The Holographic Circlette Part II: Composites, Decays, and the Zero-Sum Identity

We extend the circlette lattice model---in which the 45 first-generation Standard Model fermions correspond to valid codewords of an 8, 4 binary error-correcting code on a holographic lattice---to composite particles. We show that the XOR composite of any colour-neutral baryon is an invalid codeword at Hamming distance exactly~1 from a lepton, violating a single parity check (``a quark must carry colour''). Beta decay is the lattice correcting this error via the weak CNOT gate, which flips the isospin target bit while preserving the bridge control bit---converting d u within the quark sector. We prove a zero-sum identity: the bitwise XOR of all particles in beta decay vanishes identically, with each sector of the code independently summing to zero. The conservation laws of particle physics---charge, baryon number, lepton number, colour, generation---are the single statement that XOR is closed over the codeword space, sector by sector. We derive three new predictions: (i) ~the W^- boson is the literal XOR differential between down and up quark states, d u = 00000100 (the electron codeword), with the zero-sum holding at every Feynman vertex independently; (ii) ~the neutrino is a Majorana fermion, because the all-zeros codeword 00000000 is invariant under the matter--antimatter reversal operation; (iii) ~proton stability follows from the CNOT gate's inability to flip its own control bit (LQ), making the proton a fixed point of the local error-correction dynamics. We correct earlier arguments regarding Bell correlations, particle propagation, gravity, and the up-quark mass discrepancy, strengthening the framework in each case.