The Yuanzhi Field Theory — Paper I: An Axiomatic Constitution for Quantum Gravity and Observer Physics

The Yuanzhi Field Theory V13.0 proposes an axiomatic research programme that replaces continuous spacetime and point particles with a single algebraic substrate: an octonionic matrix model constrained by the exceptional Jordan algebra J3(O). The universe is conceived as a static, eternal algebraic structure from which spacetime, gravity, and matter emerge holographically in the large-N limit. The theory is articulated as ten core axioms and fourteen meta-axioms, addressing the foundational crises of quantum gravity, the gauge hierarchy, the cosmological constant, and the quantum measurement problem. Key mechanisms include: the entropic derivation of Einstein equations from entanglement first law; chiral fermions from anomaly inflow on intersecting M5-branes; geometric resolution of the hierarchy via a Randall-Sundrum warp factor; lepton mass ratios fixed by Mostow rigidity of hyperbolic knot volumes; time as Tomita-Takesaki modular flow synchronized by Kuramoto phase-locking; and the observer as a topological Heisenberg cut with measurement as an algebraic type transition. Meta-axioms further govern the logical and thermodynamic boundaries of the cosmic operating system, including SYK-like chaos, holographic incompleteness, causal set emergence of Lorentz symmetry, and baby universe separation. The work does not claim finality but offers a falsifiable, logically explicit map of the terrain any unified theory must navigate.