The Edge-Closure Map: The Locus Is Points and Windows, Not a Surface

AF-33's control found three edge closures at κ_WS = 0 (82 at A = 90, 126 at 132, 184 at 208 — closures the count reaches only at the spectrum's last bound level) and named the edge-closure map as the instrument that would grade them: the (A, κ_WS) locus where the bound census crosses a record closure, graded on continuity. This paper builds the map on AF-33's bench verbatim — its calibration (AF-27's A = 208 gaps) and its control reproduce, and the map's own seven charged points (the three κ_WS = 0 edges; 126 edge at A = 132 at κ_WS = 0.30/0.44/0.60; 82 edge at A = 90, κ_WS = 0.30) are all reproduced by the map's classifier before a single new interval is read. The map's content: every edge set in the plane is either a single isolated point at κ_WS = 0 or a point plus a separated window. Turning the term on from zero first binds more states — the census grows past the closure, which becomes interior — and only at larger κ_WS does the census fall back far enough for the closure to return to the edge (at 132, permanently within the scan; at 90, for a window that closes again at 0.33). At 208 the census never falls back: 184 is an edge at the control's strength and nowhere else. The remaining rows are absences, printed at the same size: at A = 40 the well binds too few states to reach 50 or 82 at any strength; 126 is unreached at A = 90 and 184 at A = 132 at all 61 strengths. Per AF-33's pre-registered grading, the edge prints of the control stand re-graded as points.