Vol3 Section 177 · P-LBG-1 through P-LBG-5

Lyman Break as a Pure {2,3,5} Lattice Node

91.125 nm = 3⁶/2³. Three additional nodal ionisation boundaries predicted at 65.610, 35.156, 42.188 nm — all pure {2,3,5}

Lyman Limit
3⁶/2³ = 91.125 nm
Earth node D=0
·
Venus Node
3⁸/(2²×5²) = 65.610 nm
D=1 boundary
·
Propositions
5
P-LBG-1 to P-LBG-5
The FOT Lyman Limit

91.125 nm = 3⁶/2³ — the formula is its own inverse

The G1 Rydberg denominator (3⁶) reappears as the ionisation wavelength numerator. The LBG phenomenon confirms this constant is cosmologically invariant — the same at z=10 as it is locally.

P-LBG-2 Nodal Ionisation Boundaries
All four nodes: pure {2,3,5}
D=0 (Earth): 3⁶/2³ = 91.125 nm
D=1 (Venus/216): 3⁸/(2²×5²) = 65.610 nm
D=2 (Mercury/115): 3²×5³/2⁵ = 35.156 nm
D=3 (Sun H-bond): 3³×5²/2⁴ = 42.188 nm
Registered Propositions

Key Results

P-LBG-1

Lyman limit = 3⁶/2³ = 91.125 nm. Formula is its own inverse at n=∞.

P-LBG-3

LBG universality at z=3 to z=10+ confirms R_G1 = 2³×10⁹/3⁶ is cosmologically invariant.

P-LBG-5

Three additional nodal boundaries predicted: 65.610, 35.156, 42.188 nm. Observable independent of redshift. Unique FOT testable prediction.

Cross-references: Vol3 Section 177 | Section 176 (P-RYD)
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.