The Riemann Projection Rebuttal: Assembly, Decompilation, and Lifted Collapse

The classical Riemann Hypothesis asks where the scalar projection ζ(s), or equivalently ξ(s), vanishes. This paper argues that scalar vanishing is not the complete collapse condition of the canonical reflected object. The completed reflection s ↔ 1 − s canonically lifts the object to a reciprocal three-coordinate state. The complex plane is only its projection. Therefore a scalar zero is a projected coincidence, not a full reflected collapse.

The construction is bidirectional. The Assembly begins from the sampled screw primitive, generates the term n⁻ˢ, and exhibits the linked component bounds of radius, phase, and chord motion. The Decompilation begins from the completed reflected object, recovers the canonical reciprocal pair D(v)=e^(αv), D(v)⁻¹=e^(−αv), and identifies the transported boundary H(v)=D(v)−D(v)⁻¹=2sinh(αv).

The morph M preserves this boundary in the lifted reflected object, while the scalar projection Π(x,y,z)=(x,y) hides it. The completed scalar kernel is recovered as the projection of the lifted reflected kernel, so the lift is not an auxiliary diagram but a factorization of the reflected kernel before projection. Since Π is not injective, scalar coincidence cannot certify full reflected collapse.

Full lifted collapse requires equality in the suppressed reciprocal coordinate, equivalently H(v)=0. For D=e^(αv) and v≠0, this forces α=0, hence Re(s)=1/2. At the sampled assembly coordinate v=log n, the same condition is Hₙ=n^α−n^(−α)=0, which for n>1 again forces α=0. Thus the critical line is the projected lifted-collapse locus of the canonical Assembly and Decompilation object.

Keywords
Riemann Hypothesis; zeta function; completed zeta function; scalar projection; lifted collapse; canonical reflection; reciprocal coordinate; sampled screw; decompilation; assembly framework; Riemann projection; critical line; nontrivial zeros; canonical reflected object; Appendix A Assemblies