The Aligned Twin-Roof Trace in the 6-Wheel / Classical Coordinate Correction, Positive Cluster Transfer, and Renormalized Residuals

This note compares the global twin-event coordinate with the ordinary prime sequence through an aligned radial trace. The trace factors exactly into a twin-counting term and a classical coordinate correction. Explicit prime-coordinate expansions yield a third-order correction formula, a universal first-order gap, and a hierarchy of renormalized residuals. Assuming an unbounded existing event sequence, positive finite cluster behavior transfers between the twin factor and the aligned trace at PNT level. A sealed finite ledger verifies the identities and diagnostics but is not used to infer twin-prime infinitude or the unresolved twin-specific limiting behavior.