The Skin Outlives the Archive: Continuation, Identity, and Unhealable Scars in a Growing Aperiodic World

A Penrose patch grown tile by tile from a seed by a local forced-placement rule reaches sites where no tile fits; the rule pins these as scars and continues elsewhere. We ask how much of the patch's own past such a world must retain, and find that the answer differs by what the past is for. On eleven recorded cases in which growth had committed to one of two sibling histories, a worker that retains only a thin band around the live frontier, run in a separate process with no access to the deleted interior, reproduces the full-patch construction exactly to the tested horizon: identical candidate menus, decisions, placements and random-stream transitions, with no illegal tile. Deleting in addition the lobes of tiles that accumulate around pinned scars, while keeping oriented boundary records and the scars' skip labels, preserves exact continuation at three band radii, in thirty-three of thirty-three trials, and cuts the largest retained band from 644 to 485 of 1,028 tiles. On the radius-2S reduced states, a fixed 528-window compatibility reader makes no A-only calls on B-committed cases under either of two numerical conventions, while a separate control on recovery skins demonstrates correct A-only calls on A-true cases. Yet the same reduced state first disagrees with full history about the legality of a dormant scar at step 35 of one world: the reduced state admits one candidate c where full history admits none. Restoring a single deleted neighbouring witness tile, or only the corner record at a single vertex, restores the full-history rejection on diagnostic copies. A pre-registered perpendicular-space address analysis shows that across all 442 sampled hidden offsets compatible with the local living skin, the ideal cut-and-project tiling places c in the gap (p_c = 1) and never contains the deleted witness tile (p_w = 0). In a pre-registered intervention test extended to step 200, unpinning the scar and allowing the constructor to place c does not resolve the cross-arm jam into a completed floor: in full history minus the witness tile and at radius 1S, the obstruction immediately re-pins on c's own outer edge at the next step, whereas at radii 2S and 3S the advancing live-only cutoff prunes c's unclosed base into the interior before two of its three vertex stars ever complete. Three uses of the past—continuation, identity readout and reconsideration of a closed site—are thereby separated: the living skin serves continuation and preserves both global branch identity and local one-sided address compatibility, whereas the shed witness corner recorded the opposing arm's collision across a structural jam that a single local placement cannot undo. Diagnostics on the full jammed bands show that the perpendicular-space offset varies as a distributed ramp around the ring, with b_perp = 0 on all 190 tested loops, and that reader discrimination localises to the two-dimensional region where the sibling histories' forced consequences diverge. All claims are finite, numerical and scoped to the recorded cases. https://github.com/kekekatie/geometric-impedance/releases/new?target=retention-paper Correspondence: [email protected]