Non-Associative Octonionic Gauge Dynamics: The OZIP Action and D1/D2 Dark Vector Resonances

We present the formal gauge-invariant action for Big Boot Gauge Theory (BBGT) constructedover the non-associative octonionic algebra OZIP. Building upon the deterministic computationalframework of the force hierarchy [1], we introduce an associator correction term into the gaugecovariant derivative, allowing standard Jacobi identity failures to be absorbed into a massive Level-4vector dark matter field (D1 at 145.2 GeV and D2 at 202.5 GeV). We demonstrate the spontaneoussymmetry reduction sequence OZIP → H → C → R, yielding Standard Model gauge groups SU(3)C ×SU(2)L × U(1)Y . Finally, we provide explicit Euler-Lagrange equations of motion, analytical decaywidths, and collider signatures for Run 3 at the Large Hadron Collider.