Pinning the Windmill: A Synchronization Model of Middle-Power-Led International Order Maintenance

This record contains the English preprint (Windmill_Strategy_preprint_v3.1.pdf), its Japanese version, and all simulation code (windmill_code_v3.zip). Version 3.1 adds the physics of the pin itself (bearing under load; friction as perpetual maintenance cost and as a protective damper), a hindcast validation on held-out history (1990–2010 calibration → 2011–2024 test, with rolling windows and coupling sweeps) that bounds the empirical claim—directional skill above uncoupled baselines, levels dominated by persistence—and an Acknowledgements section.

Dynamic ideal-point estimates from United Nations General Assembly voting (1946-2024) show that the United States has been drifting away from the axis of its own liberal order for three decades, that the departures of China and Russia have accelerated since 2015, and that Japan is the only major power whose trajectory has remained stable. Taking this as its starting point, this paper formalizes the "Windmill Strategy"-a conception in which Japan acts as the central pin of a windmill converting the divergent national-interest vectors of surrounding states into a common rotation-using the Kuramoto model of coupled oscillators and pinning control from complex-network control theory, and examines its viability through numerical experiments. In an 11-actor phase-oscillator system we compare (A) direct coupling to the great powers, (B) coupling to middle powers only, and (C) a two-layer structure in which a synchronized middle-power cluster captures the great powers via collective torque. Scenario C performs best (alignment A_t=0.76) while A fails (0.08), and removing Japan destroys the order in C; the ranking C>B>A holds in 95% of 150 random parameter perturbations. Under learning great powers, covert steering is capped at the middle-power ceiling while legitimacy restores alignment-the binding constraint is legitimacy, not stealth. Interventions during detente windows outperform those during crises. Under empirical calibration (UNGA ideal points, 2024 IMF GDP), the 2024 world is already a half-assembled windmill (A_t~0.84) that unwinds to 0.60 within 40 years without a hub but is held at 0.95 by the two-layer windmill. A pin-swap experiment shows the mathematics is a general theory not tied to any country, while centroid proximity, institutional freedom, and the east-west flank structure single out Japan by elimination. Placing a great power at the pin shows that mass is not a source of instability but an amplifier of the pin's defects. The question, we conclude, is not whether a windmill can be built but whether a middle power can succeed the departing pin of one already spinning; the model suggests a conditional yes.

[日本語要旨] 国連総会投票の動的理想点データ(1946–2024年)は、リベラル国際秩序の設計者である米国自身が30年間一貫して同秩序の軸から離反し続け、中国・ロシアの離反が2015年以降加速する一方、主要国の中で日本のみが安定した軌道を保っていることを示す。本稿はこの観察を出発点に、日本を風車の「ピン」に見立て、周辺諸国の多様な国益ベクトルを共通方向の回転(発展)へと変換する地政学的構想「風車の計」を、結合振動子の同期理論(蔵本モデル)およびピニング制御によって数理的に定式化し、その成立条件を数値実験により検討する。11アクターの位相振動子系で、(A)大国直結、(B)中堅国のみ、(C)同期した中堅クラスタの集合トルクで大国を捕捉する二層構造を比較した。C案が最良(整列度0.76、較正世界で0.95)、A案は不成立(0.08)、日本削除で秩序は消失し、序列C>B>Aはパラメータ摂動150通りの95%で保存された。学習する大国の下では隠密操縦は不可能で、成立条件は正当性である。デタント窓での介入が危機時より有効。実データ較正下では2024年の世界は既に整列度0.84の「半ば組み上がった風車」であり、ハブ不在なら40年で0.60へ解体、二層風車なら0.95を保持する。ピン交換実験は風車の数理が特定国に依存しない一般理論であることを示すと同時に、重心近接・制度的自由度・東西双翼構造により日本を消去法的に特定した。大国をピンに据える実験は、質量が不安定の源ではなく欠陥の増幅器であることを示した。問いは「風車を新設できるか」ではなく「退場しつつある旧ピンを中規模国が引き継げるか」であり、答えは条件付きの肯定である。