Nuclear Binding from Quantum Error Correction: The Parity Theorem and the Weizsäcker Stability Line

We argue that nuclear binding energy is verification savings in a quantum error-correcting vacuum. In the Mass-Energy-Information framework of Part I, particle mass equals fault-tolerant verification cost on a [[192,130,3]] CSS code. If mass is verification cost, binding energy is the reduction when two nucleons share stabilizer constraints — information deduplication.

The central result is a theorem: only proton-neutron bonds deduplicate. A p-n pair has combined CSS parity 1⊕0=1 (non-trivial boundary, deduplication occurs); p-p and n-n pairs have parity 0 (boundary dissolves, no deduplication). This follows from the CSS code structure, not from empirical observation, and provides a first-principles derivation of isospin selectivity.

The asymmetry coefficient is derived without nuclear data input: γ = (n−k) × m_e c²/(2 ln 2) = 22.85 MeV, where n−k = 62 is the syndrome dimension of the [[192,130,3]] code. This falls within the empirical range 22.5–23.6 MeV established by global nuclear mass fits, achieving precision without parameter fitting.

Maximising verification savings via Max-Cut on the FCC cluster graph yields a closed-form stability line Z_opt(A) = 2γA/(a_c A^{2/3} + 4γ) identical in algebraic structure to the Weizsäcker stability formula, matching 18 of 21 test nuclei from ²H to ²³⁸U. The three discrepancies reflect the 1.5% gap between the derived γ and the textbook fit a_a = 23.2 MeV.