Measuring Lost Futures: A Layered Reachability Model for Adaptive Systems

A hospital patient’s blood pressure may return to 120/80 after a severe haemorrhage even though the reserves that made recovery possible have been depleted. A factory may report unchanged output after closing redundant production lines, while becoming incapable of surviving the failure of its sole remaining supplier. These systems occupy apparently satisfactory present states, yet they no longer possess the same futures. Measuring Lost Futures: A Layered Reachability Model for Adaptive Systems develops a formal method for detecting this hidden difference. It defines the architecture of possibility as the actor-specific and horizon-dependent structure of viable future configurations, together with the routes through which those configurations remain reachable. A transition is evaluated through a layered resistance vector comprising time, capital, institutional authorization, and epistemic capability. These dimensions remain separate because a route that is affordable may still be legally closed, technically unintelligible, or too slow to matter. Hard gates are therefore represented independently from graded resistance, and reachability is tested component by component against explicitly declared budgets. The paper introduces accessibility memory as a history-attributable alteration of later reachability: history becomes functionally active when it changes the cost, availability, or organization of a subsequent transition under matched present conditions. Manoeuvrability is represented through a multi-horizon profile measuring reachable coverage, path independence, slack, reversibility, and inequality of access rather than through a single universal score. An eight-node computational model demonstrates operational calculability. Two systems begin with identical output of 1.00; following the same disruption, the hyper-optimized system falls to 0.12, whereas the option-preserving system retains 0.92, three independent recovery paths, and complete target coverage. Across 6,000 structurally nested parameterizations, the option-preserving regime strictly dominates in 96.3% of cases. This percentage characterizes robustness within the declared nested model family rather than an estimated empirical frequency. In a separate held-out synthetic benchmark, reachability information sharply improves prediction over a state-only comparator, while explicit accessibility-memory covariates provide no statistically reliable incremental gain. The result supports the measurement of present reachability and identifies matched-history perturbation studies as the appropriate empirical test of memory. A reanalysis of Dutch Rhine strategy data illustrates how the boundary of measurement can reverse the ranking of apparently rational interventions when avoided losses, preserved routes, and distributed consequences are included. The article concludes with a prospective 2026–2031 protocol specifying observable variables, a 20% prediction threshold, and explicit rejection conditions. The deposit contains the publication-ready article, supplementary methods, reproducible Python code, computational outputs, figures, and verification materials. The Symformism research programme is acknowledged as the intellectual genealogy of the question; the theoretical and empirical claims of this paper stand on the formal definitions, calculations, and tests reported here.