The 10 × 10 table is the torus cut open. Rolling glues the units seam (carrying); bending glues the tens seam. Broken pencils fuse, the counting line becomes one helix, and the attractor closes into a true cycle.
Bulger's toroidal Tonnetz presents a space already closed; this animation performs the closing, because the argument lives in the act. Both coordinates of the digit table are residues mod 10, so the table was never a bounded chart: it is the torus cut open along two circles and flattened. Every edge of the table is a cut, not a boundary.
Rolling glues the units seam: the cells x9 become neighbours of x0, and crossing that seam is carrying — the event on which the whole emirp analysis turns, since reversal commutes with arithmetic exactly when no orbit touches a seam. Bending glues the tens seam and the surface closes. Watch three things fuse. The table's digit-sum pencils pair up — sum s and sum s+10 join into one closed curve, so the nineteen classes of the chart become the ten curves of the torus, and what the table shows as two parallel strokes is one line seen across a cut. The counting line itself — successor by +1 — is ten broken slanted strokes on the chart and one closed (1,10) helix on the torus: ordinary counting is helical, not tabular, and "99 rolls over to 00" is not an edge event but a smooth turn. And the reverse-and-subtract attractor, five collinear jumps on the chart, closes into a genuine cycle circulating inside the digit-sum-9 band — reached by everything, containing no emirp.
The palindrome diagonal closes only when both seams glue: self-coincidence is a property of the whole space, not of either periodicity alone. What the wrap does not change is as telling as what it does: the live block, the dead band, the gold nexuses ride the surface unaltered — the torus restores the topology but cannot restore symmetry the arithmetic has broken. That is the contrast with the Tonnetz, whose torus is homogeneous because transposition really is a rotation.
Read strategically — and this reading is imported — the moral is that the boundaries at which tabular thinking stops are artifacts of the cut: "outside the box" is the discovery that the box's opposite edges were always identified. The sequel to this closing is the further fold, by reversal, into the Möbius orbifold (emirp_orbifold.html).
Grading: the identifications are forced (the lattice is (ℤ/10)²); base ten is notational; the strategic reading is imported.