one_lt_phi

In Recognition Science, $\varphi$ is forced as the unique self-similar scale factor (forcing step T6). It appears throughout the stack as the rung ratio of the $\varphi$-ladder and as the per-epoch comoving dilation.

This module studies the recognition event horizon. A signal covers eight comoving cells per epoch (T7 eight-tick cadence), while the scale dilates by $\varphi$ each epoch, so the reach in epoch $m$ is $8\varphi^{-m}$. The infinite sum $\sum_m 8\varphi^{-m}$ converges only if the common ratio $1/\varphi$ is strictly less than one, which is exactly $1<\varphi$. The closed form is $8\varphi^2=8(\varphi+1)$.

Upstream, Constants.one_lt_phi proves the inequality from the closed form $\varphi=(1+\sqrt{5})/2$ by comparing square roots; PhiSupport re-exports the same fact.

One-line wrapper: the lemma is definitionally Constants.one_lt_phi. No local arithmetic is repeated. The constants proof itself compares $\sqrt{1}<\sqrt{5}$ and rearranges to $2<1+\sqrt{5}$, hence $1<(1+\sqrt{5})/2$.

Locally, $1<\varphi$ is the hypothesis that makes the geometric series for the recognition event horizon converge to the finite de Sitter scale $8\varphi^2$, which drives Phase-9 $\Omega_\Lambda$ freeze-out (structure beyond the horizon never enters causal contact).

Downstream it is used heavily: pitch JND fractions below one via $\varphi$-powers; stellar $M/L$ bounds $1<\mathrm{ml}<5$ and geometric $M/L$ in $(1,2)$; strict monotonicity of planetary orbital rungs; pulsar bimodal ratio strictly below $\varphi^9$; bond-angle bias and stellar-assembly positivity lemmas. It is the elementary comparison that turns every $\varphi$-ladder inequality into a strict one.