α-Particle (Helium-4 Nucleus)
The τ-α-particle is the smallest doubly-saturated T² nucleon bundle: 2 protons + 2 neutrons whose proton and neutron T² shells are both closed at the magic number N_magic = 2. As a categorical four-defect composite it carries no residual T² mode for further interaction, which is the τ-native explanation of α-particle ubiquity (α-decay product, α-cluster building block, Rutherford projectile, BBN packing voxel).
τ-Definition
The τ-α-particle is the smallest doubly-saturated T² nucleon bundle: 2 protons + 2 neutrons whose proton and neutron T² shells are both closed at the magic number N_magic = 2. As a categorical four-defect composite it carries no residual T² mode for further interaction, which is the τ-native explanation of α-particle ubiquity (α-decay product, α-cluster building block, Rutherford projectile, BBN packing voxel).
Categorical invariant. Smallest stable four-defect-bundle composite on T² × R³ with both spin-isospin shells saturated; categorically inert at the T² level.
Primary registry anchor:
IV.T339
τ-Derivation Chain
-
I.K0— Universe Postulate -
IV.D12— Particle Kind on T² fiber -
IV.P166— Neutron Minimality (anchor for nucleon bundles) -
IV.D528— Nuclear Structure as multi-defect bundle -
IV.T254— Dual Magic Number Structure (proton + neutron T² shell closure at 2) -
IV.R471— Lattice encoding: doubly-saturated T² = 2×2×2 voxel -
IV.D411— α-Decay as ejection of saturated T² unit -
IV.T339— Rutherford scattering formula recovered from τ-Coulomb
SI Translation
Numerical value: 6.6446573357e-27 ± 2.0e-36 kg
Calibration anchor: PG-P01-neutron
Calibration chain:
- m_n (anchor)
- m_p via IV.T142 (proton-neutron mass split)
- B/A ≈ 7.07 MeV binding via SEMF / T²-saturation
- m_α = 2 m_p + 2 m_n − B/c² recovered in SI
Manuscript reference: manuscript-sources/book-04/part05/ch39-alpha-particle-nuclear.tex
Lean Coverage
Status: Planned