Function s_filtration 

pub fn s_filtration(
    ix: &InfonIndex<RoarPostings>,
    max_s: usize,
    noise: &HashSet<String>,
    sample_cap: usize,
) -> Vec<Level>

Sweep the overlap threshold from 1 to max_s, reporting both topologies at each level.

This is the s-filtration. At s = 1 a single shared item connects almost everything, which is the regime where an unguarded walk drifts to somewhere unrelated to where it began. Raising s demands more agreement per step: edges fall away while component counts climb, so genuine structure separates from coincidence.

sample_cap bounds the edges returned per level; the counts are always exact.