rsDampingTarget
plain-language theorem explainer
Defines the Recognition Science structural echo-damping target as the numerical constant 0.618033988750, i.e. one over the golden ratio. Downstream GWTC-3 one-member ringdown checks cite it as the predicted per-cycle QNM damping ratio. The body is a bare real literal; no proof is required.
Claim. The RS structural echo-damping target is the real number $0.618033988750$, equal to $\varphi^{-1}$ where $\varphi$ is the golden-ratio fixed point.
background
This module maps a single GWTC-3 ringdown sample member to a per-cycle quasi-normal-mode (QNM) damping ratio
$$\mathrm{damping_per_cycle} = \exp\bigl(-1/(f_{t_0}\tau_{t_0})\bigr)$$
from the reported frequency and damping time. Recognition Science predicts that structural echo-train damping sits at the Berry creation threshold $\varphi^{-1}$, with $\varphi$ the unique self-similar fixed point forced by the T5–T6 uniqueness chain for the cost $J$.
The constant here is that target written to twelve decimal places. Sibling definitions in the same file hold the empirical mean, quantiles, and $z$-score of the derived damping statistic for the HDF5 member rin/rin_S190727h_pyring_DS_1mode_10M.h5. The comparison is deliberately one-member and structural only.
proof idea
There is no proof. The declaration is a definitional abbreviation of the real literal $0.618033988750$. Downstream interval theorems simply unfold this name and discharge the resulting numeric inequalities by norm_num.
why it matters
The constant is the numerical anchor for the module’s closure theorems: damping_target_inside_68_interval and damping_target_inside_90_interval assert that the target lies strictly between the sample’s 16–84% and 5–95% quantiles; the certificate structure and the one-statement theorem package those facts together with a $z$-score bound. In the broader framework it realizes the Berry threshold $\varphi^{-1}$ (primer landmark) as a concrete GWTC-3 observable, without claiming archive-wide coverage or identity between single-mode QNM damping and the full RS echo-train damping law.
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