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Define a +/-1 Heawood face-labelling of a tire, its induced boundary Heawood sequences and restriction relation, and interface compatibility (0<->0, +1<->-1 = vertex face-sum vanishes mod 3). State the Heawood chain-pigeonhole conjecture and a tire route to the Four Colour Theorem, parallel to the medial programme. Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>