Add second full medial tire cut walk (seed 2)

Source-dual cut is a spanning tree of the dual (38 faces, 37 edges,
connected and acyclic) after 20 cut edges removed.

Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>

papers/medial_tire_cuts/experiments/full_walk/full_medial_tire_cut_walk_2.md

@@ -0,0 +1,32 @@
+# Full medial tire cut walk 2
+
+- base vertices: 20
+- deep-embedded vertices: 21
+- deep-embedded edges: 57
+- graph seed: 2
+- deep-embedded minimum degree: 3
+- chosen face: (4, 12, 11)
+- chosen source cap vertex: 20
+- root entry tooth: e3
+- recognised treads: 3
+- skipped treads: [((0, 0), 'only 0 up teeth')]
+- removed source-dual edges: 20
+- annular/cap cuts: 5
+- up-apex cuts: 15
+
+- **source-dual cut is a tree: True** (38 dual faces, 37 edges, 1 component(s), acyclic=True)
+
+- dual cut figure: `full_medial_tire_cut_walk_2_dual.png`
+- tire cut grid: `full_medial_tire_cut_walk_2_tires.png`
+- combined PDF: `full_medial_tire_cut_walk_2.pdf`
+
+| tread | depth | component | annular | up | singleton down | bite apexes | entry | closing cuts | up-apex cuts | shared/entry skipped |
+|--:|--:|--:|--:|--:|--:|--:|--:|--:|--:|--:|
+| T1 | 1 | 0 | 10 | 3 | 7 | 0 | e3 | 1 | 2 | 1 |
+| T2 | 2 | 0 | 15 | 7 | 8 | 0 | e3 | 1 | 6 | 1 |
+| T3 | 3 | 0 | 10 | 8 | 0 | 1 | e7 | 2 | 7 | 1 |
+
+## Removed Source-Dual Edges
+
+- annular/cap: `[(3, 4), (3, 9), (8, 9), (11, 20), (15, 7)]`
+- up apexes: `[(0, 3), (0, 5), (1, 2), (1, 6), (2, 9), (10, 18), (11, 12), (12, 4), (13, 5), (13, 19), (14, 6), (14, 15), (15, 16), (16, 17), (18, 19)]`