The Ladder of Time E2; Causal Compression and Protocol Locking at the Sedenion Level — The Observer-Resolution Boundary Theorem

Starting from the algebraic rigidity of the Hurwitz classification theorem for
normed division algebras, this paper systematically demonstrates the physical con
sequences of crossing the octonion threshold into the sedenion level. By construct
ing the Hurwitz-time functor, the causal structure of event space is rigorously
mapped onto the axiom retention pattern of algebraic structures, thereby estab
lishing a complete chain of deduction from algebraic degeneration to physical causal
compression. At the algebraic level, the sign flip introduced in the fourth step of the
Cayley-Dickson construction inevitably leads to the high-dimensional emergence of
a zero-divisor space, the discretization transition of the automorphism group from
a connected exceptional Lie group to a product structure, and the irreconcilable
contradiction between locally associative subalgebras and global divisibility. At the
causal level, the coexistence of zero divisors and non-associativity forces the event
space to split into multiple mutually incompatible local coarse-graining protocols,
and cross-protocol information compression becomes an operationally unavoidable
mechanism of causal resolution locking. At the operational level, the self-referential
repair operator admits no self-consistent solution on such fragmented states, and the
resulting upgrade deadlock renders the sedenion level neither internally repairable
nor externally upgradable. The paper further argues for the inevitability of the
observable universe stably residing at the octonion level: the unstable traversal
scenario is ruled out by the upgrade deadlock theorem, and the necessary-residence
scenario remains the only self-consistent cosmological explanation. The ultimate
boundary of temporal level upgrades thus exhibits a dual rigidity—thermodynamic
capping is locked at the energy level by Landauer’s principle, while algebraic de
generation is locked at the structural level by the Hurwitz theorem.