The observer event and its genuine tangent are the canonical objects constructed by the preceding null-direction theorem. The boundary projection is defined on their concrete orbit and sends each state’s sum and difference to Mathlib’s projective quotient.
Positive rapidity-dependent amplitudes disappear in projective space, so every rapidity has the same ordered pair of golden null points. The event-tangent states themselves remain distinct.
The theorem states the resulting non-injectivity directly and rules out both a rapidity decoder and a concrete observer-state decoder from the complete boundary image.