Category: Physics

Summary: Finding the gap-crossing secular coupling strength where the slowest compact-planet eigenmode becomes a balanced inner-edge, bridge-planet, and outer-edge mode rather than separate precession families.

Secular dynamics in compact multiplanet systems are well studied, but the effect of a gap-opening perturber on the structure of the slowest mode is still not fully mapped. This experiment asks when stronger coupling across that gap turns separated inner and outer precession families into a single balanced secular bridge mode.

The script builds dense symmetric Laplace-Lagrange operators for gapped compact-planet chains and uses iterative deepening with repeated eigensolves to bisect the gap-crossing coupling threshold from N=64 to 2048. It tracks whether the slow mode spreads coherently across the inner edge, bridge planet, and outer edge rather than staying split between disconnected regions.

That makes the project a structural transition study of secular architecture, not just a calculation of precession rates. The goal is to identify the onset of a bridge-localized eigenmode in a finite-size threshold map that the script notes has not been systematically established.

Method: Dense symmetric eigensolves with iterative deepening, disorder sampling, and bisection on gap-crossing secular coupling in Laplace-Lagrange operators.

What is measured: Critical secular-coupling threshold, bridge-mode transition score, inner-edge and outer-edge balance, bridge-planet weight, slow-mode localization pattern, and bracket width.