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).

Capacity-Selected Bundle-Visibility (cross-address argument). 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. 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.

Two-layer Mirror Closure (intra-address argument). The companion QTT dyadic-closure paper (doi:10.5281/zenodo.20053462) closes the residual intra-address mirror loophole in two independent layers: a categorical Fundamental-Dyadic-Closure Theorem (a dyadic bundle is defined by address-support cardinality |I|=2 with distinct sub-addresses, never by the numerical sum π+π), and three structural obstructions (Wigner-Weyl Capacity, γ₅-Non-Endomorphism, Layer-collapse). The Single-Chirality conclusion now stands on five independent logical legs: cross-address budget and localisation (this paper), plus the categorical Layer 1 and three intra-address Layer 2 obstructions of the dyadic-closure paper.

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:

1. The dyadic SU(2) gauge connection acts on the visible factor only and is therefore SU(2)_L — now an immediate corollary of the Sub-Address/A5 Lock.
2. The weak charged current is automatically V−A.
3. Right-handed neutrinos, if present, are SU(2) singlets (sterile by construction).
4. The active-neutrino mass spectrum is m₁ = 0, m₂ = m₀/ρ, m₃ = m₀ 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.

The construction reproduces the one-generation lepton charge table Q(ν_L) = 0, Q(e_L) = −1 from Q = T₃ + 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.

Load-bearing new results in this paper: the Single-Chirality Theorem (§3) and the cross-address Capacity-Selected Bundle-Visibility argument. The Orientation–Chirality Lemma Γ_w → γ₅ is reduced from load-bearing to basis-and-convention via the dyadic-closure paper's Wigner-Weyl Capacity Theorem. The Visibility-Gauge Theorem is reduced to an immediate corollary of the Sub-Address/A5 Lock. Couplings (g_W, g_Y, v), mixings, generations, the Higgs mechanism, and sin²θ_W are not derived.

Seven 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.
• Demonstration that the framework manuscript's I ⊂ W reading is not the correct definition of "dyadic" (would falsify the Layer 1 categorical argument of the dyadic-closure paper).

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).

Companion paper: Fundamental Dyadic Closure and Mirror-Doublet Exclusion in QTT (doi:10.5281/zenodo.20053462) — provides the two-layer Mirror Closure (Layer 1 categorical + Layer 2 with three obstructions) that closes the intra-address mirror loophole referenced throughout this paper.