The Escalation Cost: Intensity, Duration, and the Growing Damage of Regime Change

Institutions steer feedback systems off trailing averages of persistent variables, and after a regime change, the estimator lags reality. This paper prices that lag. Two established literatures each answer half the question - control-theoretic stability asks whether a loop is stable at its current parameters, and adaptive filtering asks how fast an estimator converges once those parameters move - and the cost of being wrong in between is what the result here combines them to compute. We prove that blind-period damage is bounded by a compound expression D = (ρ₂/ρ₁)^τ - intensity raised to duration - computable from quantities institutions already estimate; derive the unique optimal measurement window W* in closed form; and establish the adaptation-stability identity linking the two. The bound's damage ordering is validated on a 34-year rolling out-of-sample panel of seventeen U.S. inventory-to-sales series under a pre-registered panel-level test whose decision rule was amended, and the amendment disclosed, before any hashed data was touched (Section 6.3); it is corroborated on the 2008 crisis episode and boundary-tested on COVID, where the pre-registered expectation of a null was met. Simulation studies map where acting on the diagnostic helps and where it harms: value is conditional on capacity strain, asymmetric between price raises and cuts, robust to permanent customer attrition in genuinely shifted regimes yet harmful in noisy ones, and - under drifting persistence - beyond rescue by any estimator, including one handed the true parameter. Two pre-registered cross-domain extensions were WITHDRAWN when their preconditions failed, and a capacity-threshold test is reported as unadjudicable rather than negative. A dated, falsifiable forward prediction is registered publicly at release. The theorem converts steady-state stability analysis into a computable transient-cost diagnostic; the scope conditions and limits that bound it are stated, tested, and reported at the same weight as the results. Verified rebuild under the Research-to-Publication Standard v1.9.11: every load-bearing number is registered in a machine-checked ledger (claims.lock) and regenerated on demand by verify.py on hash-pinned inputs, then independently reproduced from a clean checkout; a capped single-round adversarial review under a fix-or-rebut protocol and a public corrections log are committed in the repository. Two dated, reader-runnable forward predictions are registered publicly as prospective out-of-sample falsifiers - that any firm's closed-loop spectral radius ρ, computed from its estimated demand persistence, measurement window, and feedback gain via the paper's companion-matrix construction, sorts amplifying from decaying shock responses at the threshold 1.0, and that at the next NBER-dated US recession onset the nine registered boundary-crossing inventory/sales sectors will show amplifying responses exceeding the eight registered never-crossing sectors under the pre-committed metric and one-sided Mann-Whitney test at α 0.05 - to be resolved on the same public FRED monthly series the paper uses at the stated 24-month horizon, and carried forward if no NBER-dated recession occurs before July 31, 2031. The paper is licensed CC BY-NC-ND 4.0; the accompanying plain-English companion is CC BY-NC 4.0, and the reconstruction and verification code is MIT-licensed.