Simultaneous Holotheticity and Bi-Hamiltonian Structures in Economic Growth Theory
Abstract
In this paper, we establish a rigorous geometric framework that applies the formal architecture of finite-dimensional bi-Hamiltonian structures and Nambu-Poisson mechanics to macroeconomic growth theory. Moving beyond static empirical correlations, we deploy Ryuzo Sato's principle of simultaneous holotheticity to demonstrate that economic production functions emerge natively as stable, time-independent geometric leaves of integrable flows. We construct a unified, hierarchical taxonomy of three fundamental economic growth regimes that sequentially generalize one another: the classical, unconstrained Cobb-Douglas mode; the resource-limited S-shaped econsystem response; and the capacity-bounded "overshoot-and-collapse" regime. Furthermore, we push this paradigm into non-smooth territory by investigating the structural boundary crises that occur when aggregate economic trajectories encounter definitive resource carrying capacity ceilings. We show that these capacity limits induce a catastrophic rank-collapse of the compatible contravariant Poisson pencil.
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BibTeX
@misc{finkle2026simultaneous,
title = {{Simultaneous Holotheticity and Bi-Hamiltonian Structures in Economic Growth Theory}},
author = {Sarah Finkle and Roman G. Smirnov},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.01661},
eprint = {2609.01661},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.01661},
}
RIS
TY - UNPB
TI - Simultaneous Holotheticity and Bi-Hamiltonian Structures in Economic Growth Theory
AU - Sarah Finkle
AU - Roman G. Smirnov
PY - 2026
DA - 2026/09/01
PB - arXiv
DO - 10.48550/arxiv.2609.01661
UR - https://arxiv.org/abs/2609.01661
AB - In this paper, we establish a rigorous geometric framework that applies the formal architecture of finite-dimensional bi-Hamiltonian structures and Nambu-Poisson mechanics to macroeconomic growth theory. Moving beyond static empirical correlations, we deploy Ryuzo Sato's principle of simultaneous holotheticity to demonstrate that economic production functions emerge natively as stable, time-independent geometric leaves of integrable flows. We construct a unified, hierarchical taxonomy of three fundamental economic growth regimes that sequentially generalize one another: the classical, unconstrained Cobb-Douglas mode; the resource-limited S-shaped econsystem response; and the capacity-bounded "overshoot-and-collapse" regime. Furthermore, we push this paradigm into non-smooth territory by investigating the structural boundary crises that occur when aggregate economic trajectories encounter definitive resource carrying capacity ceilings. We show that these capacity limits induce a catastrophic rank-collapse of the compatible contravariant Poisson pencil.
ER -