myconet 1.0.0

Python simulation framework for mycorrhizal network biophysics with Freiman-Villani thermodynamic analysis

MycoNet

Python simulation framework for mycorrhizal network biophysics with Freiman–Villani thermodynamic analysis.

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Overview

MycoNet implements the simulation and computational validation described in:

Mercier des Rochettes, B. (2026). MycoNet: A Python Framework for Mycorrhizal Network Biophysics. arXiv:2026.XXXXX [q-bio.QM]

Companion theory paper:

Mercier des Rochettes, B. (2026). Geometric Efficiency Bounds for Mycorrhizal Networks: A Freiman–Villani Framework. Journal of Mathematical Biology. arXiv:2026.YYYYY

The central result (Theorem 6.1): a mycorrhizal network with local Freiman index σ_r(Γ) satisfies

Ψ(Γ) ≥ C* · D / ε² · (σ_r(Γ) − K_hex)²

where K_hex = 19/7 ≈ 2.714, C* ≈ 21.8, ε is mean hyphal spacing, D is diffusivity. Networks forced by stress into irregular morphologies pay an explicit thermodynamic overhead.

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Installation

pip install myconet

From source:

git clone https://github.com/[handle]/myconet
cd myconet
pip install -e ".[dev]"

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Quick start

from myconet import MycoNetSimulation

sim     = MycoNetSimulation(seed=42)
results = sim.run(T=120, drought_onset=48)
results.summary()
results.plot()

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Reproducing the paper

# Single run (~2 min)
python examples/drought_stress.py

# 10-run ensemble, matches paper figures (~20 min)
python examples/drought_stress.py --ensemble --save fig1.png

# Unit tests (all 10, < 2 s)
pytest tests/ -v

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Key algorithms

Module	Content
myconet.freiman	Local Freiman index via k-NN + hex-integer FFT Minkowski sum
myconet.network	HyphalNetwork, hexagonal lattice generation, drift field
myconet.transport	Fokker–Planck solver, Wasserstein W₂ (Sinkhorn/POT), Fisher info
myconet.simulation	MycoNetSimulation, SimulationParams, ensemble runner

Theoretical constants (all exact):

Constant	Value	Source
K_HEX	19/7 ≈ 2.714	Lemma 4.1: hexagonal local doubling constant
C_STAR	256·49/576 ≈ 21.8	Theorem 6.1: dissipation bound constant
c0	7/24 ≈ 0.292	Proposition 4.4: Freiman–Wasserstein constant

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Citation

@software{myconet2026,
  author  = {Mercier des Rochettes, Bertrand},
  title   = {{MycoNet}: Python simulation framework for mycorrhizal network biophysics},
  year    = {2026},
  url     = {https://github.com/[handle]/myconet},
  version = {1.0.0}
}

@article{mercier2026methods,
  author  = {Mercier des Rochettes, Bertrand},
  title   = {{MycoNet}: A Python Framework for Mycorrhizal Network Biophysics},
  journal = {arXiv},
  year    = {2026},
  note    = {arXiv:2026.XXXXX [q-bio.QM]}
}

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License

MIT © 2026 Bertrand Mercier des Rochettes / Quantum Proteins AI