The Ultimate Number Domain of Complex Numbers Fieldoid J: Information-Driven Algebraic Phase Transitions: From Dynamical Equations to Testable Predictions in Non-Associative Quantum Field Theory

This paper establishes a complete dynamical theory with information density as
the order parameter, deriving a rigorous mathematical framework from the accumu
lation of information potential difference to algebraic structure phase transitions.
Based on the axioms of information conservation and computability, we construct
a perturbative expansion for non-associative quantum field theory and compute
the unique polarization correlation patterns induced by the octonion structure con
stants. We propose an amplification mechanism via topological defect condensation
at low energy scales, reducing the characteristic energy scale from 1016 GeV to the
detectable range of 10–100TeV. We predict a fixed ratio between s-channel and
t-channel scattering amplitudes, octonionic modulation of chiral anomalies, and
non-associative splitting of quantum Hall conductance plateaus as exclusive exper
imental fingerprints.