Slow or inadequate relief (low U\rho_U), combined with rapid and broad coercive responses (high K\rho_{\mathcal{K}}) large rr.
High noise environment: frequent viral incidents or one large jump (e.g., high-casualty policing event).
Polarised media and elite fragmentation (high baseline P0P_0 and low 0\eta_0).
Characteristic dynamics
P(t)P(t) enters a persistent high-plateau (fat tail distribution) with recurrent spikes; median P30P_{30} > 0.35 and P90P_{90} often > 0.20.
T(t)T(t) decays and can fall below 0.30, reducing institutional buffers.
E(t)E(t) worsens due to disrupted markets and loss of investor confidence.
H(t)H(t) grows rapidly and frequently crosses HcH_c --- thereby increasing the chance an emergent leader or movement consolidates.
Probabilistic summary (example)
Pr(Major escalation: P>Pc within 30 days)55%\Pr(\text{Major escalation: } P>P_c \text{ within 30 days}) \approx 55\%
Pr(H>Hc within 90 days)40%\Pr(H>H_c \text{ within 90 days}) \approx 40\%
Expected economic drag (median): additional 0.3--0.6 percentage point GDP loss over next quarter relative to baseline.
Policy implication: Rapid de-escalation via accommodative policy is urgent; large-scale coercion risks locking the system into a low-trust basin where reversal is slow and costly.
3. Early divergences and thresholds (operational knobs)
Critical time windows
0--7 days: Information management & first visible relief package matter most; if TT does not stabilise here, path dependence grows.
7--30 days: MFPT diagnostics show whether PP trajectories are trending to decay or persistence; this window decides the short-term ensemble split.
30--90 days: If HH grows past HcH_c, political realignment or emergence of an alternative leadership vector becomes probable.
Diagnostic metrics to monitor in real time
Rolling variance and lag-1 autocorrelation of PP and TT (rising values indicate critical slowing down).
r-index: estimated r^t=^K(t)/^U(t)\hat r_t = \hat\rho_{\mathcal{K}}(t)/\hat\rho_U(t) from observed policy actions (if r^t\hat r_t trends upwards, escalation probability increases).
dH/dt: a persistent positive slope in HH forecasts black-horse risk.
