fix(cutting): aim perimeter entries toward the next part

No-hole parts now choose the outside entry through the S03-S08 pipeline
at the part boundary: rank the native catalogue toward the NEXT cut's
placed-material centre, lazily certify each emitted lead with the shared
validator, cap at maxEntries with side coverage. The next cut is the
next unfinished part on the supplied order (re-read after every
learned-order replan) or, in sequence-free fallback, the nearest
dependency-ready remaining part with stable ordinal ties; the last part
has no target and ranks by tier then arrival distance — never the plate
origin. Target and arrival are converted to prepared LOCAL coordinates
exactly once; geometry is already rotated.

The look-ahead rank survives Follow's ordering: children sort by
nearest source first (the sequence-free tour stays nearest-first), then
contour, then the selection rank — plain OrderBy(Distance) can no longer
undo the facing. Measured fixture (three squares, 0.15 leads, origin
start): legacy cut every sheet at its arrival-nearest lower-left corner
with 10.5-unit cross-sheet rapids totalling 21.0; look-ahead cuts the
+X-facing corner with the same 21.0 total but each inter-part rapid now
starts at the facing edge instead of trailing across the whole sheet.

Uncertain validator answers are never precheck-refused: they skip the
selected slots but flow to the emitted-prefix Check and complete replay,
which stay the authority — a refused-looking incomplete is reported,
not hidden. A fully evaluated catalogue with no fitting lead surfaces
'No tested lead-in fits on part N, contour M'; budget exhaustion stays a
budget finding. Lead prechecks count separately from DFS expansions; the
pipeline itself is one counted expansion per contour. Full backtracking,
dependencies, locked/fixed programs, cutoff handling, emitted-prefix
Check and complete replay are unchanged; budgets and CuttingPartOrder
untouched. Hole parts keep the legacy path until S12.

docs/cutting-planner.md

@@ -128,6 +128,27 @@ emission; it is not a wall-clock timeout. Callers can cancel. Exhaustion may occ
 before already-generated siblings are traversed; it returns a refusal, not an
 unranked fallback or a proof of geometric impossibility.
 
+## Automatic outside entries and look-ahead
+
+For a part whose only contour is its outside (no holes), the entry is chosen
+automatically toward the NEXT cut: the ranker orders the native candidate
+catalogue by the facing side(s) of the next part's placed-material centre, and
+the shared lead validator certifies each emitted lead lazily until up to
+`maxEntries` feasible candidates remain (side coverage when the cap affords
+it). The next cut is the next unfinished part in a supplied order — recomputed
+after every learned-order replan — or, in the full fallback search, the nearest
+dependency-ready remaining part, stable-ordinal ties; the last part has no
+target and ranks by tier then distance to the tool's arrival. Between source
+parts the tour stays nearest-first; the look-ahead rank only orders the entries
+inside one part's contour stage, so distance sorting cannot undo the facing.
+Uncertain (numerically incomplete) validator answers are never precheck-refused:
+those candidates reach the emitted-prefix check and complete replay unchanged. A
+part/contour with no fitting lead in its fully evaluated catalogue is reported
+as "No tested lead-in fits on part N, contour M"; budget exhaustion stays a
+budget finding and incomplete checks are never presented as geometric
+impossibility. Lead prechecks are tracked separately from expansions. Hole
+parts keep the legacy nearest-entry path.
+
 Selected programs are replayed from the beginning with a fresh checker and fresh
 lead validation, without regenerating them or trusting cached search verdicts.
 Before replay, expected-emission geometry is independently built from the owned