Paper A0: Terminal Target and Dependency Ledger for the Completed Weil Positivity Program

This paper freezes the terminal mathematical specification of the completed Weil positivity program developed in Paper A. It is a conditional reduction and dependency audit; it does not establish global Weil positivity and does not prove the Riemann Hypothesis. At every prime-power endpoint (m) and in each parity sector, the completed endpoint form is represented by the self-adjoint block operator \[ M_m= {pmatrix} Q_m & B_m*\\ B_m & C_m {pmatrix}, C_m≥ c_m I>0. \] When the low-sector baseline (Q_m) is nonnegative, the exact Schur condition is equivalent to \[ Q_m 0, B_m Q_m=\{0\}, \] and \[ L_mᵖʳ := Q_m/2 B_m*C_m⁻¹B_m Q_m/2 P_mQ, \] where (Q_m/2) denotes the Moore–Penrose inverse square root on (RanQ_m), extended by zero on ( Q_m), and (P_mQ) is the support projection of (Q_m). Equivalently, the largest canonical principal-response singular value must be at most one. Equality is an admissible GNS-null saturation and is not a failure of Weil positivity; only a value strictly greater than one produces a genuine negative direction. Relative to the explicitly named endpoint inputs E1–E6, the paper records the terminal equivalence between the endpoint principal-response condition, nonnegativity of the completed Weil form, and the classical Weil criterion. It provides a proof-dependency graph and a four-status ledger separating: symbolically proved results; validated finite computations; open or conditional inputs; retired and no-go routes. The paper also specifies the roles of the subsequent modules: Paper A1: the cofinal arithmetic principal-response inequality; Paper A2: independently checkable finite-prefix interval certificates; Paper A3: the formal passage from completed Weil positivity to the GNS/Hilbert–Pólya realization. Paper D is maintained as a separate compatibility track and is not used in the implication toward the Riemann Hypothesis without an independently established operator-level source identity. The sole unresolved terminal theorem recorded in this paper is the cofinal estimate \[ λₘₐₓ ( Lm,±ᵖʳ ) ≤ 1 \] for all sufficiently large prime-power endpoints and in both parity sectors, together with the corresponding baseline nonnegativity and kernel-compatibility conditions.