What the numbers mean
The model starts with humanity alive, sovereign, and reciprocally necessary. It estimates five mutually exclusive states under explicit conditional hazards: H (all three remain); D (alive and sovereign, but reciprocal necessity is lost); P (alive and needed, without sovereignty); U (alive, without sovereignty or necessity); X (extinct). They sum to 100%. “Necessity” means real reciprocal human responsibility in the functioning and reproduction of civilization, not an inner feeling or a claim that every individual must be irreplaceable.
The opening rates are c = 0.1% for permanent authority loss, d = 0.5% for loss of reciprocal necessity, e = 0.1% for extinction once authority is lost, and z = 0% for direct extinction while humans still govern. These are test premises chosen to show how high per-transition success rates compound, not an empirical estimate of real-world per-transition rates. The results are conditional estimates. Evidence supports the failure mechanisms; the example rates make their implications calculable.
The state transitions
At each consequential transition, direct extinction risk z acts on H and D. Survivors can lose authority with conditional probability c. Loss of necessity has conditional probability d while sovereign and dₚ after disempowerment. People already in P or U face conditional extinction probability e. Newly disempowered people first face e on the next transition. Normally dₚ = d; after an accepted rollback closes exposure, d becomes zero while dₚ continues for people already outside human authority.
H′ = H (1 − z) (1 − c) (1 − d)
D′ = (D + H d) (1 − z) (1 − c)
P′ = P (1 − e) (1 − dₚ) + H (1 − z) c (1 − d)
U′ = (U + P dₚ) (1 − e) + (D + H d) (1 − z) c
X′ = X + (P + U) e + (H + D) z
Survival = H + D + P + U. Authority = H + D. Reciprocal necessity = H + P. Necessity can persist without authority, and authority can persist without necessity. Neither is silently substituted for the other or for a subjective sense of purpose. The rates are conditional on the current state, so the chain rule does not require claiming that all real-world events are independent. Holding these rates fixed, or making them follow a particular curve, remains an assumption about their conditional behavior.
The long-run results
With persistent c > 0 and e > 0, authority loss followed by eventual extinction is absorbing and the model tends to X = 100%. Authority loss alone does not prove extinction: with e = 0 and z = 0, continued c > 0 instead preserves survival at 100% while authority falls to 0%. If d > 0, U = 100% and necessity also disappears. If d = 0, P = 100% and necessity remains at 100% despite lost authority. If c = z = 0 and d > 0, D = 100%. If c = d = z = 0, H stays at 100%. These counterexamples are retained.
A zero long-run percentage is a mathematical limit of the stated continuing process, not a claim that current evidence measures extinction as certain or establishes an infinite physical sequence. The model does not silently convert inability to demonstrate a safe path into proof that none can exist.
Improvement and convergence
In the vanishing-risk path, every hazard is multiplied by 2^(−n / L), where L is the chosen halving interval. Their cumulative sum is finite, leaving nonzero chances of favorable states unless an earlier transition has certainty of failure. In the residual-risk path the multiplier is f + (1 − f) 2^(−n / L). A positive f preserves recurring exposure. The implementation sums the decaying part until a conservative remaining-hazard bound is below 10⁻¹², then applies the appropriate constant-hazard limit.
Making all four hazards vanish together is a demanding hypothesis. It requires a durable account of technical control, competing actors, continuing human protection, and reciprocal roles. Learning that reduces one hazard does not establish the others. The interface calls this a proposed escape because the mathematics alone does not validate the mechanism.
Ten actions and their stopping conditions
The main choices are policy decisions, not outcomes. Each loads an explicit package in the reconstruction screen. The comparison shares the current starting hazards, finite or long-run view, halving interval, residual floor, and architecture assumptions. Each decision uses its stated example stopping time; a selected decision also retains your custom edits. A failed stopping screen leaves recurring exposure in the probability model. Equal long-run percentages across several decisions follow from that continuing-exposure assumption; they do not estimate equal policy effects or equal calendar timing.
“Stop when AI tries to replicate itself” and “Stop when AI starts improving its own successors” test a deep global rollback after a warning. They additionally require the explicit assumption that the warning is detected while humans can still intervene. Their initial 20-transition delay is an editable illustration, not an estimate of when a warning will occur. If that extra condition is not granted, the model does not credit a successful stop. A successful late stop protects only the states that still retain human authority.
The globe illustrates the five model states and the four causal pathways. Its urban-to-rural sequence, distances, marker brightness, and stage timing are narrative assumptions. Mapped city locations and land shapes come from Natural Earth; its settlements are a selection, not a complete population census. Extinguishing a marker represents the loss of a viable human community, not an electrical outage. The geography animation does not assign a probability to any route or alter the probability model. Personal relationships and felt purpose can persist even when the model’s separate measure of economic and civic necessity is lost.
The rollback gate
A policy slider earns no arbitrary discount to mortality. The nine policy settings run the existing reconstruction model. A stopping scenario becomes eligible only when its conservative plateau screen passes, enforcement stays within the permitted ceiling, human technical indispensability is set to 100%, and international compute coverage is set to 100%. This deliberately strict candidate screen does not prove a safe computational floor.
Both editions load the same ten action profiles and the same reconstruction engine. Links between editions carry all technical controls, conditional hazards, horizon settings, and stopping assumptions. The technical edition displays the same conditional survival, authority, and necessity calculation. Its 27-case stress count is a separate resource test and is never converted into a survival probability.
The probability model closes further H/D exposure after the chosen number of transitions only when that screen passes and all three architecture assumptions are selected. It sets c, d, and z to zero thereafter. It does not rescue people already permanently disempowered: their e and dₚ continue. This distinguishes a barrier that works while humans still govern from an assumed rescue after control is lost.
Durable closure, the reconstruction coefficients, complete route coverage, and preservation of human services and liberty are assumptions to establish. Actual partial controls can change timing and conditional hazards, but this model does not invent a numerical conversion from a compute percentage into a survival percentage. The original simulator’s abstract cycles are not mapped to years or to these transitions.
What this model does and does not settle
It exposes consequences of persistent exposure and requirements for a stable human future. It is not a fitted empirical forecast, a claim about the intentions of all future systems, or a proof that human preferences cannot remain influential. Non-AI extinction risks, detailed transition harms, temporary losses followed by recovery, and the distribution of power among humans are not separately estimated. The permanent-loss states and the rollback’s human requirements make those commitments explicit.
Read the probability model source ↗ · Original reconstruction model ↗
Built from Chet Long’s “A technological plateau for human sovereignty,” revised 13 September 2026. This version replaces the earlier survey-anchored probability model.