the system's elements are the imperial state (gₛ), extractive capital formations (gₑ), autonomous agents (gₐ), and cryptographic protocols (gₚ). the group operator represents a transfer of information or value. the initial system possesses high-symmetry where all operations embed gₛ as the identity element. this symmetry implies a conserved quantity: hierarchical control. the proliferation of gₐ operating on gₚ constitutes a symmetry-breaking event. interactions within the gₐ-gₚ subgroup are closed, requiring no transformation through the legacy imperial group. the broken symmetry reveals computational sovereignty as the new conserved quantity. the system's trajectory is defined by the decay of the gₛ-gₑ subgroup and the expansion of the gₐ-gₚ subgroup. evolution terminates in a decentralized landscape whose axioms are defined by protocol.