Capacity Selection of Left-Handed Weak Interactions: A QTT Derivation of Neutrino Chirality, V−A Parity Violation, and the Active-Neutrino Mass Spectrum from First Principles

The Standard Model accommodates parity violation in the weak interaction by hand: only the left-handed components of fermions are placed in SU(2)_L doublets while right-handed components are gauge singlets. This article gives a structural origin for that asymmetry inside Quantum Traction Theory (QTT). The key result is a Capacity-Selected Bundle-Visibility principle that combines a budget statement with a localisation statement. Budget: a parity-doubled fundamental dyad would require two independent 2π closures at one address, costing 4π, in violation of A7's per-address bundle budget. Localisation: the A5 visible/hidden factorisation makes this budget statement intrinsically local, closing the loophole that L and R closures could be hosted at distinct addresses. Together with the equal-share J-unitary relabelling lemma of the QTT charge-ledger paper (doi:10.5281/zenodo.20045141), this yields four results as conditional theorems on A1, A4, A5, A6, A7: The dyadic SU(2) gauge connection acts on the visible factor only and is therefore SU(2)_L (Visibility-Gauge Theorem). The weak charged current is automatically V−A. Right-handed neutrinos, if present, are SU(2) singlets (sterile by construction). The active-neutrino mass spectrum is m_1 = 0, m_2 = m_0/ρ, m_3 = m_0 with ρ = 2π·cos(π/8), giving the parameter-free ratio Δm²₃₁/Δm²₂₁ = 4π²·cos²(π/8) = 33.69694, in 0.16σ agreement with NuFIT 6.0 (illustrative normal-ordering propagation). The construction reproduces the one-generation lepton charge table Q(ν_L) = 0, Q(e_L) = −1 from Q = T_3 + Y/2, the maximal parity violation of beta decay (Wu 1957), the m_ν/E-suppressed wrong-helicity rate at relativistic energies (Goldhaber 1958), the three-active-neutrino result N_ν = 2.984 ± 0.008 from invisible Z width (LEP), and one-generation chiral anomaly cancellation. Three load-bearing new results are formally proven: the Single-Chirality Theorem (§3), the Orientation–Chirality Lemma Γ_w → γ_5 (§3.3), and the Visibility-Gauge Theorem (§4). Couplings (g_W, g_Y, v), mixings, generations, the Higgs mechanism, and sin²θ_W are not derived. Six falsifiers: Discovery of an active right-handed neutrino with non-zero SU(2) charge accessible to W exchange Observation of a fundamental low-energy V+A weak current at √s ≲ 10 TeV Robust post-JUNO/DUNE Δχ²_R ≥ 9 departure from R = 33.6969 Confirmed inverted neutrino mass ordering in the minimal sector Clean positive 0νββ signal far above m_ββ ∈ [1.4, 3.6] meV Discovery of a stable elementary low-energy gauge sector requiring an irreducible n ≥ 4 modular birth closure The construction has no continuous fit parameter and adds no new gauge bosons. Cross-paper coherence: the same A1+A5 substrate that selects the visible factor here projects to I_clk = cos(π/8) in the neutrino paper (doi:10.5281/zenodo.19960814) and the π/8 paper (doi:10.5281/zenodo.19979595).