Conserved Properties under Growth, Split, and Merge

Agent identity must be treated as a relation across transformations, not a fixed set of variables — the real question is which control-relevant properties survive growth, splitting, or merging.

What decision changes?

When a system grows, delegates, is copied, or merges, do not ask whether it is 'the same system.' Ask which control-relevant properties were conserved.

Real agents do not sit inside fixed boundaries. They grow, absorb tools, delegate, create copies, outsource memory, and fuse into teams, firms, and institutions. A model becomes a deployed agentic service once connected to tools, persistent memory, and schedulers; a startup becomes a corporation; a government agency outlives every one of its employees.

If alignment is defined over fixed objects, this breaks certification: we might align a model while the real optimizer becomes the model-plus-tools-plus-users system, or certify a system at time t only to find the relevant agent has moved by t+1.

The book’s reframing treats identity as conservation rather than sameness: not “is this the same object,” but “which control-relevant properties have been conserved” — boundary closure, memory lineage, value-bundle response geometry, bearer-map continuity, correction-channel capacity, transparency policy, and control-locus continuity. Chapter 31 develops these seven properties in full for the successor case specifically.