The Lineage Ruler: From Binary Recursion to Physical Constants

This study is based on the empirical fact of spatial asymmetry between the atomic nucleus and the electron cloud: an external observer is closer to the electrons and farther from the nucleus. Combined with Coulomb's law, this leads to the proposal that macroscopic objects possess an extremely tiny net residual charge difference, on the order of 10 to the minus 52 coulombs. Starting from this point, we establish the integer power relations between the strengths of the four fundamental interactions and the fine-structure constant alpha. We then adopt the binary recursive transformation x goes to 2x+1 and 2x+3 to construct the system of lineage digits. The strengths of the four fundamental interactions are expressed as integer powers of alpha multiplied by rational coefficients: gravity as alpha to the 0, the weak interaction as alpha to the 6, electromagnetism as 4/3 times alpha to the 14, and the strong interaction as 3/4 times alpha to the minus 18. The reciprocal of the fine-structure constant is expressed as 2 to the 7 plus 3 squared plus 9 over 2 times 5 cubed, yielding 137.0360000, with a deviation of 6 times 10 to the minus 9 from the experimental value. All 28 physical constants can be expressed as lineage fractions multiplied by powers of alpha and basic energy scales, with theoretical values falling within current experimental error ranges. For the carbon-12 Hoyle resonance energy level, this paper provides an empirical relation: E equals 15 times the electron mass minus 8/3 alpha, in MeV. The theoretical value 7.6455 MeV agrees with the 2024 Nature experimental value 7.654 plus or minus 0.007 MeV within the 1.2 sigma confidence interval. The effective lineage combination 57 equals 3 times the quantity 3 plus 7 plus 9 yields 2.90 times 10 to the minus 122, matching the observed cosmological constant within 0.7 percent precision. This paper also proposes 12 falsifiable predictions along with specific experimental test schemes.