Spectral Stabilisation: A Clinical Intervention Framework for Healthcare Systems Near Collapse

Prior work established that institutional collapse is geometrically determined: the dominant eigenvalue of the system Jacobian drifts toward the unit circle under regime deformation, entropy accumulation , and non-Markovian memory, generating detectable precursor signatures in institutional time series (Scheffer et al., 2009; Dakos et al., 2023). That prior work answered the detection question. This paper answers what follows: once critical slowing down is confirmed and the spectral radius ρ(J) is estimated to be approaching unity, what interventions reduce it, and which standard management responses accelerate collapse rather than arrest it? A formal stabilisation theory is derived from the spectral architecture, producing four theorems at an elevated level of mathematical precision. The Stabilisation Condition is extended to non-normal systems via the ε-pseudospectral radius ρ ε (J), the appropriate object when the condition number κ(V) is large. The Entropy Reduction Requirement is grounded in the Kolmogorov-Sinai entropy rate and the non-equilibrium thermody-namics of dissipative systems. The Intervention Ordering Theorem is derived via the Baker-Campbell-Hausdorff expansion, making the non-commutativity of sequential operator application exact rather than approximate. The Authority Propagation Theorem is reformulated using the Perron-Frobenius theorem applied to the institutional legiti-mation graph, yielding a sharp and analytically grounded centrality threshold pinned to the spectral gap λ 1 − λ 2. Six standard NHS management responses are shown to be geometrically destabilising near ρ(J) = 1. A five-stage Spectral Stabilisation Protocol with explicit entry criteria, staged actions, and exit conditions is derived from the formal results and operationalised at ward, directorate, and trust level.