A Geodesic Transfer Proposal: Testing φ-Conservation on a Seven-Level Qudit

The framework's geodesic transfer map, the exponential of the fourteen G2 generators, conserves the octonionic associative three-form φ exactly, and this conservation underlies both the emergence of colour and the suppression of generation mixing. We propose a direct experimental test of the conservation law itself, on a platform that exists today: a seven-level qudit, whose state space matches the seven-dimensional representation of G2 on which φ is defined. Evolving the qudit along the geodesic generated by the G2 generators should leave φ invariant to numerical precision, while evolution along the complementary directions of SO(7) not in G2 should not. The predicted signature is sharp: the deviation of φ is zero under the G2 directions and of order unity otherwise — a clean discriminant rather than a small effect. We set out the state preparation, the generator implementation, and the measurement of the three-form, and we are explicit about what the test does and does not establish: it demonstrates the conservation mechanism directly, but does not by itself establish that nature realises G2 transfer. We present it as a concrete, near-term experiment bringing one structural claim of the framework into the laboratory.