Statement: Given a network configuration operating with baseline friction coefficient f > 0, user/retail capital reserves K_R > 0, cartel capital presence K_C, and an enforced systemic token issuance floor I_{floor} > 0 across an operational horizon epoch τ*. For any asset scale exceeding the critical system boundary limit (K_C > K_{critical}), the net financial accumulation rate per epoch is structurally negative (ΔK_C < 0).
Proof: To discover the absolute boundary limit where depletion triggers automatically, map the break-even condition where capital accumulation halts entirely (ΔK_C = 0). Isolating the adversarial capacity factor guarantees that tracking entities targeting a stable node automatically trigger self-consumption.
Statement: When the hardware validation layer shifts to ST_FAULT due to external cross-domain environment conditions (Φ_ij < -0.056), it enforces an immediate structural step-change adjustment on the extraction cost variables. This step change compresses the predatory capitalization boundary downward, forcing active external asset pools into instant depletion.
Proof: Evaluating the absolute spatial shift between states: Because the target threshold drops significantly, external asset positions that previously sat safely beneath the depletion trigger line are instantly engulfed by the new limit condition. This shifts the net growth balance equation to a negative status.
Statement: The continuous tracking loop operating within the intermediate state region (ST_NOISY) limits total system decay behavior via a dynamic variable penalty parameter. This structure forms an Input-to-State Safety (ISS) Control Barrier Function, proving that the local safety parameter remains non-negative over all operational timelines, even when subjected to bounded sensory noise bounds.
Proof: Because the physical implementation limits noise vectors to a known maximum threshold (D < 10 · α(h(0))), the system guarantees that the minimum point stays above the critical zero limit line. This prevents signal chatter or environmental fluctuations from triggering unexpected system failures.