feat(diagnostics): warn when parts are closer than the part spacing

Validate Nest, the posting review and console --post now report a
"Part spacing" finding for pairs of parts that do not overlap but sit
closer than the plate's part spacing. Before, only Auto Nest's
Keep/Discard review checked spacing, so hand-edited layouts could be
validated and posted with parts too close together.

Candidates are found with Auto Nest's own outline test, moved into Core
as SpacingOutline (NestLayoutCheck and NestTolerances now use it; Engine
tests unchanged). Because that outline circumscribes arcs by more than
the spacing slack, each candidate is confirmed on native contours
flattened 20x finer than the slack, so arcs placed exactly at the
spacing by interactive fills stay clear. The finding reports the
measured gap and marks the middle of the closest approach. Overlapping
pairs, cut-offs, zero spacing, the plate edge and clamps are not
reported as spacing findings.

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>

docs/post-verification.md

@@ -6,8 +6,9 @@ Choose **Nest > Validate Nest...** to inspect all plates without running the cut
 planner or selecting a post processor. It opens the editor's read-only side panel
 in **Validate Nest (live programs)** mode, distinct from the panel's unapplied
 **Plan Cutting** proposal. The validation panel checks overlapping material,
-missing lead-ins, and rapid crossings in the existing placed programs and cutting
-order. Findings identify plate and part sequence numbers in a read-only grid;
+missing lead-ins, rapid crossings in the existing placed programs and cutting
+order, and parts closer than the plate's part spacing. Findings identify plate and part
+sequence numbers in a read-only grid;
 incomplete or failed checks are never reported as clear. Select a row to switch
 the main plate view to that plate and focus the finding. A colored headline gives
 the warning count by kind (or says the check is incomplete or clear), a single line
@@ -21,7 +22,8 @@ restores normal rendering without changing drawing colors or selection.
 Overlaps use the same magenta material shading as **View > Overlap Check**. A
 DPI-scaled ring expands and fades continuously while the finding is selected;
 both its color and contrasting halo fade as it grows. For overlaps the ring marks a point inside the largest
-shared patch; for missing lead-ins it marks the contour start. Rapid warnings
+shared patch; for missing lead-ins it marks the contour start; for part spacing it marks
+the middle of the closest gap. Rapid warnings
 pulse the offending orange dashed segment continuously and mark its contacts with
 the completed contour using fixed-screen-size magenta crosshairs with white halos.
 Contacts use native lines/arcs and the rapid check's existing numerical tolerances;
@@ -32,7 +34,8 @@ findings without a usable location do not invent a marker. Closing the inspector
 clears the highlight and restores the original plate, zoom, and overlap display mode.
 
 Validation does not change placements, programs, lead-ins, or cutting order, save
-the nest, or write CNC output. Minimum spacing and plate boundaries are not checked.
+the nest, or write CNC output. Spacing to the plate edge and to clamps, and plate
+boundaries, are not checked.
 It does not verify a post processor's final output. Posting still runs its own
 fresh verification and consent flow.
 
@@ -92,6 +95,18 @@ shows the first three check categories, even when there are no findings:
   are not reported. A part whose clean material cannot be captured makes the check
   incomplete for leads near it. This line appears in the summary only when there is such
   a finding.
+- **Part spacing:** two parts closer than the plate's part spacing without sharing material
+  (overlapping pairs are reported only as overlaps). Candidate pairs come from each part's
+  clean nesting material (leads excluded) tested exactly as Auto Nest's layout check tests
+  it, with the shared `SpacingOutline` and `SpacingSlack`, so a layout Auto Nest accepted
+  stays clear. That outline circumscribes arcs by more than the slack, so each candidate is
+  confirmed on its native contours flattened 20 times finer than the slack. The review warns
+  only when that gap falls short of the spacing by more than `SpacingSlack`, which lets
+  interactive fills that place arcs exactly at the spacing pass. On curves it is therefore
+  slightly more lenient than Auto Nest's check, never stricter. Zero spacing allows contact.
+  A part inside another's cutout is held to the spacing from the hole edge. Cut-offs, the
+  plate edge and clamps are not spacing-checked. The finding gives the measured gap; this
+  line appears in the summary only when there is such a finding.
 - **Nested parts:** a part whose perimeter lies strictly inside a cutout of another part (its
   host), proven on clean material exactly as Plan Cutting proves its inner-before-host
   prerequisite. **Nested part order** warns when the nested part comes after its host in the