feat(sim): pure altitude-scrub math module + node unit suite

Per plan Task 1. position->segment, frac->currentTime, audio gains, and
integer-crossing detection; 9 node --test cases green.

Co-Authored-By: Claude Opus 4.8 (1M context) <noreply@anthropic.com>

simulator/static/scrub.js

@@ -0,0 +1,45 @@
+// Pure altitude-scrub math — no DOM. A continuous `pos` (float) is the knob:
+// integers are altitudes/detents, fractions are mid-morph blend. UMD so the
+// browser gets a `HEFScrub` global and `node --test` can require() it.
+(function (root, factory) {
+  const api = factory();
+  if (typeof module !== "undefined" && module.exports) module.exports = api;
+  else root.HEFScrub = api;
+})(typeof self !== "undefined" ? self : this, function () {
+  "use strict";
+
+  const clamp01 = (x) => Math.max(0, Math.min(1, x));
+  const wrapIndex = (i, n) => ((i % n) + n) % n;
+
+  function segmentOf(pos) {
+    const lo = Math.floor(pos);
+    return { lo, frac: pos - lo };
+  }
+
+  function accumToPos(restPos, accumDeg, stepDeg) {
+    return restPos + accumDeg / stepDeg;
+  }
+
+  function fracToTime(frac, duration) {
+    return clamp01(frac) * (duration || 0);
+  }
+
+  function crossfadeGains(frac) {
+    const f = clamp01(frac);
+    return { from: 1 - f, to: f };
+  }
+
+  // Integers strictly crossed moving prevPos -> pos, in travel order. Landing
+  // exactly on an integer counts as crossing it (it commits that altitude).
+  function integerCrossings(prevPos, pos) {
+    const out = [];
+    if (pos > prevPos) {
+      for (let k = Math.floor(prevPos) + 1; k <= pos + 1e-9; k++) out.push({ index: k, dir: 1 });
+    } else if (pos < prevPos) {
+      for (let k = Math.ceil(prevPos) - 1; k >= pos - 1e-9; k--) out.push({ index: k, dir: -1 });
+    }
+    return out;
+  }
+
+  return { clamp01, wrapIndex, segmentOf, accumToPos, fracToTime, crossfadeGains, integerCrossings };
+});