Nuclear Stability and the Periodic Table from PDL Combinatorial Axioms: Derivation of the Valley of Stability, Magic Numbers, and Assembly Rules
Year: 2026
Type: article
Abstract: The Projective Dynamic Logo (PDL) framework derives physical law from four axioms on finite signed graphs, without presupposing spacetime, particles, or fields. This paper establishes a coherent and largely parameter-free derivation of nuclear stability from the proton quintuplet (24, 28, 930, 10087, 11017) and the neutron quintuplet (24, 28, 1032, 9960, 10992) alone. The central results are: (i) the identity T/(Δn+1)² ≈ 1 is a theorem of the quintuplet, entailing N_min(Z) = Z for all Z ≤ Z_sat = 20 as an exact consequence of the neutron survival condition; (ii) the conflict saturation C(Z > 20) = 190·T_pp is exact, with Z_sat = 20 recovered without free parameters; (iii) the valley of stability N_min(Z) is reproduced exactly for all 51 elements from Z = 1 to Z = 82 by the rule N_min(Z) = Z + Σ r_exc(Z'), where the excess tally r_exc ∈ {0, 1, 2, 3} corresponds to the sub-shell structure of the harmonic oscillator with PDL spin-orbit splitting Δn/(2n_u) = 1/12; (iv) the upper boundary N_max(Z) is reproduced to 82% accuracy by linear interpolation between doubly-magic anchor nuclei; (v) the conflict identity N × Q = C(Z) holds algebraically for all (Z, N). The paper also establishes eight explicit assembly rules governing the sequential construction of nuclei from hydrogen to iron, and identifies a structural connection between OP1 of this document and the open problem of deriving the Bekenstein-Hawking coefficient 1/4 in D37/D38: both reduce to the same combinatorial question of counting coherent configurations on a collective PDL surface.
Author: Laubscher, Cédric
Language: English
Subfield: Nuclear and High Energy Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7147643157
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