Classical Attractors and Regulatory Density: Structural Correspondence Between Lohmiller-Slotine Exact Quantum Reconstruction and the CDR Cycle

Abstract Lohmiller and Slotine (2026) have demonstrated that the Schrödinger wavefunction can be computed exactly from a finite set of classical extremal action paths weighted by conserved classical density — replacing Feynman's infinite non-classical paths with a J-valued action census. This paper maps the structural correspondence between the Lohmiller-Slotine (L&S) construction and the Coherence-Decoherence-Recoherence (CDR) cycle grammar developed across the Sovereign Ideas Papers (SIP) corpus. Three correspondences are documented and epistemically graded: (1) finite extremal replacement of infinite ensembles maps at the pattern level onto attractor convergence as a state-selection mechanism, documented independently across seven domains with a formalised shared operation (density-weighted finite-attractor composition); (2) classical density ρⱼ from the continuity equation maps analogically onto the regulatory ratio ρ = R/σ from entropy balance, sharing conservation-law form but differing in formal content; (3) measurement as boundary-condition completion maps structurally onto decoherence as boundary saturation. The paper identifies L&S's thermodynamic absence — no entropy production, no dissipation, no regulatory cost — as the specific extension point where the General Theory of Regulated Stability (GTRS) framework contributes. A thermodynamic extension conjecture is proposed: L&S's kinematic density is the zero-dissipation limit of a thermodynamic density incorporating entropy production, with formal grounding in Wigner-function stochastic thermodynamics (Malouf et al. 2019) and the demonstrated equivalence of kinematic and trajectory-level entropy production definitions (Horowitz & Sagawa 2014). The conjecture is explicitly marked as open work requiring formal derivation. Keywords: classical-quantum correspondence, attractor convergence, CDR cycle, entropy production, regulatory density, Lohmiller-Slotine, GTRS, structural correspondence, open quantum systems