Coupling Geometry Case Study I: Rome, 200 BCE–476 CE

This case study applies Coupling Geometry to the Roman system from approximately 200 BCE to 476 CE — the first case in the programme’s series, and the one its geometry fits most completely. The purpose is not comprehensive history but a structured comparison: whether the framework’s six axioms and eight geometric features generate insights that the two most prominent existing accounts of Roman decline — Tainter’s complexity–collapse model and Turchin’s structural-demographic theory — do not. The analysis traces the full arc: the late Republic’s conquest-driven ratchet, the capture of expansion surplus by the senatorial aristocracy, the Gracchan reforms as the Involuntary Redistribution Theorem operating with textbook precision, and the threshold crossing of 88 BCE; the Augustan settlement as distributional restructuring disguised by superior ideological infrastructure; the Pax Romana as a managed post-threshold regime running on thin buffers; frontier closure under Hadrian and the Antonine turning point; the third-century cascade and the elite’s exit from the fiscal system; Diocletianic restructuring as coercive stabilisation; and the final cascade, in which defection from the system had become rational for the population that bore its costs. Against the comparators, the framework claims five genuine additions — the distributional mechanism in collapse, legitimacy as causal mechanism, the geometric vocabulary of irreversibility, multiple exits from above-threshold dynamics, and the territorial/positional distinction in material bases — and states its convergences and limitations explicitly. Scoring throughout is analyst-dependent and the analysis is post-hoc, working from secondary sources: the study demonstrates applicability and is not a test. Adversarial examination by sceptical scholars is invited. Introduction — Why Civilisations Rise, Flourish, Get Stuck, and Fall – Case Study II: The Stalinist System, 1945–1991