Treat each disjoint annular cycle as its own full medial tire graph

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A tread's annular frontier can split into several disjoint cycles; each
is now recognised as a separate full medial tire graph instead of
disqualifying the whole tread.

- recognise() returns a list of (g, bij), one per annular cycle
  component; add annular_cycle_components() and _recognise_one(), and
  iterate components in iter_pieces().
- Key tires/results by (depth, component) throughout both experiment
  drivers: _label_treads chains each tire to a parent-depth down tooth
  sharing its apex; _cap_cut/_assemble_cut_graph/to_json/summary and the
  dual-cut collectors/draws follow suit.

Source vertex selection for the dual-cut experiment now deep-embeds a
random face and roots at the outer-cap vertex. The source-dual figure
labels the source-graph vertices, highlights the entry medial vertex,
and uses a cap-rooted concentric layout.

For seed 7 / face (14,15,19) this recognises treads 3 and 4 as two
tires each (3.0,3.1,4.0,4.1), so every dual face is now cut.

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

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didericis

2026-06-15 12:01:36 -04:00

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papers/medial_tire_cuts/experiments/deepcap_seed7_cap.png

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