Fix tether visible-arc logic for exact internal tangency

- Treat k <= -1 as "other zone contains this rim" so a level-1 gate
  tether at exactly the level-2 anchor's range no longer draws a spurious
  full circle inside the union.
- Update doc comment to clarify external vs internal tangency cases.
- Add regression tests covering the d + rInner = rOuter boundary case.
- Add spacestation music and surface video assets.

dev/tether.test.mjs

@@ -215,6 +215,25 @@ const dist = (x, y, t) => Math.hypot(x - t.x, y - t.y);
           return arcs.length === 1 && Math.abs(arcs[0].a1 - arcs[0].a0 - TAU) < 1e-9;
         })());
 
+  // INTERNAL TANGENCY — the gate case: d + rInner = rOuter EXACTLY (a
+  // level-1 gate tether placed at exactly the level-2 anchor's range:
+  // 5120 + 5120 = 10240). The inner rim lies entirely inside the outer
+  // zone, touching at one point — it contributes nothing to the union
+  // boundary, so the inner tether draws NO line; the outer stays full.
+  // Regression: at k == −1 exactly the old branch fell into "no covered
+  // arc" and drew the whole inner circle as a spurious border inside the
+  // union (visible in-game and on the map).
+  const outerT = new Tether('outer', 0, 0, 1); outerT.radius = 10240;
+  const innerT = new Tether('inner', 5120, 0, 1); innerT.radius = 5120;
+  const fieldT = [outerT, innerT];
+  check('internal tangency: inner rim fully covered → no line inside the union',
+        Tether.visibleArcs(innerT, fieldT).length === 0);
+  check('internal tangency: outer tether stays a full circle',
+        (() => {
+          const arcs = Tether.visibleArcs(outerT, fieldT);
+          return arcs.length === 1 && Math.abs(arcs[0].a1 - arcs[0].a0 - TAU) < 1e-9;
+        })());
+
   // Partial overlap — EXACT covered length (k from the circle geometry):
   //   covered(θ) where cos(θ−β) ≥ k, k = (rA²+d²−rB²)/(2·rA·d)
   const A = new Tether('a', 0, 0, 1); // r = 5120

js/tether/Tether.js

@@ -103,9 +103,13 @@ export class Tether {
    * another zone o ⟺ |P − o| ≤ o.radius ⟺ cos(θ − β) ≥ k, where
    *   β = atan2(o.y − y, o.x − x),  k = (r² + d² − o.radius²) / (2·r·d),
    * d = |center → o|. So each other tether covers the angular interval
-   * [β − arccos k, β + arccos k] (when −1 < k < 1); k < −1 means o
-   * contains this whole rim; k ≥ 1 means no overlap. Union the covered
-   * intervals on the circle; the complement is the visible arcs.
+   * [β − arccos k, β + arccos k] (when −1 < k < 1); k ≤ −1 means o
+   * contains this whole rim — even at EXACT internal tangency (k = −1,
+   * e.g. a level-1 gate tether placed at exactly the level-2 anchor's
+   * range: 5120 + 5120 = 10240), where the rim lies entirely inside o
+   * and contributes no boundary; k ≥ 1 means externally tangent or
+   * disjoint (no covered arc). Union the covered intervals on the
+   * circle; the complement is the visible arcs.
    *
    * @returns {Array<{a0:number, a1:number}>} arcs in [0, TAU), a1 > a0, sorted
    */
@@ -123,8 +127,8 @@ export class Tether {
         continue;
       }
       const k = (r * r + d * d - o.radius * o.radius) / (2 * r * d);
-      if (k < -1) return []; // o contains this disc → the whole rim is covered
-      if (k <= -1 || k >= 1) continue; // tangent or disjoint → no covered arc
+      if (k <= -1) return []; // o contains this rim — strictly, or exactly internally tangent
+      if (k >= 1) continue; // externally tangent or disjoint → no covered arc
       const beta = Math.atan2(dy, dx);
       const half = Math.acos(k);
       covered.push([beta - half, beta + half]);