamic Failure Trap}, illustrating that the transition from a Kardashev Type II to Type III civilization is bounded by an exponential rise in the probability of runaway energetic catastrophes. To ensure physical rigor, we derive the critical mass of magnetically confined antimatter reservoirs by coupling material stress limits with thermodynamic radiative cooling constraints. Alternatively, we introduce the \textit{Quarantine Hypothesis}, suggesting that isolated GRBs do not necessarily imply civilizational extinction, but rather represent contained industrial accidents conducted in deep-space proving grounds to protect the inhabited host system. Furthermore, we perform a detailed kinematic analysis of the interstellar object 3I/ATLAS and establish a reverse Fermi estimate constraint on the galactic density of passive payloads. Finally, we deconstruct the proposed utilization of the Solar Gravitational Lens (SGL) as a technosignature detector, demonstrating how its mechanical and thermodynamic constraints align with cosmic filter boundaries.