Fundamental Action Normalization and the Scale-Invariant Origin of Dirac's Constant: Unifying Quantum Action and Metric Coupling

In standard Quantum Mechanics and Quantum Field Theory, Dirac's reduced constant (ℏ≡h/2π≈1.0545718×10−34 J⋅s) is introduced as an axiomatic postulate to evaluate phase rotations on a continuous Euclidean circle, lacking an underlying geometric derivation for the2π division. Extending the scale-invariant geometric framework established in prior preprints (Zenodo DOIs: 10.5281/zenodo.22016341, 10.5281/zenodo.22035450, 10.5281/zenodo.22037106), this work demonstrates that Dirac's constant is the exact conformal boundary projection of an irreducible 6-sector discrete action quantum:ℏ0≡6h=1.104345025×10−34 J⋅s Governed by the Conformal Scale Operator Ξ≡π/3≈1.04719755, Dirac's constant is derived ab initio as ℏ≡ℏ0⋅Ξ−1=(h/6)(3/π)=h/(2π), matching exact SI 2019 / CODATA 2024 laboratory standards. Key Mathematical Results: Magnetic Flux Quantization: The macroscopic London/Josephson flux quantum emerges as an exact geometric ratio of 3 discrete action sectors per elementary charge: Φ0=3ℏ0/e=h/(2e)≈2.067833848×10−15 Wb. Lorentz Symmetry Emergence: By analyzing the tensor isotropy of the D6 hexagonal point group and orthogonal temporal foliation (Ni→0), it is proven that no Lorentz-violating operators of dimension ≤4 are generated, strictly preserving continuous SO(1,3)Lorentz covariance and U(1)gauge invariance in the continuum limit. Quad-Domain Orthogonal Unification: The exact same scale operator (Ξ≡π/3) simultaneously unifies early-universe CMB optics (H0=70.58 km/s/Mpc, Asymmetry A=0.0708A=0.0708), galactic dynamics (a0,base≈1.274×10−10 m/s2, Gaia DR3 cutoff at 21.08 kpc21.08 kpc), nuclear baryon density (Ωb=1−3/π≈4.51%, Lithium-7 resolution), and microscopic quantum action with zero free parameters (k=0).