Casting-off's greedy first-fit + tail-only widow rebalance is replaced by a
deterministic badness-minimizing break search (optimal_breaks, a Knuth-Plass-
style dynamic program over the measure boundaries). ENGRAVER_VERSION 9 -> 10.
Objective: minimize the sum over ALL systems of the squared normalized underfill
((width_limit - w)/width_limit)^2. Squaring evens the systems; including the
FINAL system in the sum subsumes the old widow rebalance (the optimizer won't
leave a narrow final stub if a balanced partition is cheaper). It is the
additive, DP-tractable analog of the retired distribution_cost (max of the
catalog's break penalty and width-CV imbalance). On the ten-measure fixture the
search settles on 5/4 measures where greedy left a fuller-then-shorter split,
filling the final system more and pulling casting_off_quality down (~0.80 ->
~0.61) — the payoff, visible now that horizontal justification drives
system_break to ~0 so casting_off mostly sees the last system's fullness.
Break requirements (hard/soft/page) bound the DP's segments — a system may not
span a forced break — and walk_region still honours them and records skipped
content-less soft breaks as IrOverride, unchanged; optimal_breaks reports only
the automatic breaks. A system may exceed the width only as a single
unsplittable measure. Minimal still makes no optimality claim.
Deterministic: minimizes lexicographic (cost, system_count). Tests:
optimal_breaks_{balances_systems_and_avoids_a_final_widow, never_spans_a_forced_
break, is_deterministic_and_empty_when_unbounded}; the widow test now checks the
balanced measure distribution; wrapping-fixture metrics updated (casting_off
improved). Removed rebalance_widows/rebalance_region/distribution_cost + their
tests. Goldens regenerated (balanced systems; view_box stable — justification
still fills to width). 944 tests, clippy 0, docs -D warnings, conformance 8/8.
Co-Authored-By: Claude Opus 4.8 (1M context) <noreply@anthropic.com>
Levi Neuwirth
c818992835