boundaryRedshift
plain-language theorem explainer
The definition assigns the boundary redshift for reionization epoch index k to the value phi raised to k. Cosmologists modeling RS-derived reionization histories cite it when placing the five epochs on a geometric ladder. The definition is a direct one-line assignment using the self-similar constant phi from the forcing chain.
Claim. The boundary redshift for reionization epoch index $k$ is defined by $z_k = phi^k$, where $phi$ is the golden-ratio fixed point of the Recognition Science forcing chain.
background
The Reionization History from RS module treats reionization as five canonical epochs (configDim D=5): cosmic dark ages (z>20), first stars (z~20), galaxy formation (z~15), bulk reionization (z~7-10), and saturation (z<6). Each boundary redshift occupies one rung on a geometric ladder. This construction rests on the phi-ladder of the framework, where successive scales advance by the self-similar fixed point phi introduced in T6 of the unified forcing chain.
proof idea
One-line definition that directly sets the boundary redshift for index k equal to phi raised to the power k.
why it matters
This definition supplies the geometric ladder required by redshift_ratio (which proves consecutive boundaries differ by the constant factor phi), by redshift_pos (which proves positivity), and by ReionizationCert (which certifies the five-epoch structure). It realizes the geometric progression of reionization boundaries inside the RS cosmology and aligns with the eight-tick octave and D=3 spatial dimensions of the unified forcing chain.
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