predictedBounceRadius
plain-language theorem explainer
The definition maps each of the four headline LIGO/Virgo events to a bounce radius given by phi raised to the event-specific recognition rung. Gravitational-wave analysts testing echo signatures would cite these values to convert observed masses into RS-native radius predictions. It is realized as the direct substitution of the event rung into the general bounce-radius expression phi to the power N.
Claim. For each headline event $e$, the predicted bounce radius is given by $r(e) = phi^{N(e)}$, where $N(e)$ is the recognition rung assigned to $e$ by logarithmic mass scaling.
background
The module records per-event predictions for black-hole echo signatures drawn from the Recognition Science framework. HeadlineEvent enumerates the four canonical LIGO/Virgo events GW150914, GW170817, GW190521 and GW230529. The companion definition predictedRung assigns to each event an integer rung N obtained from the relation N approximately floor of log base phi of (M over M_ref), yielding the explicit values 8, 1, 10 and 2 respectively.
proof idea
The definition is a one-line wrapper that applies the general bounceRadius function to the output of predictedRung on the input event.
why it matters
This definition supplies the concrete radius values required by the BHEchoCatalogCert structure, which asserts positivity of all predicted quantities together with rung ordering. It realizes the per-event instantiation of the phi-ladder mass formula from the Recognition Science forcing chain (T5 J-uniqueness through T8 D=3), allowing direct comparison with LIGO observations. The catalog as a whole provides a falsifiable prediction set whose violation by any single high-SNR event would challenge the rung assignment rule.
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