Flow Atlas: An Effective Field Theory of Institutional Dynamics

We develop a first-principles effective field theory of institutional dynamics, grounded in a renormalisation-group (RG) analysis of legislative coherence. Starting from a stochastic process for an institutional order parameter τ, we construct a Martin–Siggia–Rose–Janssen–De Dominicis (MSRJD) path integral, identify instantation configurations, and promote the resulting Hamiltonian to a non-Hermitian operator algebra with commutator [ˆ τ,ˆ π] = iℏinst. The spectrum yields discrete coherence modes. Near a fixed point, the algebra reduces to a harmonic oscillator; coherent states recover the classical RG flow. Instanton calculus gives tunneling rates between basins. The effective Hamiltonian projects onto a tight-binding network; a non-Hermitian extension accounts for dissipation. Harmonic inversion and maximum entropy reconstruct the complex spectral density ρ(λ). The renormalisation group flow on ρ(λ) exhibits three universal phases: stable bipartisan, critical transition, and oscillatory polarisation cycles. These phases are classified by the universal unfolding of the A2 cusp catastrophe, with the control parameter space carrying a natural Frobenius manifold structure. We conjecture that the spectral RG is isomonodromic, linking it to Painlev´e VI in the two-mode reduction; the tau-function provides a scalar health metric. The framework unifies stochastic field theory, non-Hermitian spectral methods, catastrophe geometry, and integrable systems into a testable theory of legislative stability.我们基于立法一致性的重整化群（renormalisation-group, RG）分析，构建了制度动力学的第一性原理有效场论（effective field theory）。我们从制度序参量τ的随机过程（stochastic process）出发，构造了Martin–Siggia–Rose–Janssen–De Dominicis（MSRJD）路径积分（path integral），识别出瞬子构型（instanton configurations），并将所得哈密顿量（Hamiltonian）推广为满足对易关系[ˆτ, ˆπ] = iℏ_inst的非厄米算子代数（non-Hermitian operator algebra）。其能谱给出离散的一致性模式。在固定点附近，该算子代数退化为谐振子（harmonic oscillator）；相干态（coherent states）可还原经典重整化群流。瞬子演算（instanton calculus）可给出各势阱盆地间的隧穿速率（tunneling rates）。有效哈密顿量可投影至紧束缚网络（tight-binding network）；引入非厄米推广项可描述耗散（dissipation）过程。通过谐波反演（harmonic inversion）与最大熵（maximum entropy）方法，可重构复谱密度（complex spectral density）ρ(λ)。复谱密度ρ(λ)上的重整化群流展现出三类普适相：稳定两党格局、临界转变与振荡式极化周期。这些相由A2尖点突变（A2 cusp catastrophe）的普适展开进行分类，其控制参数空间具备自然的弗罗贝尼乌斯流形（Frobenius manifold）结构。我们推测谱重整化群具备等单值性（isomonodromic），将其与双模约化（two-mode reduction）下的Painlevé第六方程（Painlevé VI）相联系；τ函数（tau-function）可提供标量健康度量。该框架将随机场论、非厄米谱方法、突变几何与可积系统（integrable systems）统一为一套可检验的立法稳定性理论。