A Concatenated Quantum Code with Topologically-Protected Outer Structure on the Q3 Hypercube: Channel-Friction Semantics and Applications to Particle Physics

We introduce a concatenated quantum error-correcting code construction on the Q3 hypercube graph (the face-adjacency graph of the regular octahedron) with three structural properties not jointly present in existing constructions: (i) a topologically-protected outer Z2 layer enforced by the channel dynamics rather than by an additional encoding step, (ii) active verification semantics in which the channel performs parity-check measurement during propagation rather than only at decoding, and (iii) a closed-form channel-friction relation M= exp(φF/2), with φ= (√5−1)/2, mapping codeword frustration to an effective propagation cost. The outer Z2 protection follows from a finite-symmetry theorem on the walk operator: bit-flipsoftheouter-codebitareforbiddenatallordersbytherotationalstructureof the bridge dynamics. We prove the theorem, characterise the code’s distance structure under the concatenated decomposition, and show that the channel-friction relation is the unique fixed point of the walk’s iterative mass-transfer recursion. As a long-form application, we map the construction onto the Standard Model fermion content and derive the CKM mixing hierarchy as a code-distance phenomenon, with the ratio |Vub|/|Vcb|≈0.1 recovered from the double-spectral-gap activation threshold for outer-code transitions, matching experiment without fitted parameters. The Standard Model identification is presented as evidence for the construction’s physical relevance; the cs.IT results are independent of it. 2026-06-20 legacy erratum: This version adds a canon erratum note to the legacy paper. QEC-code basis likely useful but should reference forced-byte theorem The body is preserved as a historical derivation trail; the erratum note identifies the current ANCHOR/DRIFT status and superseded claims. 2026-06-21 canon refresh: This version incorporates the 2026-06-21 ANCHOR/DRIFT/PTMS canon refresh and rebuilt local PDF.