bounceRadius
plain-language theorem explainer
The bounce radius at recognition rung gap N is defined as phi raised to N in RS-native units with Planck length set to 1. Gravitational-wave researchers modeling black-hole echoes would cite this scaling to derive the two-way travel time across the bounce region. The definition is a direct power expression using the constant phi.
Claim. The RS bounce radius at rung gap $N$ equals $r_0(N) = phi^N$ in RS-native units (Planck length unity).
background
Recognition Science replaces the classical singularity with a bounce when the J-cost of the contracting interior diverges at the Planck scale. The module sets the bounce radius as the minimum radius reached during collapse, with echo delay given by twice that radius times log phi. Upstream results supply the same power definition: QuantumGravityFromRS states bounceRadius N as phi^N and interprets it as r_min(N) = phi^(N/2) in its native scaling.
proof idea
Direct definition: bounceRadius N is set equal to phi raised to the power N. No lemmas or tactics are invoked; the expression serves as the base case for downstream positivity and ratio theorems.
why it matters
This definition supplies the scaling law required by BHEchoesCert to certify bounce-radius positivity and the adjacent-rung ratio property. It fills the structural identity for echo delay stated in the module documentation. The power law connects directly to the phi-ladder and the self-similar fixed point forced in T5-T6 of the unified forcing chain.
Switch to Lean above to see the machine-checked source, dependencies, and usage graph.