Function delta_to_chain_cap 

pub fn delta_to_chain_cap(delta: f64) -> u32

Map a user-facing delta (max acceptable RO ratio loss, in absolute units) to a chain-walk depth cap for longest_in. Empirically calibrated against gestalt::instrument’s chain depth histogram on the mypy/sympy corpora:

delta	cap	covers
0.00	u32::MAX	exact (default)
0.01	12	p99.5+
0.05	7	p99
0.10	5	p95
0.20	3	p85
0.50	2	p70
1.00	1	only fstate, no walk

Formula: cap = ceil(1 / sqrt(delta)) clamped to ≥1 for delta > 0. Pure heuristic — the property test in tests/approx_ro.rs verifies the actual loss stays below delta on a representative corpus.