Paper Za develops the Light Frame Cadence Theory (LFCT) nuclear-binding framework, treating nuclear structure as a domain application of the same three-mode representational grammar that underlies the broader LFCT corpus. No nuclear-specific constants, operators, or fitting parameters are introduced. The analysis is built entirely from the existing LFCT architecture: mode normalizations, the structural constant epsilon = 1/pi^2, the cadence budget C_0 = 1/c, the three-level scaffold, and the five-family operator grammar. The paper organizes binding across the nuclear chart through a three-transition staged-release framework with transitions at Ca-40, Sn-100, and Pb-208. Within this structure it derives the iron-peak binding ceiling, the doubly-magic scaffold anchors, alpha-chain interpolation, the post-Ca-40 reserve-fill law, the exact seven-number magic-number sequence, the iron-peak identity B_peak = 9 epsilon^3 m_p c^2, the heavy-nucleus Coulomb-versus-asymmetry coefficient ratio a_C/a_A = 3/pi^4, the Li/Be valley wobble law, and the Stage-3 super-heavy decline architecture. Across the framework, the paper reports twelve zero-free-parameter sub-percent matches against AME2020 reference data together with exact reproduction of all seven traditional nuclear magic numbers. The work explicitly distinguishes theorem-tier ingredients, derivation-tier results under named hinges, articulation-tier structures, and remaining open questions. It serves as the nuclear-binding companion to Paper Z, which develops the separate distributed-nucleosynthesis mechanism built upon the binding structure established here. The central claim is that nuclear binding, shell structure, iron-peak saturation, heavy-element asymmetry, and super-heavy decline can be organized by one common structural grammar rather than by a collection of independent nuclear-domain fitting rules.