Abstract

We provide a dynamical interpretation of the vacuum anisotropy (projector-weight suppression) required by strong-sector and electroweak normalization within the Axis Model. Without modifying the field content, matching conditions, or Scenario–B effective theory, we show that the static anisotropic kernel used at matching can be reinterpreted as the rotating-frame Hamiltonian of an internal orientation degree of freedom on S2 ≃ SU(2)/U(1). In coherent domains, internal rotational symmetry implies conservation of an internal angular momentum, yielding stationary precession at a fixed tilt angle θ. Observable projector weights then emerge as time-averaged orientation fractions: ωeff = ⟨|⟨ê|Ψ(t)⟩|2⟩ = cos2 θ . We derive the exact relation between θ and the static kernel diagonalization angle, tan(2θ) = 2κ/(Tz − Tx) , and recover the closed form for ωeff from the spectrum of the kernel. We then state falsifiable predictions linking tilt-dependent projector weights to (i) the strong-sector effective color weight ωCeff and (ii) conditional dark-sector scaling limits in which unforced Gμ configurations align vertically. We give a minimal experimental “falsification menu” emphasizing lensing/time-delay relations and environment-dependent transitions controlled by scalar coherence.

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Keywords: Axis Model, vacuum anisotropy, kernel tilt, projector weights, internal orientation, rigid rotor, coherent vacuum, pre-geometric models, gauge coupling normalization, strong sector, electroweak normalization, emergent geometry, scalar coherence, internal angular momentum