A complete scan over 9 Rydberg constants and 3 quantum schemes finds only R_G1 and R_Z with integer quantum numbers yield pure {2,3,5} wavelengths. The exclusivity principle: these are the two and only two natural spectral constants of the Universal Force of Time.
P-RYD-3 Ratio Identity
τ_RZ/τ_R1 = 3⁷/(2⁴×5³) = 2187/2000 [exact]
λ_G1(Hβ)/λ_Z(Hβ) = 4374/4000 | 4374 = 2×3⁷ = C_sun constant Solar circumference encoded in matter/antimatter spectral ratio
Registered Propositions
Key Results
P-RYD-1
R_G1 = 2³×10⁹/3⁶ m⁻¹. Derived exactly from Hβ = 2×3⁵ nm. Pure {2,3}.
P-RYD-6
Z-DNA Paschen n=3→6 = 2³×5³ = 1000 nm exactly. The antimatter helix encodes the 1-micron infrared boundary.
A note on “constants.” Within the Universal Force of Time there are no universal constants. A quantity like the Rydberg is not one fixed number but a small family of register faces — each an exact {2, 3, 5, π} value, each reproducing the spectrum on its own scale of Τ. The Rydberg alone carries at least three: 10,966,227.11 m⁻¹ (= 10⁷π²/9), 10,967,215.73, and 10,973,936.9 m⁻¹. What conventional physics records as the constant — the CODATA 10,973,731.568157 m⁻¹ — is not a fourth fundamental number; it is a single measurement sitting between those faces, in the band they define, read from the one register our instruments occupy: the Earth-surface node, g₁. Every wavelength, and the speed of light, Planck’s value, and the fine-structure ratio with it, behaves the same way — each shifts from g₀ to g₁ to g₂ to g₃ by the lattice step δG, not by error. These are not constants; they are the values Τ wears at the register where we stand.