Eleven Fundamental Constants from Four Geometric Primitives

Eleven fundamental constants of physics — the fine-structure constant α, the Bohr radiusa0, the classical electron radius re, the elementary charge e, the speed of light c, thePlanck constant h, the electron mass me, the Newtonian gravitational constant G, and theelectromagnetic constants μ0, ε0, Z0 — are shown to admit closed-form expressions in fourprimitives: two atomic wavelengths, namely the hydrogen Lyman-limit wavelength λLy andthe reduced Compton wavelength of the electron ¯λc, together with two numbers from thecircle, π and the integer 180. Each expression reproduces the CODATA value to the precisionof the input wavelengths, with a single systematic offset — a small multiple of 0.018% perpower of c — that is traced to the definition of the SI second. The constants cluster on aninteger-indexed ladder of powers of the radian conversion (180/π), and the index correctlypredicts which constants carry the offset and which do not. The claim is structural, notdynamical: standard physics is not contradicted, and no equation of motion is altered. Whatis shown is that eleven independently measured parameters are not independent — theyare combinations of two measured lengths and the geometry of the circle. Every result isreproducible with a hand calculator; the inputs and three fully worked computations aregiven. The scope is the constants codification only; particle masses beyond the electron arenot derived and are explicitly demarcated as open.