TEBAC HP–E2N: E2 Determinant Package on GL(1) and Canonical Normalization

We construct a canonical centered heat trace and its Mellin/zeta regularization for the $GL(1)$ operator from HP--II. This yields a canonical zeta determinant \[ ζᶜᵃⁿ(L+σ) \] and a scheme-independence theorem reducing any admissible cutoff/subtraction scheme (χ,ρ,Pfinal) to the canonical object via an explicit entire correction factor. We also prove the canonical normalization limits needed to remove the constant ambiguity in the quotient \[ Q(s)\;=\;{Dcomp(s)}{ξ(s)}\,. \]