TEBAC Hilbert–Pólya for GL(1): E2-final operator choice and self-adjointness (Addendum)

This addendum fixes a final confining version of the arithmetic generator \(Lₐᵣᵢₜₕ = Lₐᵣᵢₜₕ⁽⁰⁾ + Bconf\) used in the TEBAC Hilbert--Pólya \(GL(1)\) construction (E2/GS5), and records a minimal functional-analytic package ensuring that \(Lₐᵣᵢₜₕ\) is well-defined as a lower semibounded self-adjoint operator via quadratic forms (KLMN). On the zeta channel \( Hcen = Ran(Pcen)\) the reduced operator is unitarily equivalent to a one-dimensional Schrödinger operator \(-∂_u^2 + Veff(u)\) with confining potential and compact resolvent. The note also fixes a final small-time subtraction convention \(Prefᶠⁱⁿᵃˡ(t)\) for the centered heat trace package used consistently across E2/E3/E4, thereby eliminating ``version drift'' in the \(GL(1)\) sector of the programme.