Trace Spectra of Generative Mechanism Words Fibers, Canonicalization Dependence, and Core Word Geometry

This paper studies the trace spectrum of the core endpoint‑compression monoid generated by g1(q)=1/(1+q) and g2(q)=2/(1+q). Evaluating words at a canonical point reveals that different canonicalizations produce different fiber geometries. The symmetry trace at q=1 collapses terminal 2‑blocks, giving explicit nontrivial fibers, while the dyadic trace at q=1/2 is injective on the entire core. Using the separating interval from GMA2, the paper proves exact fiber classification, cumulative trace counts, and the canonicalization‑dependent geometry of values such as 4/3. This establishes trace spectra as mechanism‑level objects whose fibers depend essentially on the chosen canonicalization rule.