The Canonical Society Theorem

After a person leaves a job, how does life continue, who bears the outstanding responsibilities, and how does the institution obtain the conditions for its next action? Given explicit sources of activity, lineage rules, and a complete responsibility contract, we construct a family of inhabited canonical societies and prove that actor generation, root-law completeness, genuine exit, and regeneration at every depth can be realized together. Every complete installed execution receives presentation, refusal that retains the bearer, action, or revision grounded in exact failure; writing occurs if and only if the disposition is action or revision. Exhaustiveness for general executions and inhabited realization at one constitutional point are proved separately. "Canonical" has its mathematical meaning: a standard construction generated from specified data and rules, with explicit compatibility relations. The main results cover continued operation. At every natural-number depth, the same actual payment jointly carries six guarantees: continuation of law and lineage, noncontracting exit, repair of capture, retention and processing of the residual bearer, revision capacity at the successor, and responsibility across actors. The visit it actually reaches is the entry to the next depth. More strongly, take any payment cycle of the defined type, any position in it, and any lawful payment at that position. The complete institutional contract enters that payment's actual target, where the target's own payment fulfills a new service or exit occurrence. The entire set of earlier paid occurrences is retained, and the new occurrence lies outside their authority image. Instantaneous exit capacity can therefore remain one throughout while the frontier of fulfilled occurrences grows strictly. Beyond every finite cutoff, the same later step also jointly generates actual law revision and a new birth supported by payment. The negative results show why these conditions cannot be omitted. Missing payment incidence, an interrupted route, and captured continuation can all produce zero exit capacity. Two sources with capacity one can likewise possess and lack, respectively, a complete portfolio of capabilities for living. In the constructed source family, even reachability readings for every domain are insufficient to choose an exact repair, and every method that processes only those readings inherits the obstruction. Retaining the already available failure kind restores each source's uniquely effective repair. Finally, old responsibility is transported through law revision until its own fulfillment settles it. For an exhausted source ledger, every sequential target from the same source that adds no rows at entry and increases no row's budget has no positive progress budget at its first whole-ledger successor. Institutional continuation thus has two requirements: every exercise of power must account for its bearers and consequences, and every new possibility must obtain its own actual source.