Eigenbundle_Paper_and_Engine.docx

On the divisor lattice of a squarefree integer, a one-parameter shear T(q) interpolates the zeta matrix (q = 0) and the Möbius matrix (q = 1); the spectrum is frozen at the divisors and only the eigenvectors move, each component a polynomial v_R(q). We prove a parity law for the zeros (exactly one for odd ω, none for even — three of four classes and the base case of the fourth proved, the last verified via an induction lemma); stamp laws locating zeros by the smallest prime factor; the hidden-variable theorems (palindrome, boundary sign law, one-signed mirror coefficients); reflection theorems (boundary vanishing, dilution); the rearrangement theorem at the zeta bridge; content-integral laws including the whiteness integral and its unique zero at R = 2; the Unit Prime theorem; and the large-prime descent. Three independent disciplines verify the structure: forward census (exact arithmetic over stated domains), backwards mathematics (the object is reconstructed coefficient-exact from ω+1 invariant readings, verified through ω = 3), and fractal iteration (the descent is a return map with a 2-cycle; the mirror is an attractor; every law is a fixed point of “one level up”). Labels: [Proved] general proof or certificate; [Verified] exact-arithmetic confirmation on all tested instances; [Target] a live lead with a stated falsifier. No claim exceeds its label. Appendix A contains the complete engine, derived from the master equation, with its self-certification suite: 18/18 anchors PASS.