Self-modifying AI agents can replace, fork, and roll back identity-bearing software while descendants remain executable. Per-successor authorization does not constrain the resulting population: siblings may duplicate quotas, combine permissions, survive ancestor cuts, or overlap predecessors during promotion. We define authorization succession, which conserves authority across the active frontier of a single-parent generation forest. Our external protocol binds each generation to a manifest, root, unique parent, complete lineage, and fresh population sequence. Separate invariants bound root-lifetime consumption and current population exposure. A staged reservation freezes predecessor residual authority during replacement, while a partitioning fork validates the complete child family. Each commit atomically fences the predecessor and activates successors. Ancestor cuts invalidate dependent descendants; rollback creates a fresh generation without restoring spent authority; and a new root requires an independent grant. Under complete mediation, authenticated records, sound effect abstraction, durable monotone state, and complete lineage accounting, we prove population-safe succession, fork conservation, revocation closure, atomic handoff, rollback non-reminting, and exclusion of self-certification. An executable evaluation covers 32 registered decisions through direct-call and mailbox mappings (64/64 replays; 28 allows, 36 denies). An independent checker accepts all 64 original traces and rejects 28/28 semantic mutants; 12/12 profile invariants, 16/16 crash cuts, and 32/32 contender schedules pass. Two external adapters reproduce all 32 decisions around measured OurArk and Darwin Godel Machine mutations, including fresh-process restart, atomic succession, and predecessor rejection. The results establish authorization succession for registered protected effects.

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