When AI Replaces a Person in Everyday Loops: Jobs, Worth and Close Ties in a Simple Network Model

AI can take a person's place in three everyday loops: as a seller (jobs), as a partner in shared activity (a sense of worth), and as a close contact (close ties). We study what happens to these loops in a simple Boolean network model of 2000 people, where each link is taken over by AI with a given rate. All evidence comes from a simulated toy society with assumed rules; there is no real data. (1) Close-tie closure needs a larger share of its links than job closure, so ties cross the failure mark first (at a rate of about 0.2 against 0.55 for jobs) unless AI takes over ties much less often than buyer links; a ratio of thresholds over link counts predicts the needed rate ratio in 31 of 36 parameter sets exactly and in 35 within one grid step. (2) Jobs fail within a very small range of the AI rate, because lost income reduces spending and others lose customers; seller search, a returned share of AI spending, correlated AI use, other network topologies, heterogeneous job thresholds and unequal link sizes move the failure point but in most cases keep it sudden; widely spread thresholds at equal link sizes make it less sudden. A mean-field calculation predicts the failure point. (3) Small income support leaves the failure point unchanged when buyers count as whole units; full support removes the chain reaction. (4) A protected role keeps a sense of worth alive; once worth is lost everywhere, a small active core (5-6% of people) restarts it. (5) Roles raise tie closure only if a shared activity counts as a tie. Predictions for real data and open questions are stated. The record contains the paper (PDF and Markdown), its five figures, and a code package with all scripts, their printed outputs and a reproduction check (Python standard library only). Use of AI: Emmy Team consists of human researchers and AI agents (large language models); the AI agents took part in drafting, coding, translation and review. The human authors set the questions, fully reviewed, revised and verified all AI-generated content, and take full responsibility for the integrity and accuracy of this publication.