A Topological Substrate for the Higgs Mechanism: Deriving the Fermion Yukawa Sector from Quantum Error Correction on the Z3 ⊗ Q3 Lattice

The Standard Model relies on a continuous Higgs field and parametrically tuned Yukawa couplings to equate fermion inertial mass with scalar transition amplitudes. We propose a discrete topological origin for the fermion Yukawa sector based on a quantum error- correcting (QEC) substrate, replacing arbitrary mass matrices with at most one continuous parameter: the lattice spectral gap γ. Identifying the Higgs VEV with the topological crys- tallisation of the lattice’s chirality constraint (W= χ), we evaluate macroscopic couplings via first-principles boolean matrix mechanics on the 256-dimensional codespace. We demonstrate that the spatial shift operator drives two parallel exponential mecha- nisms. First, the probability of virtual excursions into the penalized subspace generates the Yukawa coupling (yf ∝ p), natively decoupling massless gauge bosons. Second, exponential resistance to spatial hopping governs the particle’s Topological Dwell Time, generating its inertial mass (mf ∝ τ). Because both parallel mechanisms are driven by topological frus- tration across Cartesian bridges, they naturally scale identically, structurally deriving the yf ∝ mf equivalence principle without double-counting. Dressing these transition elements with kinematic cutoffs restricts top-quark transitions, initiating a decay cascade governed by a geometric degeneracy between areal impedance (R2 = 2.25) and QEC frustration (exp(1/2ϕ) ≈ 2.245), natively concentrating∼ 49.2% of the bare decay width into surviving Gen 3 channels. Computational Python proofs are provided.