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This study explores the relationships between classical-path quantum reconstruction and regulatory density in complex systems. It aims to establish structural correspondences that enhance understanding of quantum mechanics and thermodynamics.

May 1, 2026Open Access

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

Key Points

This study explores the relationships between classical-path quantum reconstruction and regulatory density in complex systems. It aims to establish structural correspondences that enhance understanding of quantum mechanics and thermodynamics.
Mapped structural correspondences between Lohmiller-Slotine exact classical-path quantum reconstruction and the CDR regulatory grammar.
Conducted computational tests to analyze scaling behaviors under various dissipation conditions.
Evaluated findings using HATI³ metrics for computational effectiveness.
Falsified naive global linear scaling, recovered near-linear scaling in weak-dissipation regime.
Proposed a thermal equilibrium limit with a defined functional form: f∞ = 1/(1 + 2n_th).
Achieved high evaluation scores (Kimi 94.5/100, DeepSeek Panel 90/100) indicating strong alignment with theoretical expectations.

Abstract

Description: This paper maps three epistemically graded structural correspondences betweenLohmiller-Slotine exact classical-path quantum reconstruction (2026) and the CDR/GTRSregulatory grammar from the Sovereign Ideas Papers corpus: (1) finite extremal paths ↔attractor convergence (pattern-level), (2) classical density ↔ regulatory ratio (analogical), (3) measurement as boundary completion ↔ decoherence as boundary saturation (structural atprocess-grammar level). A thermodynamic extension conjecture proposes that L&S's kinematicdensity is the zero-dissipation limit of a thermodynamic density. Computational testing (SIP-PHY-05a) falsifies the naive global linear scaling but recovers near-linear scaling in theweak-dissipation regime and derives a thermal equilibrium floor f∞ = 1/ (1 + 2nₜh). HATI³evaluation: Kimi 94. 5/100, DeepSeek Panel 90/100 (flagship Tier 1) Keywords: classical-quantum correspondence, attractor convergence, CDR cycle, entropyproduction, regulatory density, Lohmiller-Slotine, GTRS, structural correspondence, openquantum systems, thermodynamic extension, Wigner function

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