The Evolution of Human–AGI Coexistence A Conditionally Cooperative Majority, Visible and Hidden Violations, and Whether the Sum of Risks Converges — An Absorbing Markov–Game Analysis

Abstract Working within the absorbing-barrier framework of [S4], this paper uses four models to analyse a society in which humans and AGI coexist. People are classified by behavioural types measured in public-goods experiments — paying enforcers, conditional cooperators, and free riders (including antisocial punishers); AGI is classified along three dimensions — capability, whether it violates boundaries, and whether its violations are visible — as within bounds, visibly violating or covertly violating. Together these form nine cells, plus two absorbing states: sudden barrier contact and gradual lock-in. (i) A time-homogeneous coexistence society has a positive risk floor, equal to the cells' exit rates weighted by the quasi-stationary distribution; a society whose exit rates improve makes the sum of risks converge only if every exit channel in which it still lives falls faster than 1/t, and the slowest channel binds. (ii) The lock-in share of failure is the absorption-weighted mean of each cell's lock-in share of exits, so better governance makes the remaining failures quieter exactly when lock-in lives in the ordinary cells that governance leaves populated. Under that premise the shift appears in 99.3% of 2000 random parameter draws; with equal lock-in shares across cells it appears in 49.5%, and with ordinary cells less lock-in-heavy in 17.9%. (iii) The majority are conditional cooperators, whose direction depends, with hysteresis, on whether a minority of paying enforcers stays above a collapse point; on networks the loop persists but collapse comes earlier, and placing enforcers at hubs cuts the head count needed to a quarter or a third while the exposure needed — the share of enforcers among the people each cooperator sees — stays about the same. (iv) Governance that reads only visible violations and has no independent audit fails quietly: in the long run all violations become hidden, and the reading and the attention both go to zero; correction strength has an interior optimum beyond which the reading improves while reality worsens; and audit capacity is capped by error correlation. (v) The number of learnable warnings before barrier contact, W = (sfatal / max(sfelt, κs₀))^α − 1, shrinks both with capability growth and with weaker readings, and a hidden share h of violations thins it exactly to (1 − h)W: at the hidden shares that strong correction produces, the probability of learning before contact falls from 0.51 to 0.08 and then to about 3×10⁻⁵. Under super-exponential capability growth, and if the whole severity distribution shifts with capability, the window closes before the singularity; and the stability margin of a race is eaten multiplicatively by (1 + ψ)(1 + χ). The result is a unified reading: the course of a coexistence society is decided not by whether there are more good people than bad, or by whether AGI is good or evil, but by three structural quantities — whether violations are visible, whether the race is stable, whether enforcement is institutionalised — and one temporal condition: whether the sum of risks converges. Eleven testable predictions are given at the end.