BS 7910:2019 §8.9 / Clause 7 — reverse-solve the critical flaw size $a_{crit}$
Answers "under the current loading, how large a flaw can this structure tolerate before it fails". E3 runs a one-dimensional bisection reverse-solve on the delivered E1 fracture assessment engine: holding loads/material/geometry fixed, it searches along flaw size a for the critical a_{crit} where the assessment point just touches the failure assessment line (FAL) or the plastic cut-off.
a_{crit}:\quad K_r(a)=f(L_r(a))\ \text{ or }\ L_r(a)=L_{r,max}\ \text{(whichever comes first)}
E3 calls E1 every iteration; all fracture mechanics live inside E1. Shape constraint is one of two (fixed c or fixed a/c); three states: found / safe_beyond_range (safe across the whole range) / unsafe_at_min (fails at the smallest flaw).
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