Boundary-Cycle Retention as Model-Level Evidence for Homeostatic Boundary Admission in Abiogenesis

This paper presents a model-level computational test of the Homeostatic Boundary framework for abiogenesis. The central hypothesis is that proto-life should not be identified with chemistry alone, compartmentalization alone, or abstract information alone, but with the retained coupling of a boundary and an internal reaction cycle under viability pressure. The study implements an operational benchmark inspired by fatty-acid vesicles, formose-like reaction dynamics, dilution, membrane leakage, mechanical shear, cycle retention, and substrate stability. In the model, the vesicle-like boundary is treated not as a passive container but as a kinetic filter: it regulates access between an external chemical world and an internal reaction network. This biological picture is then formalized in constructor-theoretic terms as the admission of a self-world-boundary task. The core admission condition is expressed as: τₗifeᵃdm ≡ τSWBᵃdm ∧ ΣH = 1 where τSWBᵃdm denotes the admitted self-world-boundary task and ΣH = 1 denotes the minimal sustainability condition requiring cycle retention, substrate stability, and available disequilibrium to remain jointly above threshold. The computational experiment compares the full Homeostatic Boundary model against rival mechanisms, including chemistry-only, passive-container, random-boundary, boundary-only, and energy-only models. It further performs Monte Carlo sensitivity analysis across permeability, leakage, shear resistance, autocatalytic strength, tar-formation penalty, viability thresholds, and noise. The results show a robust Goldilocks pattern: low stress does not recruit boundary advantage, intermediate stress admits the boundary-cycle task, and extreme stress collapses the system. Regulated fatty-acid-like and inert-boundary systems admit the task in the recruitable band, whereas free chemistry, empty vesicles, non-autocatalytic controls, and non-SWB rival models fail to retain admission. The paper does not claim to reproduce early Earth chemistry or to prove a historical scenario for abiogenesis. Rather, it provides a model-level proof of concept: under the stated assumptions, boundary-cycle retention can be operationally distinguished from chemistry alone, boundary alone, and random boundary effects. The result is intended as a computational bridge toward future microfluidic experiments testing whether bounded formose-like networks retain viable reaction cycles better than unbounded or leaky controls.