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The bounded-face sum omits the outer face at outer-boundary vertices, so restrict the gluing identity to interior vertices (where all cluster interfaces live) and recover a colouring by carrying a single +/-1 label on the unbounded face f_inf, giving Heawood's identity on the full cubic dual for the Tait step. Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>