«Visible Gains, Invisible Losses: A Formal Approach to the Seduction Trap and the Accumulation of Social Graves»

Attractive stochastic systems often generate visible gains while accumulatinglatent structural costs. This paper introduces a rigorous spectral framework for quantifyingsuch hidden-cost dynamics within absorbing Markov models.We define the Hidden Graveyard Cost (HGC) as the expected cumulative hidden exposureprior to absorption and express it in closed form through the resolvent operator (I −Q)−1 ofthe transient subsystem. We establish that hidden-cost finiteness is equivalent to the spectralcondition ρ(Q) < 1, and we prove hyperbolic divergence HGC ∼ (1−ρ(Q))−1 as the spectralradius approaches unity. Sensitivity analysis reveals quadratic amplification near criticality,while variance explodes at cubic order, leading to instability and unpredictability.A general spectral decomposition shows that all asymptotic behavior is governed by thedominant Perron–Frobenius eigenmode. We further develop a critical bifurcation frameworkand validate theoretical predictions through numerical simulations.The results demonstrate that systemic fragility in attractive systems is spectrally encoded:resilience is determined by the distance to the spectral boundary.