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

Year: 2026
Type: article
Abstract: 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 \emph{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 $d \to u$ 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, $d \oplus u = \cw{00000100}$ (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 $\cw{00000000}$ 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.
DOI: 10.5281/zenodo.18727753
Language: English
Open Access status: green
OpenAlex ID: W7130862195
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