A Controlled Effective Geometric Qubit Model in the Helix–Light–Vortex Framework: Two-Level Projection, Finite-Correlation Dephasing, and Locked Null Tests

Abstract

The Bloch-sphere/Bloch-ball representation provides a complete kinematic description of a singlequbit density operator, but it does not assign a microscopic ontology to the two-dimensional Hilbert space. We formulate a controlled Helix–Light–Vortex (HLV)-inspired effective model in which a qubit basis is interpreted as a pair of low-energy helical resonance modes. The construction is explicitly a bridge model, not a derivation of quantum mechanics, a proof of a discrete space-bit substrate, or a derivation of the Born rule. Starting from a scalar-sector kinetic prefactor A(t) = 1+δA(t), we derive the first-order projected Hamiltonian rather than postulating a single Pauli coupling. Canonical reduction gives Heff(t) = 1 2 [ω0 +δω(t)]σz + g(t)σx up to an irrelevant identity term and a basis phase choice, where the longitudinal and transverse coefficients are fixed by matrix elements of the projected kinetic perturbation. This separation distinguishes frequency modulation, which produces Floquet sidebands under a weak probe, from transverse modulation, which produces direct and multiphoton transitions. A slowly varying deterministic χ term is not called memory. A genuine finite-correlation channel is instead introduced through an explicit Gaussian stochastic embedding. For Ornstein–Uhlenbeck correlations, the ensemble-averaged map is completely positive and trace preserving and yields |ρ01(t)| = |ρ01(0)|exp−Γ∞t + Cχ(1 −e−t/τχ) , with Γ∞ = Γ0+σ2 χτχ and C(0) χ =σ2 χτ2 χ, which automatically guarantees 0 ≤ |ρ01(t)| ≤ |ρ01(0)|. The same covariance formalism gives parameterized Bell-state and multi-qubit dephasing predictions. None of these signatures is unique to HLV. The HLV-specific claim is therefore restricted to a future parameter map that predicts modulation and correlation parameters independently of the qubit data being tested. We provide a locked null hierarchy, identifiability requirements, recovery limits, and explicit falsification criteria. The scientifically admissible status is an HLV-inspired effective quantum-information bridge whose specificity remains unestablished until it outperforms ordinary driven-qubit, colored-noise, drift, and correlated-bath models under preregistered tests.