Zenodo description, Fruit-Fly Toy Model V3

Biological Transitions as Multi-Agent Realisations of the Generative Operator Pipeline in TO/TOGT: A Fruit-Fly Connectome Toy Model
Version 3, September 2026: what the model does, and corrections

Pablo Nogueira Grossi, G6 LLC, Newark, NJ. ORCID: 0009-0000-6496-2186
Concept DOI 10.5281/zenodo.19210136; V2 10.5281/zenodo.20128568; V3 (this deposit) 10.5281/zenodo.23029951.

Abstract

A toy model of a swarm of neural clusters, motivated by the Drosophila connectome. Each cluster is a point in the plane; one step applies G = U∘F∘K∘C (compress, clip, fold with a neighbour, rescale) with coupling α around a ring. Version 3 shows that version 2's contraction claims do not hold, and measures what the model does instead.

Corrections

G is discontinuous, so it has no Lipschitz constant; version 2's L(α) = 1/2 + |α| was a definition, not derived from G.
At α = 0 one agent has four fixed points, so there is no unique fixed point.
The plotted bifurcation signature (mean |s|²) is 1 for every α, because U rescales to length 1.
Version 2's reference [11] is not registered at doi.org and is withdrawn.

What the model does (noise-free, N = 8, 40 starts, 400 steps)

Multistable: for α ≤ 0.35 every run settles fast, and 40 starts reach 40 different end states.
Cycles: the first appear at α = 0.42; for 0.5–0.65 more runs cycle than settle.
Irregular: from α = 0.7 some runs neither settle nor repeat within 400 steps; at 0.95 none do.

Lean 4.32.0 / Mathlib v4.32.0, no sorry, axioms propext, Classical.choice, Quot.sound only: C_jumps, U_norm, four_fixed_points. The measurements are numerical and reproducible with python multi_orbit_bioswarm_v3.py --check.

Files

multi_orbit_bioswarm_v3.pdf, .tex: the revised paper, with figures/
BioSwarmCheck.lean and bioswarmcheck.axioms.txt
multi_orbit_bioswarm.py (version 2 operators, unchanged) and multi_orbit_bioswarm_v3.py (measurements, figures, checks)
CHANGES_BioSwarm_V3.md, OPEN_QUESTIONS_BioSwarm.md