<!-- SOLID CITY · part 2502 -->
to ARRIVE at
    // it — the junction pad stands on honest fill so the three
    // roads that meet here meet LEVEL, because the face east of
    // this shoulder forbids the traverse to dive to the climb.
    var probeB2 = smith.buildRoad({ points: ROAD_DEFS[1].slice(headIdx), width: 7.6, furniture: 'bench' });
    var nodeY = probeB2.stations[0].y;
    var bB1 = buildOne('B1', ROAD_DEFS[1].slice(0, headIdx + 1), 'bench', null, nodeY, null, null, { width: 5.6, over: 30 });
    var headSt = bB1.stations[bB1.stations.length - 1];
    var bB2 = buildOne('B2', ROAD_DEFS[1].slice(headIdx), 'bench', headSt.y, null, null, { width: 5.6, over: 30 });
    var hBC = surfSt(bB2, 945, -1487.5);
    buildOne('C', ROAD_DEFS[2], 'bench', hBC.y, null, hBC);
    // the spur is hosted by THE PAD: a junction is a level place,
    // and a guest leaving it should be held to the pad's own
    // plane — not to the arrival pitch of whichever road happened
    // to be built first. (Its host was the climb's last station,
    // and when the climb's line moved, the spur's first metres
    // were clamped to a falling plane: a 72% kink at the seam.)
    var headPad = { x: 915, z: -1285, y: headSt.y, grade: 0, bank: 0, fx: 0, fz: 1, rx: 1, rz: 0 };
    buildOne('S', ROAD_DEFS[3], 'bench', headSt.y, null, headPad);
    var hA = surfSt(bB1, 430, -1065);
    buildOne('A1', ROAD_DEFS[0].slice(1).reverse(), 'street', null, hA.y);
    buildOne('A2', [[430, -1065], [640, -1005]], 'street', hA.y, null, hA);
    apronAt(915, -1285, headSt);
    apronAt(945, -1487.5, hBC);
    apronAt(430, -1065, hA);
    // THE CLEARANCE OF SURFACES: the drive reads VOID at a
    // sample when the HIGHEST standing triangle there rises
    // above the world's gate — the road's own profile plus 1.6.
    // Where benches braid, an upper road's shoulder can be that
    // highest triangle over a lower road's line, and the lower
    // road is voided beneath a surface it cannot use. The law
    // therefore strikes the ARGMAX ONLY: the single highest
    // triangle at each voided sample, pass after pass, until no
    // centreline sample of any road is voided by a road's own
    // triangles. Nothing else is struck — a triangle that merely
    // rises over a neighbour's line is a bench, and benches are
    // the country these roads are built in. Struck triangles
    // remain in the eye; they are removed from the standing only.
    // THE OWN-SHEET PROTECTION (the hardening, 2026-10-14): the
    // law as first written knew heights but not ownership. At the
    // braid head the spur's young line still runs within metres
    // of the climb's first stations while the spur's own profile
    // already lies more than the gate below them — so the spur's
    // samples read the CLIMB'S OWN RIBBON as a towering bench and
    // struck it, and the standing kept a pinhole at (918,−1292)
    // where a walker on the climb dipped two metres through
    // honest pavement to the sheet below and faced a wall where
    // his road should have carried him. A triangle is therefore
    // asked whose sheet it serves before it is struck: if at the
    // sample it stands within 0.75 m of SOME road's own profile,
    // and the sample lies within that road's corridor — its
    // half-width and a pace more — it is a working surface of its
    // own road, and the law strikes NOTHING at that sample. The
    // threshold itself does not move: 1.6 is this survey's
    // measure of a void, a build-time law of clearance, and is
    // NOT the walker's step gate that governs living feet.
    (function clearSurfaces() {
      if (ROADS_REJECTED) return;   // THE REJECTION: no road surfaces to protect
      var tris = [];
      for (var i = triBase; i < standTris.length; i += 9) {
        tris.push({ i: i, cx: (standTris[i] + standTris[i + 3] + standTris[i + 6]) / 3, cz: (standTris[i + 2] + standTris[i + 5] + standTris[i + 8]) / 3, drop: false });
      }
      var cell = 16, grid = {};
      tris.forEach(function (t) { var k = Math.floor(t.cx / cell) + ':' + Math.floor(t.cz / cell); (grid[k] = grid[k] || []).push(t); });
      function triYAtLocal(x, z) {
        var best = -Infinity, arg = null;
        var bx = Math.floor(x / cell), bz = Math.floor(z / cell);
        for (var a2 = -1; a2 <= 1; a2++) for (var b2 = -1; b2 <= 1; b2++) {
          var list = grid[(bx + a2) + ':' + (bz + b2)]; if (!list) continue;
          for (var q = 0; q < list.length; q++) {
            var t = list[q]; if (t.drop) continue;
            var ax = standTris[t.i], ay = standTris[t.i + 1], az = standTris[t.i + 2], bxx = standTris[t.i + 3], by = standTris[t.i + 4], bzz = standTris[t.i + 5], cx2 = standTris[t.i + 6], cy = standTris[t.i + 7], cz2 = standTris[t.i + 8];
            var d = (bzz - cz2) * (ax - cx2) + (cx2 - bxx) * (az - cz2);
            if (Math.abs(d) < 1e-9) continue;
            var w0 = ((bzz - cz2) * (x - cx2) + (cx2 - bxx) * (z - cz2)) / d;