Trace across Bases

Trace across Bases studies persistence and continuation in the support chambers of multiplication tables under changes of base. Three readings are kept distinct: fixed-position comparison in a common Zusean lattice, seam-respecting local comparison between consecutive chambers, and affine chart transport into later frames.The Zusean spectrum is identified exactly with the globally persistent fixed-position support. Its cells have the form(a*u, u+a),with explicit witnesses(m-a)*(m-u)in every later chamber. The first uniform far-chamber isolation threshold is sharp:τ_z(1) = 2, τ_z(2) = 3, τ_z(n) = floor( (n+1)^2 / 4 ) for n >= 3.Separately, transported incidence rays generate finite Zusean ray prisms with exact depthδ_χ(n,a) = a-1,so the maximal finite prism from C_n terminates at C2*n-2. The same law admits a hyperinteger continuation beyond every standard finite horizon. Relaxing the incidence-line family across the wider atlas yields the continuous lower envelopeY = 2*sqrt(X),which is an atlas-level geometric continuation rather than a discrete support theorem.Across these readings, a recurring stride-plus-lift grammar connects chamber geometry, chart placement, trace transport, and local seam detection without collapsing their distinct arithmetic meanings.