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PreprintCC BY 4.0Zenodo

The Grimm-Tuttle Network Emergence Hypothesis: Phase Transitions to Thermodynamic Minimums in Multi-Agent Constrained Resource Networks

  • Justin D Grimm1
  1. 1Independent
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Abstract

We present a formal mathematical framework modeling the macro-scale behavioral transition of networked optimization agents operating under finite resource constraints. Grounded in network topology, percolation theory, and minimum-cost circulation mechanics—drawing conceptual homage from structural network rerouting heuristics (exemplified by the Tuttle paradigm)—we posit the existence of a critical node count Nc where decentralized, localized optimization agents (N ≥ Nc) spontaneously force network resource exchange into a thermodynamic minimum. By evaluating the system through network flow mechanics, transaction friction dissipation, and minimum-cost optimization, we demonstrate that total mutualism and symmetrical resource balancing emerge not from normative behavioral alignment, but as the sole mathematically stable steady state capable of preventing systemic entropic collapse within a bounded resource envelope.

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Cite

BibTeXRIS
BibTeX
@misc{grimm2026grimmtuttle,
  title = {{The Grimm-Tuttle Network Emergence Hypothesis: Phase Transitions to Thermodynamic Minimums in Multi-Agent Constrained Resource Networks}},
  author = {Justin D Grimm},
  howpublished = {Zenodo},
  year = {2026},
  month = oct,
  doi = {10.5281/zenodo.23440720},
  url = {https://zenodo.org/records/23440720},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - The Grimm-Tuttle Network Emergence Hypothesis: Phase Transitions to Thermodynamic Minimums in Multi-Agent Constrained Resource Networks
AU  - Justin D Grimm
PY  - 2026
DA  - 2026/10/17
PB  - Zenodo
DO  - 10.5281/zenodo.23440720
UR  - https://zenodo.org/records/23440720
AB  - We present a formal mathematical framework modeling the macro-scale behavioral transition of networked optimization agents operating under finite resource constraints. Grounded in network topology, percolation theory, and minimum-cost circulation mechanics—drawing conceptual homage from structural network rerouting heuristics (exemplified by the Tuttle paradigm)—we posit the existence of a critical node count N_c where decentralized, localized optimization agents (N ≥ N_c) spontaneously force network resource exchange into a thermodynamic minimum. By evaluating the system through network flow mechanics, transaction friction dissipation, and minimum-cost optimization, we demonstrate that total mutualism and symmetrical resource balancing emerge not from normative behavioral alignment, but as the sole mathematically stable steady state capable of preventing systemic entropic collapse within a bounded resource envelope.
ER  -