Series Paper — SS-Line
Strong Sector Series
SS-8: Interstitial-Neutron Binding in Alpha-Cluster Nuclei: The 2E/V Scaling Law from Simplicial Polytope Geometry
Twelve concurrent interstitial-neutron binding predictions from a single geometric average over polytope edges
Two sub-1.5% hits at most symmetric polytopes
Abstract: SS-8 derives single-neutron interstitial binding in alpha-cluster nuclei from CPP primitives as Delta_1 = (2E/V) B_pair = (6 - 12/N_alpha) B_pair, where V = N_alpha is the alpha-polytope vertex count, E = 3V - 6 its simplicial edge count, and B_pair = M_0/phi ≈ 2.342 MeV is the inherited K_3-mode quantum from SS-5/SS-7. Twelve concurrent zero-parameter predictions at N_ex = 2 across strict N = Z alpha chains for N_alpha in {3,…,14} hold the effective-coordination residual below 15% for eleven of twelve rows, with sub-1.5% agreement at the two most symmetric polytopes: ²⁶Mg (octahedron, -0.2%) and ⁴²Ca (gyroelongated square bipyramid, -1.0%). The derivation inherits hypotheses C1–C4 from SS-5/SS-7 and introduces D1–D3 with D1 promoted to a conditional theorem at Level-1+2 independence. A secondary extension covers 30 additional cells at N_ex ∈ {3,…,8}.
- ²⁶Mg octahedron Δ_1 to -0.2%, ⁴²Ca to -1.0%
- 12 concurrent zero-parameter predictions at N_ex=2
- 30-cell secondary extension grid at N_ex ∈ {3,…,8}