map/mapGenerator.js

import { CUSTOM_NAMES, NAME_PARTS } from "./names.js";
import {
  applyLandscapeUnitAdminPartition,
  generateAdminRegions,
  lockSmallUrbanComponentsToMunicipality,
  mergeTinyMunicipalities,
  removeMunicipalExclaves,
  smoothAdminRegionsTerrainAware,
  snapAdminBoundariesToTerrain,
} from "./adminRegions.js";
import { pickEntities } from "./entitySelection.js";
import { createMapFields } from "./fields.js";
import { MinHeap } from "./graph.js";
import { CELL_SIZE, INF, MAP_H, MAP_W, SIZE, clamp, indexOf, inside, nearMapEdge, xyOf } from "./grid.js";
import { fbm, hash2, lerp, rand, smoothstep, valueNoise } from "./random.js";

export { CELL_SIZE, MAP_H, MAP_W, indexOf } from "./grid.js";

function neighbors8(x, y) {
  const out = [];
  for (let dy = -1; dy <= 1; dy++) {
    for (let dx = -1; dx <= 1; dx++) {
      if (dx === 0 && dy === 0) continue;
      const nx = x + dx;
      const ny = y + dy;
      if (inside(nx, ny)) out.push([nx, ny, Math.hypot(dx, dy)]);
    }
  }
  return out;
}

function neighbors4(x, y) {
  const out = [];
  for (const [dx, dy] of [[1, 0], [-1, 0], [0, 1], [0, -1]]) {
    const nx = x + dx;
    const ny = y + dy;
    if (inside(nx, ny)) out.push([nx, ny, 1]);
  }
  return out;
}

function distanceToNearest(points, x, y, fallback = 999) {
  let best = fallback;
  for (const p of points) best = Math.min(best, Math.hypot(p.x - x, p.y - y));
  return best;
}

function aStar(start, goal, costAt) {
  const startIndex = indexOf(start.x, start.y);
  const goalIndex = indexOf(goal.x, goal.y);
  if (startIndex === goalIndex) return [[start.x, start.y]];

  const score = new Float32Array(SIZE);
  const cameFrom = new Int32Array(SIZE);
  const closed = new Uint8Array(SIZE);
  score.fill(INF);
  cameFrom.fill(-1);

  const heap = new MinHeap();
  score[startIndex] = 0;
  heap.push({ i: startIndex, f: Math.hypot(start.x - goal.x, start.y - goal.y) });

  let guard = 0;
  while (heap.length > 0 && guard++ < SIZE * 3) {
    const current = heap.pop();
    if (!current || closed[current.i]) continue;
    closed[current.i] = 1;

    if (current.i === goalIndex) {
      const path = [];
      let p = goalIndex;
      while (p !== -1) {
        const [x, y] = xyOf(p);
        path.push([x, y]);
        if (p === startIndex) break;
        p = cameFrom[p];
      }
      return path.reverse();
    }

    const [cx, cy] = xyOf(current.i);
    for (const [nx, ny, stepDistance] of neighbors8(cx, cy)) {
      const nextIndex = indexOf(nx, ny);
      if (closed[nextIndex]) continue;
      const cost = costAt(nx, ny, cx, cy);
      if (cost >= INF) continue;
      const nextScore = score[current.i] + cost * stepDistance;
      if (nextScore < score[nextIndex]) {
        score[nextIndex] = nextScore;
        cameFrom[nextIndex] = current.i;
        heap.push({ i: nextIndex, f: nextScore + Math.hypot(nx - goal.x, ny - goal.y) * 0.78 });
      }
    }
  }
  return [];
}

function influenceFromPaths(paths, radius) {
  const grid = new Float32Array(SIZE);
  for (const path of paths) {
    for (const [x, y] of path) {
      for (let dy = -radius; dy <= radius; dy++) {
        for (let dx = -radius; dx <= radius; dx++) {
          const nx = x + dx;
          const ny = y + dy;
          if (!inside(nx, ny)) continue;
          const d = Math.hypot(dx, dy);
          if (d > radius) continue;
          const i = indexOf(nx, ny);
          grid[i] = Math.max(grid[i], 1 / (1 + d));
        }
      }
    }
  }
  return grid;
}

function pointKey(p) {
  return `${p.x},${p.y}`;
}

function getDegree(degreeMap, p) {
  return degreeMap.get(pointKey(p)) || 0;
}

function incrementDegree(degreeMap, p) {
  degreeMap.set(pointKey(p), getDegree(degreeMap, p) + 1);
}

function nearestConnectable(points, target, degreeMap, maxDegree = 3) {
  if (!points.length) return null;
  const sorted = points
    .map((p) => ({ ...p, d: Math.hypot(p.x - target.x, p.y - target.y), degree: getDegree(degreeMap, p) }))
    .sort((a, b) => (a.degree >= maxDegree ? 22 : 0) + a.d + a.degree * 7 - ((b.degree >= maxDegree ? 22 : 0) + b.d + b.degree * 7));
  return sorted.find((p) => p.degree < maxDegree) || sorted[0];
}

function corridorPenalty(grid, x, y, hubs, endpoints, strength = 6) {
  if (!grid) return 0;
  const value = grid[indexOf(x, y)];
  if (value <= 0.0001) return 0;

  const nearEndpoint = distanceToNearest(endpoints, x, y) <= 3.2;
  if (nearEndpoint) return 0;

  const hubDistance = distanceToNearest(hubs, x, y);
  if (hubDistance <= 3.5) return 0;
  if (hubDistance <= 7.5) return value * strength * 0.28;
  return value * strength;
}

function nodeAvoidPenalty(points, x, y, endpoints, radius = 3.0, strength = 5.0) {
  if (!points || points.length === 0) return 0;
  if (distanceToNearest(endpoints, x, y) <= radius + 0.4) return 0;
  const d = distanceToNearest(points, x, y);
  if (d >= radius) return 0;
  return (radius - d) * strength;
}

function makeTransportCost(baseCost, existingPaths, hubs, endpoints, radius = 4, strength = 6, avoidPoints = [], avoidRadius = 3.0, avoidStrength = 5.0) {
  const grid = existingPaths.length ? influenceFromPaths(existingPaths, radius) : null;
  return (x, y, cx, cy) => {
    const base = baseCost(x, y, cx, cy);
    if (base >= INF) return base;
    return base
      + corridorPenalty(grid, x, y, hubs, endpoints, strength)
      + nodeAvoidPenalty(avoidPoints, x, y, endpoints, avoidRadius, avoidStrength);
  };
}

function pathLength(path) {
  let total = 0;
  for (let i = 1; i < path.length; i++) total += Math.hypot(path[i][0] - path[i - 1][0], path[i][1] - path[i - 1][1]);
  return total;
}

function pathEndpointDistance(path) {
  if (!path || path.length < 2) return 0;
  const a = path[0];
  const b = path[path.length - 1];
  return Math.hypot(a[0] - b[0], a[1] - b[1]);
}

function pathCompactness(path) {
  const direct = pathEndpointDistance(path);
  if (direct <= 0.001) return INF;
  return pathLength(path) / direct;
}

function pathOverlapRatio(path, existingPaths, radius = 2) {
  if (!path?.length || !existingPaths?.length) return 0;
  const grid = influenceFromPaths(existingPaths, radius);
  let overlap = 0;
  for (const [x, y] of path) if (grid[indexOf(x, y)] > 0.18) overlap++;
  return overlap / Math.max(1, path.length);
}

function compactPathArray(paths, { minLength = 8, maxOverlap = 0.35, maxCount = 99 } = {}) {
  const kept = [];
  for (const path of paths.slice().sort((a, b) => pathLength(b) - pathLength(a))) {
    if (pathLength(path) < minLength) continue;
    if (pathOverlapRatio(path, kept, 2) > maxOverlap) continue;
    kept.push(path);
    if (kept.length >= maxCount) break;
  }
  paths.splice(0, paths.length, ...kept);
}

function bresenhamCells(a, b) {
  const cells = [];
  let x0 = a[0];
  let y0 = a[1];
  const x1 = b[0];
  const y1 = b[1];
  const dx = Math.abs(x1 - x0);
  const dy = Math.abs(y1 - y0);
  const sx = x0 < x1 ? 1 : -1;
  const sy = y0 < y1 ? 1 : -1;
  let err = dx - dy;
  while (true) {
    cells.push([x0, y0]);
    if (x0 === x1 && y0 === y1) break;
    const e2 = 2 * err;
    if (e2 > -dy) { err -= dy; x0 += sx; }
    if (e2 < dx) { err += dx; y0 += sy; }
  }
  return cells;
}

function smoothPathByLineOfSight(path, passable, maxSegment = 9) {
  if (!path || path.length < 3) return path || [];
  const out = [path[0]];
  let i = 0;
  while (i < path.length - 1) {
    let best = i + 1;
    const limit = Math.min(path.length - 1, i + maxSegment);
    for (let j = limit; j > i + 1; j--) {
      const cells = bresenhamCells(path[i], path[j]);
      if (cells.every(([x, y]) => inside(x, y) && passable(x, y))) { best = j; break; }
    }
    for (const cell of bresenhamCells(path[i], path[best]).slice(1)) out.push(cell);
    i = best;
  }
  return out;
}

function averagePathField(path, field) {
  if (!path?.length) return 0;
  let sum = 0;
  for (const [x, y] of path) sum += field[indexOf(x, y)] || 0;
  return sum / path.length;
}

function influenceFromPoints(points, radius, weightFn = () => 1) {
  const grid = new Float32Array(SIZE);
  for (const p of points) {
    const weight = weightFn(p);
    for (let dy = -radius; dy <= radius; dy++) {
      for (let dx = -radius; dx <= radius; dx++) {
        const nx = p.x + dx;
        const ny = p.y + dy;
        if (!inside(nx, ny)) continue;
        const d = Math.hypot(dx, dy);
        if (d > radius) continue;
        const i = indexOf(nx, ny);
        grid[i] = Math.max(grid[i], weight / (1 + d));
      }
    }
  }
  return grid;
}

function samplePath(path, step) {
  const out = [];
  for (let i = step; i < path.length - step; i += step) {
    const [x, y] = path[i];
    out.push({ x, y, score: 1 });
  }
  return out;
}

function smoothMask(mask, passes = 2) {
  let current = new Uint8Array(mask);
  for (let pass = 0; pass < passes; pass++) {
    const next = new Uint8Array(current);
    for (let y = 1; y < MAP_H - 1; y++) {
      for (let x = 1; x < MAP_W - 1; x++) {
        const i = indexOf(x, y);
        let count = 0;
        for (let dy = -1; dy <= 1; dy++) {
          for (let dx = -1; dx <= 1; dx++) {
            if (current[indexOf(x + dx, y + dy)]) count++;
          }
        }
        if (count >= 5) next[i] = 1;
        else if (count <= 3) next[i] = 0;
      }
    }
    current = next;
  }
  return current;
}

function largestConnectedMask(mask) {
  const seen = new Uint8Array(SIZE);
  let best = [];
  const queue = [];

  for (let i = 0; i < SIZE; i++) {
    if (!mask[i] || seen[i]) continue;
    const component = [];
    queue.length = 0;
    queue.push(i);
    seen[i] = 1;

    for (let q = 0; q < queue.length; q++) {
      const cur = queue[q];
      component.push(cur);
      const [x, y] = xyOf(cur);
      for (const [nx, ny] of neighbors8(x, y)) {
        const ni = indexOf(nx, ny);
        if (!mask[ni] || seen[ni]) continue;
        seen[ni] = 1;
        queue.push(ni);
      }
    }

    if (component.length > best.length) best = component;
  }

  const out = new Uint8Array(SIZE);
  for (const i of best) out[i] = 1;
  return out;
}

function componentCount(mask) {
  const seen = new Uint8Array(SIZE);
  const queue = [];
  let count = 0;
  for (let i = 0; i < SIZE; i++) {
    if (!mask[i] || seen[i]) continue;
    count++;
    queue.length = 0;
    queue.push(i);
    seen[i] = 1;
    for (let q = 0; q < queue.length; q++) {
      const [x, y] = xyOf(queue[q]);
      for (const [nx, ny] of neighbors8(x, y)) {
        const ni = indexOf(nx, ny);
        if (!mask[ni] || seen[ni]) continue;
        seen[ni] = 1;
        queue.push(ni);
      }
    }
  }
  return count;
}


function makePrefectureMask(seed, sea, elevation, slope, river) {
  const candidates = [];
  for (let y = 8; y < MAP_H - 8; y++) {
    for (let x = 8; x < MAP_W - 8; x++) {
      const i = indexOf(x, y);
      if (sea[i]) continue;
      const centrality = 1 - Math.hypot((x / MAP_W) - 0.5, (y / MAP_H) - 0.5) / 0.72;
      const score = centrality * 0.28 + (1 - slope[i]) * 0.42 + (1 - Math.abs(elevation[i] - 0.42)) * 0.22 + Math.min(0.16, river[i] * 0.08);
      candidates.push({ x, y, score });
    }
  }

  const regionSeeds = pickEntities(candidates, {
    max: 1,
    minDistance: 18,
    threshold: 0.35,
    seed: seed + 904,
    jitter: 0.02,
  });

  const mask = new Uint8Array(SIZE);
  const dist = new Float32Array(SIZE);
  dist.fill(INF);
  const heap = new MinHeap();
  const landCells = sea.reduce((a, v) => a + (v ? 0 : 1), 0);
  const target = Math.floor(landCells * (0.23 + rand(seed, 906) * 0.08));

  for (const s of regionSeeds) {
    const i = indexOf(s.x, s.y);
    dist[i] = 0;
    heap.push({ i, f: 0 });
  }

  let claimed = 0;
  while (heap.length > 0 && claimed < target) {
    const current = heap.pop();
    if (!current) continue;
    const ci = current.i;
    if (current.f > dist[ci] + 1e-5 || mask[ci]) continue;
    const [cx, cy] = xyOf(ci);
    if (sea[ci]) continue;

    mask[ci] = 1;
    claimed++;

    for (const [nx, ny, step] of neighbors8(cx, cy)) {
      const ni = indexOf(nx, ny);
      if (sea[ni] || mask[ni]) continue;
      const edgePenalty = nearMapEdge(nx, ny, 2) ? 4.2 : nearMapEdge(nx, ny, 5) ? 1.8 : 0;
      const ridgePenalty = Math.max(0, elevation[ni] - 0.5) * 5.4 + Math.max(0, elevation[ni] - elevation[ci]) * 3.2;
      const slopePenalty = slope[ni] * 4.1;
      const riverPenalty = river[ni] > 0.65 ? 2.2 : river[ni] > 0.32 ? 0.9 : 0;
      const cost = Math.max(0.18, 1 + edgePenalty + ridgePenalty + slopePenalty + riverPenalty + Math.abs(elevation[ni] - elevation[ci]) * 4.2) * step;
      const nd = dist[ci] + cost;
      if (nd < dist[ni]) {
        dist[ni] = nd;
        heap.push({ i: ni, f: nd });
      }
    }
  }

  return largestConnectedMask(smoothMask(mask, 2));
}

function generateRegionalPrefectures(seed, sea, elevation, slope, river, ridgeField, flowAccum, anchorMask) {
  const centers = [];
  let sx = 0;
  let sy = 0;
  let sc = 0;
  for (let y = 0; y < MAP_H; y++) {
    for (let x = 0; x < MAP_W; x++) {
      const i = indexOf(x, y);
      if (anchorMask[i]) { sx += x; sy += y; sc++; }
    }
  }
  if (sc > 0) centers.push({ x: Math.round(sx / sc), y: Math.round(sy / sc), score: 2, kind: "Current Prefecture" });

  const candidates = [];
  const ax = centers[0]?.x ?? MAP_W / 2;
  const ay = centers[0]?.y ?? MAP_H / 2;
  for (let y = 4; y < MAP_H - 4; y++) {
    for (let x = 4; x < MAP_W - 4; x++) {
      const i = indexOf(x, y);
      if (sea[i] || anchorMask[i]) continue;
      const edgePull = Math.max(Math.abs(x / MAP_W - 0.5), Math.abs(y / MAP_H - 0.5));
      const awayFromCurrent = Math.hypot(x - ax, y - ay) / Math.hypot(MAP_W, MAP_H);
      const settleable = (1 - slope[i]) * 0.24 + Math.max(0, 0.62 - elevation[i]) * 0.28 + flowAccum[i] * 0.08;
      const score = edgePull * 0.55 + awayFromCurrent * 0.38 + settleable + hash2(x, y, seed + 6100) * 0.06;
      candidates.push({ x, y, score, kind: "Neighbor Prefecture" });
    }
  }
  centers.push(...pickEntities(candidates, {
    max: 9 + Math.floor(rand(seed, 6101) * 6),
    minDistance: 22,
    threshold: 0.38,
    seed: seed + 6102,
    jitter: 0.02,
  }));

  const regionId = new Int16Array(SIZE);
  regionId.fill(-1);
  const dist = new Float32Array(SIZE);
  dist.fill(INF);
  const heap = new MinHeap();
  centers.forEach((center, id) => {
    const i = indexOf(center.x, center.y);
    if (sea[i]) return;
    regionId[i] = id;
    dist[i] = 0;
    heap.push({ i, f: 0 });
  });

  let guard = 0;
  while (heap.length > 0 && guard++ < SIZE * 16) {
    const cur = heap.pop();
    if (!cur || cur.f > dist[cur.i] + 1e-5) continue;
    const [cx, cy] = xyOf(cur.i);
    const curRegion = regionId[cur.i];
    for (const [nx, ny, step] of neighbors8(cx, cy)) {
      const ni = indexOf(nx, ny);
      if (sea[ni]) continue;
      const ridge = Math.max(ridgeField[ni], ridgeField[cur.i]);
      const riverBarrier = Math.max(river[ni], river[cur.i]);
      const divide = ridge * 7.8 + Math.max(0, elevation[ni] - 0.54) * 4.4 + slope[ni] * 3.8;
      const watershed = Math.max(0, flowAccum[cur.i] - flowAccum[ni]) * 0.7;
      const riverCost = riverBarrier > 0.72 ? 4.6 : riverBarrier > 0.35 ? 1.9 : 0;
      const stepCost = Math.max(0.22, 1 + divide + riverCost + watershed + Math.abs(elevation[ni] - elevation[cur.i]) * 3.2) * step;
      const nd = dist[cur.i] + stepCost;
      if (nd < dist[ni]) {
        dist[ni] = nd;
        regionId[ni] = curRegion;
        heap.push({ i: ni, f: nd });
      }
    }
  }
  return { regionId, centers };
}

function extractRegionBorderSegments(regionId, sea) {
  const segments = [];
  for (let y = 0; y < MAP_H; y++) {
    for (let x = 0; x < MAP_W; x++) {
      const i = indexOf(x, y);
      if (sea[i] || regionId[i] < 0) continue;
      const a = regionId[i];
      if (x + 1 < MAP_W && !sea[indexOf(x + 1, y)]) {
        const b = regionId[indexOf(x + 1, y)];
        if (b >= 0 && a !== b) segments.push([[x + 1, y], [x + 1, y + 1]]);
      }
      if (y + 1 < MAP_H && !sea[indexOf(x, y + 1)]) {
        const b = regionId[indexOf(x, y + 1)];
        if (b >= 0 && a !== b) segments.push([[x, y + 1], [x + 1, y + 1]]);
      }
    }
  }
  return segments;
}

function extractMaskBorder(mask, sea = null) {
  const segments = [];
  for (let y = 0; y < MAP_H; y++) {
    for (let x = 0; x < MAP_W; x++) {
      const i = indexOf(x, y);
      const a = mask[i];
      if (x + 1 < MAP_W) {
        const ni = indexOf(x + 1, y);
        const b = mask[ni];
        if (a !== b && !(sea && (sea[i] || sea[ni]))) segments.push([[x + 1, y], [x + 1, y + 1]]);
      }
      if (y + 1 < MAP_H) {
        const ni = indexOf(x, y + 1);
        const b = mask[ni];
        if (a !== b && !(sea && (sea[i] || sea[ni]))) segments.push([[x, y + 1], [x + 1, y + 1]]);
      }
    }
  }
  return segments;
}

function extractAdminBorderSegments(adminId, prefectureMask) {
  const segments = [];
  for (let y = 0; y < MAP_H; y++) {
    for (let x = 0; x < MAP_W; x++) {
      const i = indexOf(x, y);
      if (!prefectureMask[i]) continue;
      const a = adminId[i];
      if (a < 0) continue;
      if (x + 1 < MAP_W && prefectureMask[indexOf(x + 1, y)]) {
        const b = adminId[indexOf(x + 1, y)];
        if (b >= 0 && a !== b) segments.push([[x + 1, y], [x + 1, y + 1]]);
      }
      if (y + 1 < MAP_H && prefectureMask[indexOf(x, y + 1)]) {
        const b = adminId[indexOf(x, y + 1)];
        if (b >= 0 && a !== b) segments.push([[x, y + 1], [x + 1, y + 1]]);
      }
    }
  }
  return segments;
}

function tagInsidePrefecture(points, prefectureMask) {
  return points.map((p) => ({ ...p, insidePrefecture: Boolean(prefectureMask[indexOf(p.x, p.y)]) }));
}

function defaultName(seed, id, entity, nameFields, attempt = 0) {
  return contextualDefaultName(seed, id, entity, NAME_PARTS, nameFields, attempt);
}

function attachIdsAndNames(points, prefix, seed, kindOverride = null, nameFields = null, usedNames = null) {
  return points.map((p, i) => {
    const id = `${prefix}-${i}`;
    const kind = kindOverride || p.kind;

    const customName = CUSTOM_NAMES[id];
    const customProbability = NAME_PROBABILITIES?.customName ?? 1.0;

    const useCustomName =
      Boolean(customName) &&
      hash2(i + prefix.length * 101, seed + i * 37, seed + 99991) < customProbability;

    let name = useCustomName ? customName : null;

    if (!name) {
      for (let attempt = 0; attempt < 8; attempt++) {
        name = defaultName(seed + prefix.length * 1000, id, { ...p, kind }, nameFields, attempt);
        if (!usedNames || !usedNames.has(name)) break;
      }
    }

    if (usedNames && name) usedNames.add(name);

    return {
      ...p,
      id,
      name,
      insidePrefecture: Boolean(p.insidePrefecture),
    };
  });
}

function applyOutputOptions(map, options = {}) {
  if (options.includeDebugFields !== false) return map;
  const slim = { ...map };
  delete slim.settlementCluster;
  delete slim.ridgeField;
  delete slim.valleyField;
  delete slim.basinField;
  delete slim.coastalLowland;
  delete slim.flowAccum;
  delete slim.erosionField;
  delete slim.depositionField;
  return slim;
}

function recalculatePopulationAfterLanduse(modernCities, satelliteCities, populationDensity, landuse, prefectureMask, sea, stationInfluence, roadInfluence, railInfluence) {
  populationDensity.fill(0);
  const allCities = [...modernCities, ...satelliteCities];
  for (const city of allCities) {
    const urbanR = Math.max(4, city.urbanRadius || 8);
    const coreR = Math.max(2, city.coreRadius || 3);
    const popScale = clamp((Math.log10(Math.max(12000, city.population || 12000)) - 4) / 2.25, 0.16, 1.65);
    const r = Math.ceil(urbanR * 2.2);
    for (let dy = -r; dy <= r; dy++) {
      for (let dx = -r; dx <= r; dx++) {
        const x = city.x + dx;
        const y = city.y + dy;
        if (!inside(x, y)) continue;
        const i = indexOf(x, y);
        if (sea[i] || !prefectureMask[i]) continue;
        const d = Math.hypot(dx, dy);
        const lu = landuse[i];
        const landuseWeight = lu === 3 ? 1.85 : lu === 2 ? 1.42 : lu === 4 ? 1.05 : lu === 7 ? 0.82 : lu === 8 ? 0.68 : 0.10;
        const radial = 1 / (1 + Math.pow(d / urbanR, 2.5));
        const core = Math.exp(-(d * d) / (coreR * coreR * 2.0));
        const transit = Math.max(stationInfluence?.[i] || 0, (railInfluence?.[i] || 0) * 0.55, (roadInfluence?.[i] || 0) * 0.24);
        populationDensity[i] += popScale * landuseWeight * (radial * 0.78 + core * 0.38 + transit * 0.18);
      }
    }
  }
  let maxDensity = 0;
  for (let i = 0; i < SIZE; i++) if (prefectureMask[i] && !sea[i]) maxDensity = Math.max(maxDensity, populationDensity[i]);
  if (maxDensity > 0) for (let i = 0; i < SIZE; i++) populationDensity[i] = clamp(populationDensity[i] / maxDensity);

  for (const city of allCities) {
    let urbanCells = 0;
    let coreCells = 0;
    let densitySum = 0;
    const r = Math.ceil((city.urbanRadius || 8) * 2.0);
    for (let dy = -r; dy <= r; dy++) {
      for (let dx = -r; dx <= r; dx++) {
        const x = city.x + dx;
        const y = city.y + dy;
        if (!inside(x, y)) continue;
        const i = indexOf(x, y);
        if (!prefectureMask[i] || sea[i]) continue;
        const d = Math.hypot(dx, dy);
        if (d > r) continue;
        const lu = landuse[i];
        if (lu >= 2 && lu <= 8) {
          urbanCells++;
          densitySum += populationDensity[i];
          if (lu === 3) coreCells++;
        }
      }
    }
    const base = city.isPrefecturalCapital ? 90000 : city.kind === "Satellite City" ? 16000 : 32000;
    const urbanComponent = urbanCells * (city.isPrefecturalCapital ? 1500 : city.kind === "Satellite City" ? 900 : 1200);
    const coreComponent = coreCells * 3200;
    const densityComponent = densitySum * 650;
    city.population = Math.round((base + urbanComponent + coreComponent + densityComponent) / 1000) * 1000;
    city.urbanRadius = clamp(5.0 + Math.sqrt(city.population) / 95, city.kind === "Satellite City" ? 5 : 7, city.isPrefecturalCapital ? 34 : 28);
    city.coreRadius = clamp(1.8 + Math.sqrt(city.population) / 360, 2.2, 9);
  }
}

export function generateMap(seedInput = 114514, options = {}) {
  const seed = Number(seedInput) >>> 0;

  let prefectureMask;
  let prefectureBorder;

  const {
    elevation,
    moisture,
    slope,
    sea,
    river,
    floodplain,
    plain,
    agriculture,
    ridgeField,
    valleyField,
    basinField,
    coastalLowland,
    flowAccum,
    erosionField,
    depositionField,
    flowTo,
    portSuitability,
    crossingSuitability,
    passSuitability,
  } = createMapFields();

  const coastAngle = rand(seed, 11) * Math.PI * 2;
  const coastX = Math.cos(coastAngle);
  const coastY = Math.sin(coastAngle);
  const coastThreshold = 0.22 + rand(seed, 12) * 0.22;
  const coastStrength = 0.15 + rand(seed, 13) * 0.23;

  const seaLevel = 0.285;

  const mountainBlobs = Array.from({ length: 2 + Math.floor(rand(seed, 98) * 3) }, (_, i) => ({
    x: rand(seed, 100 + i) * MAP_W,
    y: rand(seed, 200 + i) * MAP_H,
    r: 10 + rand(seed, 300 + i) * 24,
    h: 0.08 + rand(seed, 400 + i) * 0.16,
  }));

  const ridgeBands = Array.from({ length: 5 + Math.floor(rand(seed, 97) * 4) }, (_, i) => ({
    x: rand(seed, 1500 + i) * MAP_W,
    y: rand(seed, 1600 + i) * MAP_H,
    angle: rand(seed, 1700 + i) * Math.PI * 2,
    width: 3 + rand(seed, 1800 + i) * 7,
    length: 42 + rand(seed, 1900 + i) * 92,
    h: 0.11 + rand(seed, 2000 + i) * 0.22,
  }));

  for (let y = 0; y < MAP_H; y++) {
    for (let x = 0; x < MAP_W; x++) {
      const nx = x / (MAP_W - 1) - 0.5;
      const ny = y / (MAP_H - 1) - 0.5;
      const i = indexOf(x, y);

      const warpX = (fbm(x * 0.62 + 180, y * 0.62 - 90, seed + 3101) - 0.5) * 13;
      const warpY = (fbm(x * 0.62 - 70, y * 0.62 + 210, seed + 3201) - 0.5) * 13;
      const wx = x + warpX;
      const wy = y + warpY;

      let mountains = 0;
      for (const blob of mountainBlobs) {
        const d = Math.hypot(wx - blob.x, wy - blob.y) / blob.r;
        mountains += Math.exp(-d * d * 2.35) * blob.h;
      }

      let ridges = 0;
      for (const ridge of ridgeBands) {
        const dx = wx - ridge.x;
        const dy = wy - ridge.y;
        const along = dx * Math.cos(ridge.angle) + dy * Math.sin(ridge.angle);
        const perp = -dx * Math.sin(ridge.angle) + dy * Math.cos(ridge.angle);
        const lengthFade = smoothstep(1 - Math.abs(along) / ridge.length);
        const serration = 0.72 + valueNoise(wx + along * 0.15, wy + perp * 0.15, seed + 2220, 8) * 0.56;
        ridges += Math.exp(-(perp * perp) / (ridge.width * ridge.width)) * lengthFade * ridge.h * serration;
      }

      const directionalCoast = nx * coastX + ny * coastY;
      const coastWave = (fbm(wx * 0.72, wy * 0.72, seed + 2222) - 0.5) * 0.12 + (valueNoise(wx, wy, seed + 2233, 18) - 0.5) * 0.08;
      const coastLower = smoothstep((directionalCoast + coastWave - coastThreshold) / 0.26);
      // Four terrain-noise bands from continental structure to fine surface roughness.
      const terrainLarge = fbm(wx * 0.36 + 40, wy * 0.36 - 60, seed + 710);
      const terrainRegional = fbm(wx * 0.95 + 80, wy * 0.95 - 20, seed + 777);
      const terrainLocal = fbm(wx * 2.05 + 17, wy * 2.05 - 31, seed + 1777);
      const terrainFine = valueNoise(wx * 2.9 + 11, wy * 2.9 - 19, seed + 2444, 4.5);
      const fineDissection = Math.abs(terrainLocal - 0.5) * 0.08 + Math.abs(terrainFine - 0.5) * 0.035;
      const basin = 0.1 * Math.sin((nx * 3.1 + ny * 1.7 + rand(seed, 15)) * Math.PI) - 0.045 * Math.cos((nx * 5.2 - ny * 3.6 + rand(seed, 16)) * Math.PI);
      const rawElevation =
        0.30 * terrainLarge +
        0.235 * terrainRegional +
        0.105 * terrainLocal +
        0.055 * terrainFine +
        mountains * 0.54 +
        ridges * 1.22 +
        basin +
        fineDissection -
        coastLower * (coastStrength + 0.19) +
        0.055;

      elevation[i] = clamp(0.5 + (rawElevation - 0.5) * 1.26);
      ridgeField[i] = clamp(ridges * 4.8 + Math.max(0, mountains - 0.10) * 0.95 + fineDissection * 2.0);
      basinField[i] = clamp(Math.max(0, -basin) * 3.0 + (1 - coastLower) * Math.max(0, 0.42 - elevation[i]) * 0.7);
      moisture[i] = clamp(0.44 * fbm(wx + 400, wy - 200, seed + 333) + 0.18 * valueNoise(wx, wy, seed + 343, 11) + 0.22 * (1 - Math.abs(ny * 1.7)) + 0.28 * coastLower - Math.max(0, elevation[i] - 0.62) * 0.22);
    }
  }

  for (let y = 0; y < MAP_H; y++) {
    for (let x = 0; x < MAP_W; x++) {
      const i = indexOf(x, y);
      const nx = x / (MAP_W - 1) - 0.5;
      const ny = y / (MAP_H - 1) - 0.5;
      const directionalCoast = nx * coastX + ny * coastY;
      const coastNoise = (fbm(x * 0.95, y * 0.95, seed + 2222) - 0.5) * 0.14 + (valueNoise(x, y, seed + 2233, 13) - 0.5) * 0.08;
      const oceanSide = directionalCoast + coastNoise > coastThreshold + 0.055;
      if (elevation[i] < seaLevel || oceanSide) sea[i] = 1;
      if (sea[i]) elevation[i] = Math.min(elevation[i], seaLevel - 0.018 + hash2(x, y, seed + 2311) * 0.012);
    }
  }

  // Align coastal elevation with the sea mask. This prevents artificial one-cell cliffs
  // when the directional coastline cuts through a high terrain cell.
  for (let y = 0; y < MAP_H; y++) {
    for (let x = 0; x < MAP_W; x++) {
      const i = indexOf(x, y);
      if (sea[i]) continue;
      let nearestSea = INF;
      for (let dy = -7; dy <= 7; dy++) {
        for (let dx = -7; dx <= 7; dx++) {
          const nx = x + dx;
          const ny = y + dy;
          if (!inside(nx, ny) || !sea[indexOf(nx, ny)]) continue;
          nearestSea = Math.min(nearestSea, Math.hypot(dx, dy));
        }
      }
      if (nearestSea <= 7) {
        const coastalCap = seaLevel + 0.018 + nearestSea * 0.028 + Math.max(0, fbm(x * 1.4, y * 1.4, seed + 2350) - 0.5) * 0.022;
        elevation[i] = Math.min(elevation[i], coastalCap);
        coastalLowland[i] = clamp(1 - nearestSea / 7);
      }
    }
  }

  for (let y = 1; y < MAP_H - 1; y++) {
    for (let x = 1; x < MAP_W - 1; x++) {
      const gx = elevation[indexOf(x + 1, y)] - elevation[indexOf(x - 1, y)];
      const gy = elevation[indexOf(x, y + 1)] - elevation[indexOf(x, y - 1)];
      slope[indexOf(x, y)] = clamp(Math.sqrt(gx * gx + gy * gy) * 10.5);
    }
  }

  const landOrder = [];
  for (let y = 1; y < MAP_H - 1; y++) {
    for (let x = 1; x < MAP_W - 1; x++) {
      const i = indexOf(x, y);
      if (sea[i]) continue;
      let low = i;
      let best = elevation[i] + 0.012 * hash2(x, y, seed + 2468);
      let localMean = 0;
      let localMax = elevation[i];
      let localMin = elevation[i];
      let nCount = 0;
      for (const [nx, ny] of neighbors8(x, y)) {
        const ni = indexOf(nx, ny);
        const ev = elevation[ni];
        localMean += ev;
        localMax = Math.max(localMax, ev);
        localMin = Math.min(localMin, ev);
        nCount++;
        const directed = ev + 0.008 * hash2(nx, ny, seed + 2469);
        if (directed < best || sea[ni]) {
          best = directed;
          low = ni;
        }
      }
      if (low !== i) flowTo[i] = low;
      localMean /= Math.max(1, nCount);
      const hollow = Math.max(0, localMean - elevation[i]);
      const relief = localMax - localMin;
      valleyField[i] = clamp(hollow * 8.4 + Math.max(0, 0.42 - elevation[i]) * 0.32 + moisture[i] * 0.08 - ridgeField[i] * 0.18);
      basinField[i] = clamp(basinField[i] + hollow * 2.4 + (relief < 0.055 && elevation[i] < 0.55 ? 0.18 : 0));
      flowAccum[i] = 0.7 + moisture[i] * 0.7 + valleyField[i] * 0.55;
      landOrder.push(i);
    }
  }
  landOrder.sort((a, b) => elevation[b] - elevation[a]);
  for (const i of landOrder) {
    const to = flowTo[i];
    if (to >= 0 && to !== i) flowAccum[to] += flowAccum[i] * 0.82;
  }
  let maxFlowAccum = 0;
  for (let i = 0; i < SIZE; i++) if (!sea[i]) maxFlowAccum = Math.max(maxFlowAccum, flowAccum[i]);
  if (maxFlowAccum > 0) {
    for (let i = 0; i < SIZE; i++) flowAccum[i] = clamp(flowAccum[i] / maxFlowAccum);
  }
  for (let i = 0; i < SIZE; i++) {
    if (!sea[i]) valleyField[i] = clamp(valleyField[i] * 0.68 + Math.pow(flowAccum[i], 0.55) * 0.48);
  }

  // First-order fluvial shaping: cut valley floors on steep/high-flow cells and
  // deposit gently in coastal lowlands and basin floors. This gives visible
  // river valleys without destroying the macro terrain structure.
  const shapedElevation = new Float32Array(elevation);
  for (let y = 1; y < MAP_H - 1; y++) {
    for (let x = 1; x < MAP_W - 1; x++) {
      const i = indexOf(x, y);
      if (sea[i]) continue;
      const flow = Math.pow(flowAccum[i], 0.46);
      const incisionNoise = 0.82 + hash2(x, y, seed + 8120) * 0.36;
      const steepValley = clamp(flow * (0.058 + slope[i] * 0.21 + ridgeField[i] * 0.046) * incisionNoise);
      const lateralCut = clamp(Math.pow(flowAccum[i], 0.66) * valleyField[i] * 0.078);
      const lowSettling = clamp(flow * (coastalLowland[i] * 0.036 + basinField[i] * 0.020 + (elevation[i] < 0.40 ? 0.012 : 0)) * (1 - slope[i] * 0.82));
      erosionField[i] = steepValley + lateralCut;
      depositionField[i] = lowSettling;
      shapedElevation[i] = clamp(elevation[i] - steepValley - lateralCut + lowSettling * 0.72, seaLevel + 0.006, 1);
    }
  }
  elevation.set(shapedElevation);

  for (let y = 1; y < MAP_H - 1; y++) {
    for (let x = 1; x < MAP_W - 1; x++) {
      const i = indexOf(x, y);
      if (sea[i]) continue;
      const gx = elevation[indexOf(x + 1, y)] - elevation[indexOf(x - 1, y)];
      const gy = elevation[indexOf(x, y + 1)] - elevation[indexOf(x, y - 1)];
      slope[i] = clamp(Math.sqrt(gx * gx + gy * gy) * 10.5);
      valleyField[i] = clamp(valleyField[i] + erosionField[i] * 2.1 + depositionField[i] * 0.8 - ridgeField[i] * 0.06);
      basinField[i] = clamp(basinField[i] + depositionField[i] * 1.6);
    }
  }

  const sourceCandidates = [];
  for (let y = 4; y < MAP_H - 4; y++) {
    for (let x = 4; x < MAP_W - 4; x++) {
      const i = indexOf(x, y);
      if (sea[i]) continue;
      const score = elevation[i] * 0.38 + moisture[i] * 0.24 + ridgeField[i] * 0.08 + flowAccum[i] * 0.56 + valleyField[i] * 0.28 + hash2(x, y, seed + 9000) * 0.06;
      if (elevation[i] > 0.40 && elevation[i] < 0.82 && moisture[i] > 0.28 && flowAccum[i] > 0.020 && ridgeField[i] < 0.88) sourceCandidates.push({ x, y, score });
    }
  }

  const sources = pickEntities(sourceCandidates, {
    max: 20 + Math.floor(rand(seed, 910) * 28),
    minDistance: 8,
    threshold: 0.53 + rand(seed, 911) * 0.11,
    seed,
  });

  function nearestWaterGoal(from) {
    let bestSea = null;
    let bestScore = INF;
    for (let y = 0; y < MAP_H; y++) {
      for (let x = 0; x < MAP_W; x++) {
        const i = indexOf(x, y);
        if (!sea[i]) continue;
        const d = Math.hypot(x - from.x, y - from.y);
        const score = d - coastalLowland[indexOf(Math.max(0, Math.min(MAP_W - 1, from.x)), Math.max(0, Math.min(MAP_H - 1, from.y)))] * 2;
        if (score < bestScore) {
          bestScore = score;
          bestSea = { x, y };
        }
      }
    }
    return bestSea;
  }

  function riverRouteCost(x, y, cx, cy) {
    const i = indexOf(x, y);
    const ci = indexOf(cx, cy);
    if (sea[i]) return 0.18;
    const uphill = Math.max(0, elevation[i] - elevation[ci]);
    const downhill = Math.max(0, elevation[ci] - elevation[i]);
    if (!sea[i] && uphill > 0.035 && flowAccum[i] < flowAccum[ci] + 0.015) return INF;
    return Math.max(
      0.18,
      1 +
        uphill * 86 +
        slope[i] * 0.38 +
        elevation[i] * 0.42 -
        downhill * 2.1 -
        valleyField[i] * 0.92 -
        flowAccum[i] * 0.72 -
        moisture[i] * 0.18 -
        coastalLowland[i] * 0.22
    );
  }

  function forceRiverToWater(path) {
    if (!path.length) return path;
    const [ex, ey] = path[path.length - 1];
    if (sea[indexOf(ex, ey)]) return path;
    const goal = nearestWaterGoal({ x: ex, y: ey });
    if (!goal) return path;
    const startElevation = elevation[indexOf(ex, ey)];
    const tail = aStar({ x: ex, y: ey }, goal, (x, y, cx, cy) => {
      const i = indexOf(x, y);
      const ci = indexOf(cx, cy);
      if (!sea[i] && elevation[i] > Math.max(startElevation + 0.045, elevation[ci] + 0.030)) return INF;
      return riverRouteCost(x, y, cx, cy);
    });
    if (tail.length <= 2) return path;
    return path.concat(tail.slice(1));
  }

  function confluenceAnglePenalty(nx, ny, dx, dy, lengthSoFar) {
    if (lengthSoFar < 7 || river[indexOf(nx, ny)] < 0.24) return 0;
    let best = 0.16;
    const inLen = Math.hypot(dx, dy) || 1;
    for (const [rx, ry] of neighbors8(nx, ny)) {
      if (river[indexOf(rx, ry)] < 0.22) continue;
      const rdx = rx - nx;
      const rdy = ry - ny;
      const cos = clamp((dx * rdx + dy * rdy) / Math.max(0.001, inLen * Math.hypot(rdx, rdy)), -1, 1);
      const angle = Math.acos(cos);
      const shallow = angle < 0.45 ? 0.28 : 0;
      best = Math.min(best, Math.abs(angle - Math.PI * 0.62) * 0.045 + shallow);
    }
    return best;
  }

  function traceRiverPath(startX, startY, bonusSeed = 0) {
    let x = startX;
    let y = startY;
    let lastDx = 0;
    let lastDy = 0;
    const path = [];
    const seen = new Set();
    let accum = 0;

    for (let step = 0; step < 600; step++) {
      const i = indexOf(x, y);
      if (seen.has(i)) break;
      seen.add(i);
      path.push([x, y]);
      river[i] += 0.44 + path.length / 160 + flowAccum[i] * 0.55;
      accum += river[i] + flowAccum[i];
      if (sea[i]) break;

      let best = null;
      let bestValue = INF;
      const currentElevation = elevation[i];
      const preferred = flowTo[i];

      for (const [nx, ny] of neighbors8(x, y)) {
        const ni = indexOf(nx, ny);
        const dx = nx - x;
        const dy = ny - y;
        const drop = currentElevation - elevation[ni];
        const uphill = Math.max(0, -drop);
        if (!sea[ni] && uphill > 0.032 && flowAccum[ni] < flowAccum[i] + 0.018) continue;
        let surrounding = 0;
        let surroundingCount = 0;
        for (const [vx, vy] of neighbors8(nx, ny)) {
          surrounding += elevation[indexOf(vx, vy)];
          surroundingCount++;
        }
        const valley = Math.max(0, surrounding / Math.max(1, surroundingCount) - elevation[ni]);
        const sameDirection = lastDx || lastDy ? (dx * lastDx + dy * lastDy) / Math.max(0.001, Math.hypot(dx, dy) * Math.hypot(lastDx, lastDy)) : 0;
        const straightPenalty = Math.max(0, sameDirection) * 0.075;
        const turnPenalty = sameDirection < -0.35 ? 0.24 : 0;
        const sideSwing = Math.abs(dx * lastDy - dy * lastDx);
        const meanderPhase = Math.sin((path.length + bonusSeed * 0.013) * 0.73) * 0.5 + 0.5;
        const meander = sideSwing * (0.032 + meanderPhase * 0.026);
        const flowBonus = ni === preferred ? 0.62 : 0;
        const junctionPenalty = confluenceAnglePenalty(nx, ny, dx, dy, path.length);
        const noise = (hash2(nx, ny, seed + bonusSeed + step * 11) - 0.5) * 0.04;
        const value =
          elevation[ni] * 1.45 +
          uphill * 88 -
          Math.max(0, drop) * 2.05 -
          valley * 1.05 -
          valleyField[ni] * 1.72 -
          flowAccum[ni] * 0.94 -
          moisture[ni] * 0.14 -
          coastalLowland[ni] * 0.28 -
          (river[ni] > 0 ? 0.22 : 0) -
          flowBonus +
          slope[ni] * 0.04 +
          straightPenalty +
          turnPenalty +
          junctionPenalty * 1.35 -
          meander +
          noise -
          (sea[ni] ? 0.6 : 0);

        if (value < bestValue) {
          bestValue = value;
          best = [nx, ny, dx, dy];
        }
      }
      if (!best) break;
      x = best[0];
      y = best[1];
      lastDx = best[2];
      lastDy = best[3];
    }

    const forced = forceRiverToWater(path);
    if (forced.length > path.length) {
      for (const [rx, ry] of forced.slice(path.length)) {
        const ri = indexOf(rx, ry);
        river[ri] += 0.32 + flowAccum[ri] * 0.4;
        accum += river[ri] + flowAccum[ri];
      }
    }
    return { path: forced, accum };
  }

  function traceSmallStreamPath(startX, startY, bonusSeed = 0) {
    let x = startX;
    let y = startY;
    let lastDx = 0;
    let lastDy = 0;
    const path = [];
    const seen = new Set();
    for (let step = 0; step < 160; step++) {
      const i = indexOf(x, y);
      if (seen.has(i)) break;
      seen.add(i);
      path.push([x, y]);
      river[i] += 0.12 + flowAccum[i] * 0.18;
      if ((river[i] > 0.48 && path.length > 5) || sea[i]) break;
      let best = null;
      let bestValue = INF;
      for (const [nx, ny] of neighbors8(x, y)) {
        const ni = indexOf(nx, ny);
        const dx = nx - x;
        const dy = ny - y;
        const drop = elevation[i] - elevation[ni];
        const sameDirection = lastDx || lastDy ? (dx * lastDx + dy * lastDy) / Math.max(0.001, Math.hypot(dx, dy) * Math.hypot(lastDx, lastDy)) : 0;
        const value = elevation[ni] * 1.2 + Math.max(0, -drop) * 26 - Math.max(0, drop) * 1.4 - valleyField[ni] * 1.15 - flowAccum[ni] * 0.55 - moisture[ni] * 0.12 + Math.max(0, sameDirection) * 0.04 - Math.abs(dx * lastDy - dy * lastDx) * 0.018 + (hash2(nx, ny, seed + bonusSeed + step * 13) - 0.5) * 0.05;
        if (value < bestValue) { bestValue = value; best = [nx, ny, dx, dy]; }
      }
      if (!best) break;
      x = best[0];
      y = best[1];
      lastDx = best[2];
      lastDy = best[3];
    }
    return path;
  }

  const riverPaths = [];
  const riverScores = [];
  for (const source of sources) {
    const { path, accum } = traceRiverPath(source.x, source.y, 0);
    if (path.length > 6) {
      riverPaths.push(path);
      riverScores.push(path.length + accum * 0.18);
    }
  }

  const preliminaryMainRiverCells = new Set(riverPaths.slice().sort((a, b) => b.length - a.length).slice(0, 5).flatMap((path) => path.map(([x, y]) => `${x},${y}`)));
  const tributarySources = pickEntities(sourceCandidates
    .filter((p) => !preliminaryMainRiverCells.has(`${p.x},${p.y}`))
    .map((p) => ({ ...p, score: p.score + flowAccum[indexOf(p.x, p.y)] * 0.75 + valleyField[indexOf(p.x, p.y)] * 0.24 })), {
      max: 14 + Math.floor(rand(seed, 915) * 20),
      minDistance: 6,
      threshold: 0.45,
      seed: seed + 916,
      jitter: 0.02,
    });
  for (const source of tributarySources) {
    const { path, accum } = traceRiverPath(source.x, source.y, 4000 + source.x * 7 + source.y * 11);
    if (path.length > 8) {
      riverPaths.push(path);
      riverScores.push(path.length * 0.7 + accum * 0.12);
    }
  }

  const streamPaths = [];
  const streamSources = pickEntities(sourceCandidates
    .map((p) => ({ ...p, score: valleyField[indexOf(p.x, p.y)] * 0.46 + flowAccum[indexOf(p.x, p.y)] * 0.36 + moisture[indexOf(p.x, p.y)] * 0.18 + hash2(p.x, p.y, seed + 918) * 0.05 }))
    .filter((p) => p.score > 0.18), {
      max: 22 + Math.floor(rand(seed, 919) * 20),
      minDistance: 4,
      threshold: 0.18,
      seed: seed + 919,
      jitter: 0.015,
    });
  for (const source of streamSources) {
    const path = traceSmallStreamPath(source.x, source.y, 7000 + source.x * 5 + source.y * 17);
    if (path.length > 4) streamPaths.push(path);
  }

  if (riverPaths.length === 0 && sourceCandidates.length > 0) {
    const fallback = sourceCandidates.slice().sort((a, b) => b.score - a.score)[0];
    let bestSea = null;
    let bestSeaDist = INF;
    for (let y = 0; y < MAP_H; y++) {
      for (let x = 0; x < MAP_W; x++) {
        if (!sea[indexOf(x, y)]) continue;
        const d = Math.hypot(x - fallback.x, y - fallback.y);
        if (d < bestSeaDist) {
          bestSeaDist = d;
          bestSea = { x, y };
        }
      }
    }
    if (bestSea) {
      const fallbackPath = aStar(fallback, bestSea, (x, y, cx, cy) => {
        const i = indexOf(x, y);
        const ci = indexOf(cx, cy);
        if (sea[i]) return 0.25;
        const uphill = Math.max(0, elevation[i] - elevation[ci]) * 24;
        const downhill = Math.max(0, elevation[ci] - elevation[i]) * 1.8;
        return Math.max(0.24, 1 + uphill + slope[i] * 0.7 + elevation[i] * 0.8 - downhill - Math.min(0.55, river[i] * 0.1));
      });
      if (fallbackPath.length > 6) {
        let accum = 0;
        for (const [x, y] of fallbackPath) {
          const i = indexOf(x, y);
          river[i] += 0.42;
          accum += river[i];
        }
        riverPaths.push(fallbackPath);
        riverScores.push(fallbackPath.length + accum * 0.18);
      }
    }
  }

  function sanitizeDownhillRiverPath(path, tolerance = 0.040) {
    if (!path || path.length < 2) return path || [];
    const out = [path[0]];
    for (let k = 1; k < path.length; k++) {
      const [px, py] = out[out.length - 1];
      const [x, y] = path[k];
      const pi = indexOf(px, py);
      const i = indexOf(x, y);
      if (!sea[i] && elevation[i] > elevation[pi] + tolerance) break;
      out.push(path[k]);
      if (sea[i]) break;
    }
    return out.length >= 2 ? out : [];
  }
  function trimMountainHeadwaters(path) {
    if (!path || path.length < 4) return path || [];
    let start = 0;
    while (start < path.length - 3) {
      const [x, y] = path[start];
      const i = indexOf(x, y);
      if (sea[i]) break;
      if (elevation[i] <= 0.72 && (valleyField[i] >= 0.18 || flowAccum[i] >= 0.05)) break;
      start++;
    }
    return path.slice(start);
  }
  for (let r = 0; r < riverPaths.length; r++) riverPaths[r] = sanitizeDownhillRiverPath(trimMountainHeadwaters(riverPaths[r]), 0.032);
  for (let r = riverPaths.length - 1; r >= 0; r--) if (riverPaths[r].length < 2) riverPaths.splice(r, 1);
  for (let r = 0; r < streamPaths.length; r++) streamPaths[r] = sanitizeDownhillRiverPath(trimMountainHeadwaters(streamPaths[r]), 0.026);
  for (let r = streamPaths.length - 1; r >= 0; r--) if (streamPaths[r].length < 2) streamPaths.splice(r, 1);
  river.fill(0);
  for (const path of riverPaths) {
    for (let k = 0; k < path.length; k++) {
      const [x, y] = path[k];
      const i = indexOf(x, y);
      river[i] += 0.42 + k / 170 + flowAccum[i] * 0.55;
    }
  }
  for (const path of streamPaths) {
    for (let k = 0; k < path.length; k++) {
      const [x, y] = path[k];
      const i = indexOf(x, y);
      river[i] += 0.11 + flowAccum[i] * 0.18;
    }
  }

  const expandedRiver = new Float32Array(river);
  for (let y = 1; y < MAP_H - 1; y++) {
    for (let x = 1; x < MAP_W - 1; x++) {
      const i = indexOf(x, y);
      if (river[i] <= 0) continue;
      for (const [nx, ny] of neighbors8(x, y)) {
        expandedRiver[indexOf(nx, ny)] = Math.max(expandedRiver[indexOf(nx, ny)], river[i] * 0.35);
      }
    }
  }
  river.set(expandedRiver);

  // Second fluvial pass uses the actual traced river network. Main channels cut
  // visible V-shaped valleys; lower reaches accumulate alluvial deposits.
  const fluvialElevation = new Float32Array(elevation);
  for (let y = 1; y < MAP_H - 1; y++) {
    for (let x = 1; x < MAP_W - 1; x++) {
      const i = indexOf(x, y);
      if (sea[i] || river[i] <= 0.02) continue;
      const r = clamp(river[i] / 3.4);
      const channelCut = clamp(Math.pow(r, 0.55) * (0.060 + slope[i] * 0.145 + ridgeField[i] * 0.038));
      const valleyWiden = clamp(Math.pow(r, 0.72) * (0.020 + Math.max(0, elevation[i] - seaLevel) * 0.058 + valleyField[i] * 0.040));
      const alluvium = clamp(Math.pow(r, 0.72) * (coastalLowland[i] * 0.030 + basinField[i] * 0.020 + (slope[i] < 0.10 ? 0.010 : 0)));
      erosionField[i] = clamp(erosionField[i] + channelCut + valleyWiden);
      depositionField[i] = clamp(depositionField[i] + alluvium);
      fluvialElevation[i] = clamp(elevation[i] - channelCut - valleyWiden + alluvium, seaLevel + 0.005, 1);
      valleyField[i] = clamp(valleyField[i] + r * 0.62 + channelCut * 6.4);
      basinField[i] = clamp(basinField[i] + alluvium * 3.2);
    }
  }
  // Lateral valley carving around the traced river network deepens valleys and
  // makes ridge/valley contrast legible at the map scale.
  for (const path of riverPaths) {
    for (const [rx, ry] of path) {
      const ri = indexOf(rx, ry);
      const r = clamp(river[ri] / 3.0);
      const radius = r > 0.48 ? 2 : 1;
      for (let dy = -radius; dy <= radius; dy++) {
        for (let dx = -radius; dx <= radius; dx++) {
          const nx = rx + dx;
          const ny = ry + dy;
          if (!inside(nx, ny)) continue;
          const ni = indexOf(nx, ny);
          if (sea[ni]) continue;
          const d = Math.hypot(dx, dy);
          if (d > radius || d === 0) continue;
          const weight = (radius + 0.35 - d) / (radius + 0.35);
          const carve = Math.max(0, weight) * (0.008 + r * 0.026) * Math.max(0.45, slope[ni] + 0.22);
          fluvialElevation[ni] = clamp(fluvialElevation[ni] - carve, seaLevel + 0.005, 1);
          erosionField[ni] = clamp(erosionField[ni] + carve * 3.0);
          valleyField[ni] = clamp(valleyField[ni] + carve * 12.0);
        }
      }
    }
  }

  // Restore rugged summit relief after strong river incision. This prevents highlands
  // from becoming unnaturally flat or visually concave while keeping valleys cut.
  for (let y = 1; y < MAP_H - 1; y++) {
    for (let x = 1; x < MAP_W - 1; x++) {
      const i = indexOf(x, y);
      if (sea[i]) continue;
      const high = clamp((fluvialElevation[i] - 0.62) / 0.26);
      const summit = high * clamp(ridgeField[i] * 1.4 - flowAccum[i] * 0.8);
      const rugged = (valueNoise(x * 2.1 + 19, y * 2.1 - 23, seed + 9661, 3.2) - 0.5) * 0.035;
      const uplift = summit * (0.018 + Math.max(0, rugged));
      if (uplift > 0) {
        fluvialElevation[i] = clamp(fluvialElevation[i] + uplift, seaLevel + 0.005, 1);
        erosionField[i] = Math.max(0, erosionField[i] - uplift * 0.6);
      }
    }
  }

  elevation.set(fluvialElevation);

  // Broad alluvial/coastal/basin plains. The plain score alone is not enough;
  // the elevation surface must also be locally calm, otherwise every lowland
  // still reads as rugged terrain. Smooth only low, wet depositional cells and
  // leave ridges/headwaters untouched.
  for (let pass = 0; pass < 4; pass++) {
    const nextElevation = new Float32Array(elevation);
    for (let y = 2; y < MAP_H - 2; y++) {
      for (let x = 2; x < MAP_W - 2; x++) {
        const i = indexOf(x, y);
        if (sea[i]) continue;
        const lowland = clamp(
          coastalLowland[i] * 0.72 +
          basinField[i] * 0.54 +
          valleyField[i] * 0.34 +
          Math.pow(flowAccum[i], 0.58) * 0.24 -
          ridgeField[i] * 0.62 -
          Math.max(0, elevation[i] - 0.54) * 1.65 -
          slope[i] * 0.74
        );
        if (lowland <= 0.12) continue;
        let sum = 0;
        let weight = 0;
        for (let dy = -2; dy <= 2; dy++) {
          for (let dx = -2; dx <= 2; dx++) {
            const nx = x + dx;
            const ny = y + dy;
            const ni = indexOf(nx, ny);
            if (sea[ni]) continue;
            const d = Math.hypot(dx, dy);
            if (d > 2.25) continue;
            const compatible = clamp(1 - Math.abs(elevation[ni] - elevation[i]) / 0.11);
            const w = compatible / (1 + d);
            sum += elevation[ni] * w;
            weight += w;
          }
        }
        if (weight <= 0) continue;
        const localMean = sum / weight;
        const terrace = Math.round(localMean * 42) / 42;
        const target = lerp(localMean, terrace, 0.28);
        nextElevation[i] = clamp(lerp(elevation[i], target, lowland * 0.42), seaLevel + 0.006, 1);
        if (lowland > 0.55) {
          depositionField[i] = clamp(depositionField[i] + lowland * 0.018);
          erosionField[i] = Math.max(0, erosionField[i] - lowland * 0.012);
        }
      }
    }
    elevation.set(nextElevation);
  }

  for (let y = 1; y < MAP_H - 1; y++) {
    for (let x = 1; x < MAP_W - 1; x++) {
      const i = indexOf(x, y);
      if (sea[i]) continue;
      const gx = elevation[indexOf(x + 1, y)] - elevation[indexOf(x - 1, y)];
      const gy = elevation[indexOf(x, y + 1)] - elevation[indexOf(x, y - 1)];
      slope[i] = clamp(Math.sqrt(gx * gx + gy * gy) * 11.2);
    }
  }

  // Re-trim visible river paths after fluvial reshaping changes local elevation.
  for (let r = 0; r < riverPaths.length; r++) riverPaths[r] = sanitizeDownhillRiverPath(trimMountainHeadwaters(riverPaths[r]), 0.028);
  for (let r = riverPaths.length - 1; r >= 0; r--) if (riverPaths[r].length < 2) riverPaths.splice(r, 1);
  for (let r = 0; r < streamPaths.length; r++) streamPaths[r] = sanitizeDownhillRiverPath(trimMountainHeadwaters(streamPaths[r]), 0.022);
  for (let r = streamPaths.length - 1; r >= 0; r--) if (streamPaths[r].length < 2) streamPaths.splice(r, 1);

  const mainRivers = riverPaths
    .map((p, i) => ({ path: p, score: riverScores[i] }))
    .sort((a, b) => b.score - a.score)
    .slice(0, Math.min(6, riverPaths.length))
    .map((x) => x.path);

  if (mainRivers.length === 0 && riverPaths.length > 0) mainRivers.push(riverPaths[0]);
  if (mainRivers.length === 0) {
    let start = null;
    let startScore = -INF;
    for (let y = 4; y < MAP_H - 4; y++) {
      for (let x = 4; x < MAP_W - 4; x++) {
        const i = indexOf(x, y);
        if (sea[i]) continue;
        const score = elevation[i] * 0.55 + moisture[i] * 0.35 - slope[i] * 0.15;
        if (score > startScore) {
          startScore = score;
          start = { x, y };
        }
      }
    }
    if (start) {
      let goal = null;
      let goalDist = INF;
      for (let y = 0; y < MAP_H; y++) {
        for (let x = 0; x < MAP_W; x++) {
          if (!sea[indexOf(x, y)]) continue;
          const d = Math.hypot(x - start.x, y - start.y);
          if (d < goalDist) {
            goalDist = d;
            goal = { x, y };
          }
        }
      }
      if (goal) {
        const fallbackPath = aStar(start, goal, (x, y, cx, cy) => {
          const i = indexOf(x, y);
          const ci = indexOf(cx, cy);
          if (sea[i]) return 0.2;
          const uphillBias = Math.max(0, elevation[i] - elevation[ci]) * 22;
          const downhillBias = Math.max(0, elevation[ci] - elevation[i]) * 1.7;
          return Math.max(0.25, 1 + uphillBias + slope[i] * 0.65 + elevation[i] * 0.8 - downhillBias);
        });
        if (fallbackPath.length > 4) {
          riverPaths.push(fallbackPath);
          mainRivers.push(fallbackPath);
          for (const [x, y] of fallbackPath) river[indexOf(x, y)] += 0.4;
        }
      }
    }
  }

  const mainRiverCells = new Set(mainRivers.flatMap((path) => path.map(([x, y]) => `${x},${y}`)));
  const tributaryRivers = riverPaths.filter((path) => path.some(([x, y]) => !mainRiverCells.has(`${x},${y}`)) && !mainRivers.includes(path));
  const smallStreams = streamPaths.filter((path) => path.length >= 5);

  prefectureMask = makePrefectureMask(seed, sea, elevation, slope, river);
  prefectureBorder = extractMaskBorder(prefectureMask, sea);
  const regionalPrefectures = generateRegionalPrefectures(seed, sea, elevation, slope, river, ridgeField, flowAccum, prefectureMask);
  const prefectureRegionId = regionalPrefectures.regionId;
  const regionalPrefectureBorders = extractRegionBorderSegments(prefectureRegionId, sea);

  for (let y = 1; y < MAP_H - 1; y++) {
    for (let x = 1; x < MAP_W - 1; x++) {
      const i = indexOf(x, y);
      if (sea[i]) continue;
      const low = 1 - clamp((elevation[i] - 0.28) / 0.4);
      const flat = 1 - slope[i];
      const valleyPlain = valleyField[i] * 0.44 + basinField[i] * 0.36 + coastalLowland[i] * 0.55;
      plain[i] = clamp(low * 0.44 + flat * 0.58 + valleyPlain - ridgeField[i] * 0.28 - (elevation[i] > 0.62 ? 0.48 : 0));

      let nearRiver = 0;
      for (let dy = -4; dy <= 4; dy++) {
        for (let dx = -4; dx <= 4; dx++) {
          const nx = x + dx;
          const ny = y + dy;
          if (!inside(nx, ny)) continue;
          nearRiver = Math.max(nearRiver, river[indexOf(nx, ny)] / (1 + Math.hypot(dx, dy)));
        }
      }

      const fan = clamp(valleyField[i] * (1 - coastalLowland[i]) * (elevation[i] > 0.34 && elevation[i] < 0.58 ? 0.9 : 0.35) * (1 - slope[i] * 0.55));
      floodplain[i] = clamp(nearRiver * plain[i] * 0.92 + coastalLowland[i] * nearRiver * 0.22);
      agriculture[i] = clamp(plain[i] * 0.58 + fan * 0.26 + basinField[i] * 0.2 + moisture[i] * 0.14 + clamp(nearRiver) * 0.32 - slope[i] * 0.34 - ridgeField[i] * 0.18 - floodplain[i] * 0.06);
    }
  }

  for (let y = 2; y < MAP_H - 2; y++) {
    for (let x = 2; x < MAP_W - 2; x++) {
      const i = indexOf(x, y);
      if (sea[i]) continue;
      let seaNear = 0;
      let riverNear = 0;
      let sheltered = 0;

      for (let dy = -5; dy <= 5; dy++) {
        for (let dx = -5; dx <= 5; dx++) {
          const nx = x + dx;
          const ny = y + dy;
          if (!inside(nx, ny)) continue;
          const d = Math.hypot(dx, dy);
          if (sea[indexOf(nx, ny)]) seaNear += 1 / (1 + d);
          riverNear = Math.max(riverNear, river[indexOf(nx, ny)] / (1 + d));
        }
      }

      for (let dy = -2; dy <= 2; dy++) {
        for (let dx = -2; dx <= 2; dx++) {
          const nx = x + dx;
          const ny = y + dy;
          if (inside(nx, ny) && !sea[indexOf(nx, ny)]) sheltered += 1;
        }
      }

      const isDelta = riverNear > 0.22 && coastalLowland[i] > 0.18;
      const bayShelter = sheltered * 0.012 + seaNear * 0.055 + coastalLowland[i] * 0.16;
      portSuitability[i] = clamp(bayShelter + riverNear * 0.24 + (isDelta ? 0.22 : 0) + plain[i] * 0.08 - slope[i] * 0.48 - ridgeField[i] * 0.16);
    }
  }

  for (let y = 3; y < MAP_H - 3; y++) {
    for (let x = 3; x < MAP_W - 3; x++) {
      const i = indexOf(x, y);
      if (sea[i]) continue;
      const r = river[i];
      if (r < 0.2 || r > 1.85) continue;
      let bankPlain = 0;
      for (const [nx, ny] of neighbors8(x, y)) bankPlain += plain[indexOf(nx, ny)];
      crossingSuitability[i] = clamp(r * 0.34 + (bankPlain / 8) * 0.54 + valleyField[i] * 0.18 - slope[i] * 0.55 - floodplain[i] * 0.06);
    }
  }

  for (let y = 4; y < MAP_H - 4; y++) {
    for (let x = 4; x < MAP_W - 4; x++) {
      const i = indexOf(x, y);
      if (sea[i]) continue;
      const e = elevation[i];
      if (e < 0.43 || e > 0.82) continue;
      const ewHigh = (elevation[indexOf(x - 3, y)] + elevation[indexOf(x + 3, y)]) / 2;
      const nsHigh = (elevation[indexOf(x, y - 3)] + elevation[indexOf(x, y + 3)]) / 2;
      const diagLow = Math.min(
        elevation[indexOf(x - 3, y - 3)],
        elevation[indexOf(x + 3, y + 3)],
        elevation[indexOf(x - 3, y + 3)],
        elevation[indexOf(x + 3, y - 3)]
      );
      passSuitability[i] = clamp((Math.max(ewHigh, nsHigh) - e) * 2.2 + (e - diagLow) * 0.55 + valleyField[i] * 0.28 - ridgeField[i] * 0.18 - slope[i] * 0.2);
    }
  }

  function pickPoints(scoreArray, { threshold, max, minDistance, seedOffset = 0, predicate = () => true }) {
    const candidates = [];
    for (let y = 2; y < MAP_H - 2; y++) {
      for (let x = 2; x < MAP_W - 2; x++) {
        const i = indexOf(x, y);
        if (!predicate(x, y, i)) continue;
        const score = scoreArray[i] + hash2(x, y, seed + seedOffset) * 0.08;
        if (score >= threshold) candidates.push({ x, y, score });
      }
    }
    return pickEntities(candidates, { max, minDistance, threshold, seed: seed + seedOffset });
  }

  let ports = pickPoints(portSuitability, {
    threshold: 0.3 + rand(seed, 1001) * 0.08,
    max: 3 + Math.floor(rand(seed, 1002) * 7),
    minDistance: 10,
    seedOffset: 1000,
    predicate: (x, y, i) => !sea[i],
  }).map((p) => {
    const i = indexOf(p.x, p.y);
    let seaEdge = 0;
    for (let dy = -3; dy <= 3; dy++) for (let dx = -3; dx <= 3; dx++) {
      const nx = p.x + dx;
      const ny = p.y + dy;
      if (inside(nx, ny) && sea[indexOf(nx, ny)]) seaEdge += 1 / (1 + Math.hypot(dx, dy));
    }
    const harborPotential = p.score + coastalLowland[i] * 0.28 + river[i] * 0.08 + seaEdge * 0.025 - slope[i] * 0.2;
    return { ...p, harborPotential, seaEdge, portClass: "fishing", kind: "Fishing Port" };
  }).sort((a, b) => b.harborPotential - a.harborPotential)
    .map((p, n) => {
      const isLakeLike = p.seaEdge < 0.25 && river[indexOf(p.x, p.y)] > 0.32;
      const portClass = isLakeLike ? "lake" : n === 0 ? "major" : n < 3 && p.harborPotential > 0.34 ? "regional" : "fishing";
      const kind = portClass === "major" ? "Major Port" : portClass === "regional" ? "Regional Port" : portClass === "lake" ? "Lake Port" : "Fishing Port";
      return { ...p, portClass, kind, score: p.harborPotential };
    });
  if (!ports.some((p) => p.portClass === "major")) {
    const fallbackMajor = ports.find((p) => p.portClass !== "lake") || ports[0];
    if (fallbackMajor) {
      fallbackMajor.portClass = "major";
      fallbackMajor.kind = "Major Port";
      fallbackMajor.score += 0.16;
    }
  }
  const majorPorts = ports.filter((p) => p.portClass === "major");
  const commercialPorts = ports.filter((p) => p.portClass === "major" || p.portClass === "regional");

  let crossings = pickPoints(crossingSuitability, {
    threshold: 0.28 + rand(seed, 1011) * 0.08,
    max: 8 + Math.floor(rand(seed, 1012) * 15),
    minDistance: 8,
    seedOffset: 1010,
    predicate: (x, y, i) => !sea[i],
  }).map((p) => ({ ...p, kind: "River Crossing" }));

  let passes = pickPoints(passSuitability, {
    threshold: 0.16 + rand(seed, 1021) * 0.08,
    max: 4 + Math.floor(rand(seed, 1022) * 10),
    minDistance: 9,
    seedOffset: 1020,
    predicate: (x, y, i) => !sea[i],
  }).map((p) => ({ ...p, kind: "Pass" }));

  const settlementCluster = new Float32Array(SIZE);
  for (let y = 2; y < MAP_H - 2; y++) {
    for (let x = 2; x < MAP_W - 2; x++) {
      const i = indexOf(x, y);
      if (sea[i]) continue;
      const valleyCorridor = clamp(valleyField[i] * 0.62 + river[i] * 0.16);
      const lowlandCorridor = clamp(coastalLowland[i] * 0.38 + basinField[i] * 0.34 + plain[i] * 0.24 + agriculture[i] * 0.18);
      const terrainGate = clamp(1.0 - slope[i] * 1.18 - ridgeField[i] * 0.52 - Math.max(0, elevation[i] - 0.62) * 1.35, 0.08, 1);
      const localPatch = valueNoise(x * 0.7, y * 0.7, seed + 1037, 10);
      const broadPatch = fbm(x * 0.32 + 71, y * 0.32 - 19, seed + 1038);
      settlementCluster[i] = clamp((valleyCorridor + lowlandCorridor) * terrainGate * (0.72 + broadPatch * 0.42 + localPatch * 0.18));
    }
  }

  const settlementScore = new Float32Array(SIZE);
  for (let y = 2; y < MAP_H - 2; y++) {
    for (let x = 2; x < MAP_W - 2; x++) {
      const i = indexOf(x, y);
      if (sea[i]) continue;
      let nearFeature = 0;
      for (const p of [...ports, ...crossings, ...passes]) nearFeature = Math.max(nearFeature, 1 / (1 + Math.hypot(x - p.x, y - p.y) / 4));
      const riverPull = Math.min(0.32, river[i] * 0.14 + valleyField[i] * 0.16);
      const mountainVillage = valleyField[i] * clamp(elevation[i] - 0.42, 0, 0.3) * 0.52;
      const remoteMountainPenalty = Math.max(0, elevation[i] - 0.58) * Math.max(0, ridgeField[i] - 0.22) * (1 - valleyField[i]) * 0.75;
      const base = agriculture[i] * 0.50 + plain[i] * 0.14 + nearFeature * 0.23 + riverPull + basinField[i] * 0.13 + coastalLowland[i] * 0.08 + mountainVillage - slope[i] * 0.48 - ridgeField[i] * 0.24 - floodplain[i] * 0.06 - remoteMountainPenalty;
      settlementScore[i] = clamp(base * (0.74 + settlementCluster[i] * 0.66) + settlementCluster[i] * 0.13);
    }
  }

  let villages = pickPoints(settlementScore, {
    threshold: 0.32 + rand(seed, 1031) * 0.1,
    max: 28 + Math.floor(rand(seed, 1032) * 44),
    minDistance: 3 + Math.floor(rand(seed, 1033) * 3),
    seedOffset: 1030,
    predicate: (x, y, i) => !sea[i],
  }).map((p) => ({ ...p, kind: "Village" }));

  const marketScore = new Float32Array(SIZE);
  for (let y = 4; y < MAP_H - 4; y++) {
    for (let x = 4; x < MAP_W - 4; x++) {
      const i = indexOf(x, y);
      if (sea[i]) continue;

      let villagePull = 0;
      let nearbyVillages = 0;
      for (const v of villages) {
        const d = Math.hypot(x - v.x, y - v.y);
        if (d < 24) {
          villagePull += 1 / (1 + d);
          nearbyVillages++;
        }
      }

      let featurePull = 0;
      for (const p of [...ports, ...crossings]) featurePull = Math.max(featurePull, 1 / (1 + Math.hypot(x - p.x, y - p.y) / 3));
      const confluence = river[i] > 0.36 && valleyField[i] > 0.24 ? 0.12 : 0;
      marketScore[i] = clamp(villagePull * 1.25 + featurePull * 0.34 + plain[i] * 0.2 + basinField[i] * 0.16 + confluence + coastalLowland[i] * 0.08 + river[i] * 0.035 - slope[i] * 0.32 - ridgeField[i] * 0.18 + nearbyVillages * 0.012);
    }
  }

  let markets = pickPoints(marketScore, {
    threshold: 0.2 + rand(seed, 1041) * 0.08,
    max: 6 + Math.floor(rand(seed, 1042) * 12),
    minDistance: 11,
    seedOffset: 1040,
    predicate: (x, y, i) => !sea[i],
  }).map((p) => ({ ...p, kind: "Market Town" }));

  const defenseScore = new Float32Array(SIZE);
  for (let y = 3; y < MAP_H - 3; y++) {
    for (let x = 3; x < MAP_W - 3; x++) {
      const i = indexOf(x, y);
      if (sea[i]) continue;
      const hillShoulder = clamp(1 - Math.abs(elevation[i] - 0.50) / 0.24);
      let riverArms = 0;
      for (const [nx, ny] of neighbors8(x, y)) if (river[indexOf(nx, ny)] > 0.32) riverArms++;
      const confluence = riverArms >= 3 ? 0.38 : riverArms === 2 ? 0.18 : 0;
      const roadJunctionProxy = (
        (distanceToNearest(markets, x, y) < 7 ? 1 : 0) +
        (distanceToNearest(crossings, x, y) < 6 ? 1 : 0) +
        (distanceToNearest(passes, x, y) < 7 ? 1 : 0) +
        (distanceToNearest(commercialPorts, x, y) < 8 ? 1 : 0)
      ) >= 2 ? 0.32 : 0;
      const hillEdge = plain[i] > 0.2 && elevation[i] > 0.36 && elevation[i] < 0.62 && (slope[i] > 0.12 || ridgeField[i] > 0.12) ? 0.3 : 0;
      const mountainRidgeCastle = elevation[i] > 0.56 && ridgeField[i] > 0.3 && valleyField[i] > 0.1 ? 0.28 : 0;
      const validCastleSite = confluence > 0 || roadJunctionProxy > 0 || hillEdge > 0 || mountainRidgeCastle > 0;
      defenseScore[i] = validCastleSite
        ? clamp(hillShoulder * 0.28 + confluence + roadJunctionProxy + hillEdge + mountainRidgeCastle + slope[i] * 0.05 - floodplain[i] * 0.42 - coastalLowland[i] * 0.12)
        : 0;
    }
  }

  let castles = pickPoints(defenseScore, {
    threshold: 0.34 + rand(seed, 1051) * 0.08,
    max: 2 + Math.floor(rand(seed, 1052) * 4),
    minDistance: 15,
    seedOffset: 1050,
    predicate: (x, y, i) => !sea[i] && defenseScore[i] > 0,
  }).map((p) => ({
    ...p,
    kind: elevation[indexOf(p.x, p.y)] > 0.55 ? "Mountain Castle" : elevation[indexOf(p.x, p.y)] > 0.38 ? "Hilltop Castle" : "Flatland Castle",
  }));

  function normalEdgePenalty(x, y) {
    if (nearMapEdge(x, y, 1)) return INF;
    if (nearMapEdge(x, y, 2)) return 7;
    if (nearMapEdge(x, y, 4)) return 2.8;
    return 0;
  }

  function premodernCost(x, y) {
    const i = indexOf(x, y);
    if (sea[i]) return INF;
    const crossingBonus = distanceToNearest(crossings, x, y) < 4 ? 0.65 : 0;
    const passBonus = distanceToNearest(passes, x, y) < 4 ? 0.45 : 0;
    const riverPenalty = river[i] > 0.28 ? (crossingBonus ? 0.45 : 2.4) : 0;
    const highMountain = elevation[i] > 0.72 ? 4.2 : elevation[i] > 0.58 ? 1.4 : 0;
    return Math.max(0.35, 1 + slope[i] * 5.8 + riverPenalty + highMountain + floodplain[i] * 0.62 - plain[i] * 0.32 - valleyField[i] * 0.42 - coastalLowland[i] * 0.12 - passBonus + normalEdgePenalty(x, y) + hash2(x, y, seed + 111) * 0.16);
  }

  const premodernRoads = [];
  function addPremodernRoad(a, b) {
    const path = aStar(a, b, premodernCost);
    if (path.length > 3) premodernRoads.push(path);
  }

  for (const castle of castles) {
    const near = pickEntities([...markets, ...ports, ...crossings, ...passes].map((p) => ({ ...p, score: 1 / (1 + Math.hypot(p.x - castle.x, p.y - castle.y)) })), { max: 2 + Math.floor(rand(seed, castle.x + castle.y) * 3), minDistance: 1, threshold: 0 });
    for (const p of near) addPremodernRoad(castle, p);
  }
  for (const market of markets) {
    const near = pickEntities([...markets.filter((p) => p !== market), ...ports, ...crossings].map((p) => ({ ...p, score: 1 / (1 + Math.hypot(p.x - market.x, p.y - market.y)) })), { max: 1 + Math.floor(rand(seed, market.x + market.y + 20) * 3), minDistance: 1, threshold: 0 });
    for (const p of near) addPremodernRoad(market, p);
  }

  function urbanSiteSuitability(p) {
    const i = indexOf(p.x, p.y);
    if (sea[i]) return 0;
    const portBonus = p.kind === "Port Town" || p.portClass === "major" || p.portClass === "regional" ? 0.18 : 0;
    const historicalBonus = p.kind === "Market City" || p.kind === "Castle Town" ? 0.05 : 0;
    return clamp(
      plain[i] * 0.46 +
      agriculture[i] * 0.18 +
      basinField[i] * 0.20 +
      coastalLowland[i] * 0.20 +
      valleyField[i] * 0.12 +
      portBonus + historicalBonus -
      slope[i] * 0.58 -
      ridgeField[i] * 0.34 -
      Math.max(0, elevation[i] - 0.55) * 1.35
    );
  }

  function cityPopulationCap(p) {
    const i = indexOf(p.x, p.y);
    const suitability = urbanSiteSuitability(p);
    if (suitability < 0.18 || elevation[i] > 0.66 || slope[i] > 0.82 || ridgeField[i] > 0.72) return 85000;
    if (suitability < 0.28 || elevation[i] > 0.60 || slope[i] > 0.62) return 180000;
    if (suitability < 0.38) return 420000;
    return INF;
  }

  let castleTowns = castles.map((c) => ({ x: c.x, y: c.y, score: c.score + 0.45, kind: "Castle Town" }));
  const cityCandidates = [
    ...castleTowns.map((p) => ({ ...p, score: p.score + 0.4 })),
    ...ports.map((p) => ({ ...p, kind: "Port Town", score: p.score + 0.28 })),
    ...markets.map((p) => ({ ...p, kind: "Market City", score: p.score + 0.12 })),
  ].map((p) => {
    const i = indexOf(p.x, p.y);
    const suitability = urbanSiteSuitability(p);
    return {
      ...p,
      urbanSuitability: suitability,
      score: p.score + suitability * 0.72 - slope[i] * 0.20 - ridgeField[i] * 0.16 - Math.max(0, elevation[i] - 0.58) * 0.78,
    };
  }).filter((p) => p.urbanSuitability >= 0.10 || p.kind === "Castle Town");

  let modernCities = pickEntities(cityCandidates, {
    max: 7 + Math.floor(rand(seed, 1061) * 10),
    minDistance: 9,
    threshold: 0.33 + rand(seed, 1062) * 0.12,
    seed: seed + 1060,
  }).map((p, n) => {
    const rank = n === 0 ? "Prefectural Capital" : n < 4 ? "Regional Center" : "Small City";
    const r = rand(seed, 1600 + n * 13 + p.x * 3 + p.y);
    const rawScale = Math.pow(1 - n / Math.max(1, cityCandidates.length + 1), 1.55) * 0.58 + Math.pow(r, 3.4) * 0.42;
    const rankBase = rank === "Prefectural Capital" ? 420000 : rank === "Regional Center" ? 115000 : 26000;
    const rankSpread = rank === "Prefectural Capital" ? 1450000 : rank === "Regional Center" ? 520000 : 185000;
    const pi = indexOf(p.x, p.y);
    const suitability = p.urbanSuitability ?? urbanSiteSuitability(p);
    const geographyBoost = clamp(plain[pi] * 0.34 + agriculture[pi] * 0.18 + basinField[pi] * 0.2 + coastalLowland[pi] * 0.18 + valleyField[pi] * 0.12 + suitability * 0.24 + (p.kind === "Port Town" ? 0.22 : 0));
    const rawPopulation = Math.round((rankBase + rankSpread * Math.pow(rawScale + geographyBoost * 0.18, 1.75)) / 1000) * 1000;
    const population = Math.min(rawPopulation, cityPopulationCap(p));
    const urbanRadius = clamp(7.5 + Math.sqrt(population) / 80 + (rank === "Prefectural Capital" ? 3.0 : rank === "Regional Center" ? 1.5 : 0), 8, 32);
    const coreRadius = clamp(2.6 + Math.sqrt(population) / 320, 3, 9);
    const urbanWeight = clamp(0.74 + Math.log10(Math.max(10000, population)) * 0.36, 1.15, 3.05);
    return { ...p, population, urbanRadius, coreRadius, urbanWeight, rank, kind: p.kind || "City" };
  });

  function fallbackCapitalCandidate() {
    const pools = [...markets, ...ports, ...villages].filter((p) => p && prefectureMask[indexOf(p.x, p.y)] && !sea[indexOf(p.x, p.y)]);
    let best = null;
    let bestScore = -INF;
    for (const p of pools) {
      const i = indexOf(p.x, p.y);
      const score = urbanSiteSuitability(p) * 1.6 + plain[i] * 0.32 + populationDensityProxyForCapital(i) + (p.kind?.includes("Port") ? 0.18 : 0) + (p.score || 0);
      if (score > bestScore) { bestScore = score; best = p; }
    }
    if (best) return { ...best, kind: "Market City", population: 360000, urbanRadius: 15, coreRadius: 4.6, urbanWeight: 1.9, score: bestScore };

    for (let y = 4; y < MAP_H - 4; y++) {
      for (let x = 4; x < MAP_W - 4; x++) {
        const i = indexOf(x, y);
        if (!prefectureMask[i] || sea[i]) continue;
        const score = plain[i] * 0.72 + agriculture[i] * 0.24 + basinField[i] * 0.18 + coastalLowland[i] * 0.14 - slope[i] * 0.72 - ridgeField[i] * 0.32;
        if (score > bestScore) { bestScore = score; best = { x, y, score, kind: "Market City" }; }
      }
    }
    return best ? { ...best, population: 320000, urbanRadius: 14, coreRadius: 4.2, urbanWeight: 1.7 } : null;
  }

  function populationDensityProxyForCapital(i) {
    return settlementScore[i] * 0.18 + marketScore[i] * 0.12;
  }

  if (modernCities.length === 0 || !modernCities.some((city) => prefectureMask[indexOf(city.x, city.y)])) {
    const fallbackCapital = fallbackCapitalCandidate();
    if (fallbackCapital) modernCities.unshift(fallbackCapital);
  }

  if (modernCities.length > 0) {
    modernCities.sort((a, b) => (b.population || 0) + b.score * 90000 - ((a.population || 0) + a.score * 90000));
    let capitalIndex = -1;
    let capitalScore = -INF;
    for (let i = 0; i < modernCities.length; i++) {
      const city = modernCities[i];
      const ci = indexOf(city.x, city.y);
      if (!prefectureMask[ci] || sea[ci]) continue;
      const suitability = urbanSiteSuitability(city);
      const score = suitability * 900000 + (city.population || 0) * 0.55 + (city.score || 0) * 120000 - slope[ci] * 180000 - Math.max(0, elevation[ci] - 0.58) * 360000;
      if (score > capitalScore) { capitalScore = score; capitalIndex = i; }
    }
    if (capitalIndex > 0) modernCities.unshift(modernCities.splice(capitalIndex, 1)[0]);
    const capCell = indexOf(modernCities[0].x, modernCities[0].y);
    const capPopulation = prefectureMask[capCell]
      ? Math.max(modernCities[0].population || 0, 620000)
      : Math.min(modernCities[0].population || 0, 180000);
    modernCities[0] = {
      ...modernCities[0],
      rank: prefectureMask[capCell] ? "Prefectural Capital" : "Regional Center",
      kind: prefectureMask[capCell] ? "Prefectural Capital" : (modernCities[0].kind || "City"),
      isPrefecturalCapital: Boolean(prefectureMask[capCell]),
      population: capPopulation,
      urbanRadius: prefectureMask[capCell] ? Math.max(modernCities[0].urbanRadius || 0, 18) : modernCities[0].urbanRadius,
      coreRadius: prefectureMask[capCell] ? Math.max(modernCities[0].coreRadius || 0, 5.5) : modernCities[0].coreRadius,
      urbanWeight: prefectureMask[capCell] ? Math.max(modernCities[0].urbanWeight || 0, 2.15) : modernCities[0].urbanWeight,
    };
    for (let i = 1; i < modernCities.length; i++) modernCities[i] = { ...modernCities[i], isPrefecturalCapital: false };
  }

  const capital = modernCities.find((city) => city.isPrefecturalCapital && prefectureMask[indexOf(city.x, city.y)]) || modernCities.find((city) => prefectureMask[indexOf(city.x, city.y)]) || markets.find((p) => prefectureMask[indexOf(p.x, p.y)]) || ports.find((p) => prefectureMask[indexOf(p.x, p.y)]) || { x: Math.floor(MAP_W / 2), y: Math.floor(MAP_H / 2), score: 1, population: 0, urbanRadius: 12, coreRadius: 4, urbanWeight: 1, isPrefecturalCapital: true };

  const populationDensity = new Float32Array(SIZE);
  let maxPopulationDensity = 0;
  for (let y = 0; y < MAP_H; y++) {
    for (let x = 0; x < MAP_W; x++) {
      const i = indexOf(x, y);
      if (sea[i]) continue;
      let density = 0;
      for (const city of modernCities) {
        const populationScale = clamp((Math.log10(Math.max(10000, city.population || 10000)) - 4) / 2.25, 0.12, 1.55);
        const d = Math.hypot(city.x - x, city.y - y);
        const urbanR = Math.max(5, city.urbanRadius || 11);
        const coreR = Math.max(2.4, city.coreRadius || 4);
        density += populationScale * 1.55 / (1 + Math.pow(d / urbanR, 2.35));
        density += populationScale * 1.05 * Math.exp(-(d * d) / (coreR * coreR * 2.2));
      }
      for (const market of markets) {
        const d = Math.hypot(market.x - x, market.y - y);
        density += 0.22 / (1 + Math.pow(d / 7.5, 2.2));
      }
      for (const village of villages) {
        const d = Math.hypot(village.x - x, village.y - y);
        density += 0.055 / (1 + Math.pow(d / 4.2, 2));
      }
      density *= clamp(0.48 + plain[i] * 0.62 + agriculture[i] * 0.14 + basinField[i] * 0.22 + coastalLowland[i] * 0.18 + valleyField[i] * 0.1 - slope[i] * 1.05 - ridgeField[i] * 0.48 - Math.max(0, elevation[i] - 0.58) * 1.05, 0.018, 1.22);
      populationDensity[i] = density;
      if (density > maxPopulationDensity) maxPopulationDensity = density;
    }
  }
  if (maxPopulationDensity > 0) {
    for (let i = 0; i < SIZE; i++) populationDensity[i] = clamp(populationDensity[i] / maxPopulationDensity);
  }

  function densityValue(x, y) {
    return populationDensity[indexOf(x, y)] || 0;
  }

  function midDensityAffinity(x, y) {
    const d = densityValue(x, y);
    return clamp(1 - Math.abs(d - 0.38) / 0.38);
  }

  function nearPassPoint(x, y, radius = 5) {
    return distanceToNearest(passes, x, y) <= radius;
  }

  function mountainBarrierPenalty(x, y, type = "rail") {
    const i = indexOf(x, y);
    const e = elevation[i];
    const s = slope[i];
    const pass = nearPassPoint(x, y, type === "express" ? 7 : type === "rail" ? 6 : 5);
    if (e > 0.84) return INF;
    if (pass && e > 0.80 && s > 0.16) return INF;
    if (!pass && e > 0.78) return INF;
    if (!pass && e > 0.70 && s > 0.16) return INF;
    if (!pass && e > 0.66 && s > 0.28) return INF;
    if (!pass && e > 0.72) return type === "express" ? 260 : type === "rail" ? 330 : type === "minor" ? 80 : 155;
    if (!pass && e > 0.64 && s > 0.20) return type === "express" ? 145 : type === "rail" ? 180 : type === "minor" ? 54 : 96;
    const passDiscount = pass ? (type === "minor" ? 0.35 : 0.22) : 1;
    const mountain = Math.max(0, e - 0.48);
    const steep = Math.max(0, s - 0.15);
    const typeFactor = type === "express" ? 360 : type === "rail" ? 430 : type === "minor" ? 115 : 210;
    return (mountain * mountain * typeFactor + steep * steep * 150 + ridgeField[i] * 9.5) * passDiscount;
  }

  function transportAccessPoint(node, mode = "road", salt = 0) {
    if (!node || nearMapEdge(node.x, node.y, 1) || node.kind === "External Gateway") return node;
    const minR = mode === "express" ? 10 : mode === "rail" ? 2 : 4;
    const maxR = mode === "express" ? 20 : mode === "rail" ? 6 : 10;
    let best = null;
    let bestScore = -INF;
    for (let dy = -maxR; dy <= maxR; dy++) {
      for (let dx = -maxR; dx <= maxR; dx++) {
        const d = Math.hypot(dx, dy);
        if (d < minR || d > maxR) continue;
        const x = node.x + dx;
        const y = node.y + dy;
        if (!inside(x, y)) continue;
        const i = indexOf(x, y);
        if (sea[i]) continue;
        const barrier = mode === "express" || mode === "rail" ? mountainBarrierPenalty(x, y, mode) : mountainBarrierPenalty(x, y, "road");
        if (barrier >= INF) continue;
        const targetD = (minR + maxR) * 0.5;
        const flatness = plain[i] * 1.0 + agriculture[i] * 0.2 + valleyField[i] * 0.26 + coastalLowland[i] * 0.16 - slope[i] * 1.22 - ridgeField[i] * 0.72 - Math.max(0, elevation[i] - 0.58) * 2.35;
        const ring = -Math.abs(d - targetD) * 0.08;
        const riverPenalty = river[i] > 0.5 ? 0.45 : river[i] * 0.12;
        const density = densityValue(x, y);
        const densityAffinity = mode === "rail" ? density * 0.9 : mode === "express" ? midDensityAffinity(x, y) * 0.52 - Math.max(0, density - 0.72) * 0.9 : density * 0.24;
        const noise = hash2(x, y, seed + salt + (mode === "rail" ? 6000 : mode === "express" ? 7000 : 5000)) * 0.12;
        const score = flatness + densityAffinity + ring - riverPenalty - barrier * 0.012 + noise;
        if (score > bestScore) {
          bestScore = score;
          best = { x, y, score: node.score || 0.5, kind: `${mode} Access`, parent: node };
        }
      }
    }
    return best || node;
  }

  function routePoint(node, mode, salt = 0) {
    return transportAccessPoint(node, mode, salt);
  }

  const townAvoidNodes = [...modernCities, ...markets, ...ports];

  const urbanCenters = modernCities.map((city, n) => {
    let best = { x: city.x, y: city.y, score: city.score + 0.5 };
    let bestScore = -INF;
    const searchR = Math.max(2, Math.round(city.coreRadius));
    for (let dy = -searchR; dy <= searchR; dy++) {
      for (let dx = -searchR; dx <= searchR; dx++) {
        const x = city.x + dx;
        const y = city.y + dy;
        if (!inside(x, y)) continue;
        const i = indexOf(x, y);
        if (sea[i]) continue;
        const d = Math.hypot(dx, dy);
        const score = plain[i] * 0.54 + agriculture[i] * 0.16 - slope[i] * 0.36 - d * 0.06 + hash2(x, y, seed + 1700 + n) * 0.07;
        if (score > bestScore) { bestScore = score; best = { x, y, score: city.score + 0.5, cityIndex: n, parent: city }; }
      }
    }
    return { ...best, kind: city.rank === "Prefectural Capital" ? "Central Business District" : "Urban Center", population: Math.round(city.population * (city.rank === "Prefectural Capital" ? 0.18 : 0.12)), insidePrefecture: Boolean(prefectureMask[indexOf(best.x, best.y)]) };
  });

  function railCost(x, y) {
    const i = indexOf(x, y);
    if (sea[i]) return INF;
    const barrier = mountainBarrierPenalty(x, y, "rail");
    if (barrier >= INF) return INF;
    const density = densityValue(x, y);
    const highPenalty = Math.max(0, elevation[i] - 0.52) * 14 + barrier;
    const riverPenalty = river[i] > 0.5 ? 1.6 : river[i] > 0.25 ? 0.7 : 0;
    return Math.max(0.42, 1 + slope[i] * 22 + highPenalty + riverPenalty + floodplain[i] * 0.28 - density * 0.88 - plain[i] * 0.28 - valleyField[i] * 0.62 - coastalLowland[i] * 0.48 + ridgeField[i] * 1.4 + normalEdgePenalty(x, y) + hash2(x, y, seed + 222) * 0.08);
  }

  const railways = [];
  const branchRailways = [];
  const railDegree = new Map();
  const railCore = [capital];
  const railHubs = [...modernCities, ...commercialPorts];

  function addRailRoute(a, b, bucket = railways) {
    const start = routePoint(a, "rail", a.x * 19 + a.y * 23);
    const goal = routePoint(b, "rail", b.x * 19 + b.y * 23 + 11);
    const existingRails = [...railways, ...branchRailways];
    const cost = makeTransportCost(railCost, existingRails, railHubs, [start, goal], 5, 10.5, townAvoidNodes, 2.4, 4.2);
    const path = aStar(start, goal, cost);
    const length = pathLength(path);
    const direct = pathEndpointDistance(path);
    const overlap = pathOverlapRatio(path, existingRails, 2);
    const densityPurpose = averagePathField(path, populationDensity) + averagePathField(path, plain) * 0.28 + averagePathField(path, valleyField) * 0.2;
    const isMain = bucket === railways;
    if (path.length > 3 && direct >= (isMain ? 18 : 12) && length >= (isMain ? 22 : 14) && pathCompactness(path) < (isMain ? 3.1 : 3.4) && overlap < (isMain ? 0.30 : 0.20) && densityPurpose > (isMain ? 0.18 : 0.12)) {
      bucket.push(path);
      incrementDegree(railDegree, a);
      incrementDegree(railDegree, b);
      return true;
    }
    return false;
  }

  const transportCities = modernCities.filter((city) => (city.population || 0) >= 120000);
  const mainRailTargets = transportCities.filter((city) => city !== capital).slice(0, 2 + Math.floor(rand(seed, 1070) * 3));
  for (const city of mainRailTargets) {
    const anchor = nearestConnectable(railCore, city, railDegree, 3) || capital;
    if (addRailRoute(anchor, city, railways)) railCore.push(city);
  }
  for (const city of modernCities.filter((city) => city !== capital && !mainRailTargets.includes(city))) {
    const anchor = nearestConnectable(railCore, city, railDegree, 2) || capital;
    if (anchor && rand(seed, city.x * 10 + city.y) > 0.2) {
      if (addRailRoute(city, anchor, branchRailways)) railCore.push(city);
    }
  }
  for (const port of majorPorts.slice(0, 1 + Math.floor(rand(seed, 1071) * 2))) {
    const anchor = nearestConnectable(railCore, port, railDegree, 2) || capital;
    if (anchor && addRailRoute(port, anchor, branchRailways)) railCore.push(port);
  }

  compactPathArray(railways, { minLength: 17, maxOverlap: 0.34, maxCount: 5 });
  compactPathArray(branchRailways, { minLength: 11, maxOverlap: 0.22, maxCount: 9 });

  const railInfluence = influenceFromPaths([...railways, ...branchRailways], 5);
  const stationCandidates = [
    ...modernCities.map((p, i) => ({ ...routePoint(p, "rail", 1900 + i), score: p.score + 0.46, kind: "Major Station", population: p.population })),
    ...railways.flatMap((path) => samplePath(path, 18 + Math.floor(rand(seed, path.length) * 14))).map((p) => ({ ...p, kind: "Station", score: 0.52 + agriculture[indexOf(p.x, p.y)] * 0.2 })),
    ...branchRailways.flatMap((path) => samplePath(path, 16 + Math.floor(rand(seed, path.length + 99) * 14))).map((p) => ({ ...p, kind: "Station", score: 0.42 + agriculture[indexOf(p.x, p.y)] * 0.2 })),
  ];

  let stations = pickEntities(stationCandidates, { max: 14 + Math.floor(rand(seed, 1080) * 22), minDistance: 6, threshold: 0.38, seed: seed + 1080 });

  const industrialScore = new Float32Array(SIZE);
  for (let y = 4; y < MAP_H - 4; y++) {
    for (let x = 4; x < MAP_W - 4; x++) {
      const i = indexOf(x, y);
      if (sea[i]) continue;
      const nearPort = 1 / (1 + distanceToNearest(majorPorts.length ? majorPorts : commercialPorts, x, y) / 5);
      const nearCity = distanceToNearest(modernCities, x, y);
      const cityEdge = nearCity > 5 && nearCity < 20 ? 0.22 : nearCity <= 5 ? -0.25 : 0;
      industrialScore[i] = clamp(plain[i] * 0.24 + coastalLowland[i] * 0.24 + railInfluence[i] * 0.38 + nearPort * 0.58 + river[i] * 0.04 + cityEdge - slope[i] * 0.36 - ridgeField[i] * 0.18 - floodplain[i] * 0.03);
    }
  }

  let industrialZones = pickPoints(industrialScore, {
    threshold: 0.31 + rand(seed, 1091) * 0.09,
    max: 4 + Math.floor(rand(seed, 1092) * 13),
    minDistance: 10,
    seedOffset: 1090,
    predicate: (x, y, i) => !sea[i],
  }).map((p) => ({ ...p, kind: "Industrial Zone" }));

  function roadCost(x, y) {
    const i = indexOf(x, y);
    if (sea[i]) return INF;
    const barrier = mountainBarrierPenalty(x, y, "road");
    if (barrier >= INF) return INF;
    const density = densityValue(x, y);
    const nodeAvoid = distanceToNearest(townAvoidNodes, x, y) < 2.2 ? 2.0 : 0;
    return Math.max(0.35, 1 + slope[i] * 17.8 + barrier + Math.max(0, elevation[i] - 0.54) * 9.2 + nodeAvoid + (river[i] > 0.45 ? 0.85 : 0) + floodplain[i] * 0.22 - density * 0.50 - plain[i] * 0.22 - valleyField[i] * 0.28 - coastalLowland[i] * 0.20 + ridgeField[i] * 1.15 + normalEdgePenalty(x, y) + hash2(x, y, seed + 333) * 0.08);
  }

  function expresswayCost(x, y) {
    const i = indexOf(x, y);
    if (sea[i]) return INF;
    const barrier = mountainBarrierPenalty(x, y, "express");
    if (barrier >= INF) return INF;
    const density = densityValue(x, y);
    const midDensity = midDensityAffinity(x, y);
    const cityDistance = distanceToNearest(modernCities, x, y);
    const cityAvoid = cityDistance < 5 ? 22.0 : cityDistance < 9 ? 11.0 : cityDistance < 13 ? 4.0 : distanceToNearest(markets, x, y) < 4 ? 3.2 : 0;
    const densityPenalty = density > 0.66 ? (density - 0.66) * 9.5 : density < 0.08 ? (0.08 - density) * 2.4 : 0;
    const highPenalty = barrier + (elevation[i] > 0.72 ? 26 : elevation[i] > 0.62 ? 8.5 : 0);
    return Math.max(0.42, 1 + slope[i] * 23.0 + highPenalty + cityAvoid + densityPenalty + (river[i] > 0.45 ? 1.0 : 0) - midDensity * 0.82 - plain[i] * 0.16 - valleyField[i] * 0.16 - coastalLowland[i] * 0.18 + ridgeField[i] * 1.20 + normalEdgePenalty(x, y) + hash2(x, y, seed + 444) * 0.015);
  }

  const nationalRoads = [];
  const roadDegree = new Map();
  function transportDemand(p) {
    const pop = Math.sqrt(Math.max(0, p.population || 0)) / 700;
    const capitalBoost = p.isPrefecturalCapital || p.rank === "Prefectural Capital" ? 2.1 : 0;
    const portBoost = p.portClass === "major" ? 1.4 : p.portClass === "regional" ? 0.8 : p.portClass ? 0.35 : 0;
    const historyBoost = p.kind?.includes("Castle") ? 0.55 : p.kind === "Market Town" ? 0.42 : 0;
    const gatewayBoost = p.kind === "External Gateway" ? 1.1 : 0;
    return 0.35 + pop + capitalBoost + portBoost + historyBoost + gatewayBoost;
  }

  function sameCorridorAffinity(a, b) {
    const ai = indexOf(a.x, a.y);
    const bi = indexOf(b.x, b.y);
    return Math.min(0.6, (basinField[ai] + basinField[bi]) * 0.14 + (valleyField[ai] + valleyField[bi]) * 0.10 + (coastalLowland[ai] + coastalLowland[bi]) * 0.10);
  }

  const roadTargetCandidates = [...modernCities.filter((p) => (p.population || 0) >= 90000), ...ports, ...markets, ...castles]
    .map((p) => ({ ...p, demand: transportDemand(p), score: (p.score || 0.4) + transportDemand(p) * 0.24 + ((p.population || 0) >= 180000 ? 0.18 : 0.05) }));
  const pickedRoadTargets = pickEntities(roadTargetCandidates, {
    max: 8 + Math.floor(rand(seed, 1101) * 10),
    minDistance: 9,
    threshold: 0,
    seed: seed + 1100,
  });
  const roadTargets = [
    capital,
    ...pickedRoadTargets
      .filter((p) => Math.hypot(p.x - capital.x, p.y - capital.y) > 2)
      .sort((a, b) => transportDemand(b) - transportDemand(a)),
  ];
  const roadHubs = [...modernCities, ...ports, ...markets, ...stations];
  const roadCore = [capital];

  function addNationalRoad(a, b) {
    const start = routePoint(a, "road", a.x * 31 + a.y * 37);
    const goal = routePoint(b, "road", b.x * 31 + b.y * 37 + 17);
    const existing = [...nationalRoads, ...railways, ...branchRailways];
    const path = aStar(start, goal, makeTransportCost(roadCost, existing, roadHubs, [start, goal], 3, 5.8, townAvoidNodes, 3.2, 5.4));
    const direct = pathEndpointDistance(path);
    const urbanPasses = modernCities.filter((city) => path.some(([x, y]) => Math.hypot(x - city.x, y - city.y) <= Math.max(6, Math.min(13, (city.urbanRadius || 8) * 0.78)))).length;
    const passBonusOk = urbanPasses >= 2 || direct >= 24;
    if (path.length > 3 && direct >= 16 && pathLength(path) >= 20 && pathCompactness(path) < 3.35 && pathOverlapRatio(path, existing, 2) < 0.48 && passBonusOk) {
      nationalRoads.push(path);
      incrementDegree(roadDegree, a);
      incrementDegree(roadDegree, b);
      return true;
    }
    return false;
  }

  for (const target of roadTargets.slice(1, 8 + Math.floor(rand(seed, 1102) * 7))) {
    const anchor = nearestConnectable(roadCore, target, roadDegree, 3) || capital;
    if (addNationalRoad(anchor, target)) roadCore.push(target);
  }
  const roadLinkCandidates = [];
  for (let i = 0; i < roadTargets.length; i++) {
    for (let j = i + 1; j < roadTargets.length; j++) {
      const a = roadTargets[i];
      const b = roadTargets[j];
      const d = Math.hypot(a.x - b.x, a.y - b.y);
      if (d < 18 || d > 58) continue;
      const demand = Math.sqrt(transportDemand(a) * transportDemand(b));
      roadLinkCandidates.push({ a, b, score: demand / (1 + d / 18) + sameCorridorAffinity(a, b) + hash2(a.x + b.x, a.y + b.y, seed + 1111) * 0.05 });
    }
  }
  roadLinkCandidates.sort((a, b) => b.score - a.score);
  let extraRoadLinks = 0;
  for (const link of roadLinkCandidates) {
    if (extraRoadLinks >= 4) break;
    if (getDegree(roadDegree, link.a) >= 4 || getDegree(roadDegree, link.b) >= 4) continue;
    if (addNationalRoad(link.a, link.b)) {
      extraRoadLinks++;
    }
  }

  // National roads should behave like long trunk corridors: they intentionally
  // pass near as many urbanized cells/cities as possible, unlike expressways.
  const trunkCities = modernCities
    .filter((city) => prefectureMask[indexOf(city.x, city.y)] && (city.population || 0) >= 90000)
    .slice()
    .sort((a, b) => a.x - b.x || a.y - b.y);
  for (let i = 0; i < trunkCities.length - 1; i += 2) {
    const a = trunkCities[i];
    const b = trunkCities[Math.min(trunkCities.length - 1, i + 2)];
    if (a && b && Math.hypot(a.x - b.x, a.y - b.y) >= 22 && getDegree(roadDegree, a) < 5) addNationalRoad(a, b);
  }

  const expressTargets = pickEntities(modernCities.filter((p) => p !== capital && (p.population || 0) >= 180000).map((p) => ({ ...p, score: p.score + Math.hypot(p.x - capital.x, p.y - capital.y) / 80 + 0.15 })).concat(majorPorts.map((p) => ({ ...p, score: p.score + 0.55 }))), {
    max: 1 + Math.floor(rand(seed, 1120) * 3),
    minDistance: 20,
    threshold: 0.05,
    seed: seed + 1120,
  });

  const expressways = [];
  const expressDegree = new Map();
  const expressCore = [capital];

  function addExpressway(a, b, bucket = expressways) {
    const start = routePoint(a, "express", a.x * 41 + a.y * 43);
    const goal = routePoint(b, "express", b.x * 41 + b.y * 43 + 29);
    const existing = [...expressways, ...nationalRoads, ...railways, ...branchRailways];
    let path = aStar(start, goal, makeTransportCost(expresswayCost, existing, roadHubs, [start, goal], 5, 10.8, townAvoidNodes, 8.5, 14.0));
    path = smoothPathByLineOfSight(path, (x, y) => expresswayCost(x, y, x, y) < INF && slope[indexOf(x, y)] < 0.54 && elevation[indexOf(x, y)] < 0.78, 10);
    const direct = pathEndpointDistance(path);
    if (path.length > 8 && direct >= 26 && pathLength(path) >= 30 && pathCompactness(path) < 2.35 && pathOverlapRatio(path, existing, 2) < 0.30) {
      bucket.push(path);
      incrementDegree(expressDegree, a);
      incrementDegree(expressDegree, b);
      return true;
    }
    return false;
  }

  for (const target of expressTargets) {
    const anchor = nearestConnectable(expressCore, target, expressDegree, 2) || capital;
    if (addExpressway(anchor, target)) expressCore.push(target);
  }

  const ringRoads = [];
  const ringExpressways = [];
  const ringRailways = [];

  function ringAnchorCandidates(city, mode, targetRadius, sectors = 8) {
    const anchors = [];
    const minR = Math.max(5, targetRadius - 5);
    const maxR = targetRadius + 7;
    for (let s = 0; s < sectors; s++) {
      const angle0 = (s / sectors) * Math.PI * 2;
      let best = null;
      let bestScore = -INF;
      for (let dy = -Math.ceil(maxR); dy <= Math.ceil(maxR); dy++) {
        for (let dx = -Math.ceil(maxR); dx <= Math.ceil(maxR); dx++) {
          const d = Math.hypot(dx, dy);
          if (d < minR || d > maxR) continue;
          const angle = Math.atan2(dy, dx);
          let delta = Math.abs(Math.atan2(Math.sin(angle - angle0), Math.cos(angle - angle0)));
          if (delta > Math.PI / sectors * 0.95) continue;
          const x = city.x + dx;
          const y = city.y + dy;
          if (!inside(x, y)) continue;
          const i = indexOf(x, y);
          if (sea[i] || !prefectureMask[i]) continue;
          const barrier = mode === "road" ? mountainBarrierPenalty(x, y, "road") : mountainBarrierPenalty(x, y, mode === "express" ? "express" : "rail");
          if (barrier >= INF) continue;
          const density = densityValue(x, y);
          const densityTerm = mode === "rail" ? density * 0.75 : mode === "express" ? midDensityAffinity(x, y) * 0.72 : density * 0.28 + midDensityAffinity(x, y) * 0.22;
          const score = plain[i] * 0.72 + agriculture[i] * 0.12 + densityTerm - slope[i] * 1.25 - Math.max(0, elevation[i] - 0.58) * 1.3 - barrier * 0.01 - Math.abs(d - targetRadius) * 0.035 + hash2(x, y, seed + 4100 + s * 37 + mode.length * 101) * 0.08;
          if (score > bestScore) {
            bestScore = score;
            best = { x, y, score, kind: `${mode} ring anchor`, parent: city };
          }
        }
      }
      if (best) anchors.push(best);
    }
    return anchors;
  }

  function ringCost(baseCost, city, targetRadius, mode) {
    return (x, y, cx, cy) => {
      const base = baseCost(x, y, cx, cy);
      if (base >= INF) return base;
      const d = Math.hypot(x - city.x, y - city.y);
      const tooClose = Math.max(0, targetRadius * 0.46 - d);
      const tooFar = Math.max(0, d - targetRadius * 1.55);
      const bandPenalty = tooClose * 0.34 + tooFar * 0.16 + Math.abs(d - targetRadius) * 0.018;
      const density = densityValue(x, y);
      const densityBias = mode === "rail" ? -density * 0.42 : mode === "express" ? -midDensityAffinity(x, y) * 0.32 + Math.max(0, density - 0.82) * 0.8 : -density * 0.12;
      return Math.max(0.36, base + bandPenalty + densityBias);
    };
  }

  function softRingRailCost(x, y) {
    const i = indexOf(x, y);
    const barrier = mountainBarrierPenalty(x, y, "rail");
    if (sea[i] || barrier >= INF) return INF;
    const density = densityValue(x, y);
    return Math.max(0.38, 1 + slope[i] * 14 + barrier + Math.max(0, elevation[i] - 0.56) * 22 + (river[i] > 0.5 ? 1.3 : river[i] * 0.6) - density * 0.62 - plain[i] * 0.20 + normalEdgePenalty(x, y) + hash2(x, y, seed + 7222) * 0.05);
  }

  function softRingExpressCost(x, y) {
    const i = indexOf(x, y);
    const barrier = mountainBarrierPenalty(x, y, "express");
    if (sea[i] || barrier >= INF) return INF;
    return Math.max(0.38, 1 + slope[i] * 13 + barrier + Math.max(0, elevation[i] - 0.58) * 20 + (river[i] > 0.5 ? 1.0 : river[i] * 0.5) - midDensityAffinity(x, y) * 0.42 - plain[i] * 0.14 + normalEdgePenalty(x, y) + hash2(x, y, seed + 7444) * 0.05);
  }

  function addEnvironmentalRing(city, mode, bucket, baseCost, existingPaths, targetRadius) {
    const anchors = ringAnchorCandidates(city, mode, targetRadius, mode === "road" ? 7 : 8);
    if (anchors.length < 3) return 0;
    let made = 0;
    const cost = ringCost(baseCost, city, targetRadius, mode);
    for (let i = 0; i < anchors.length - (anchors.length < 4 ? 1 : 0); i++) {
      const a = anchors[i];
      const b = anchors[(i + 1) % anchors.length];
      if (Math.hypot(a.x - b.x, a.y - b.y) > targetRadius * 1.85) continue;
      const path = aStar(a, b, makeTransportCost(cost, [...existingPaths, ...bucket], roadHubs, [a, b], mode === "road" ? 3 : 4, mode === "road" ? 4.8 : 7.0, townAvoidNodes, mode === "express" ? 3.8 : 2.2, mode === "express" ? 4.8 : 2.8));
      if (path.length >= 5 && path.length <= targetRadius * 8.0) {
        bucket.push(path);
        made++;
      }
    }
    return made;
  }

  function flexibleRingAnchors(city, targetRadius, maxAnchors = 6) {
    const candidates = [];
    const maxR = targetRadius + 11;
    const minR = Math.max(5, targetRadius * 0.45);
    for (let dy = -Math.ceil(maxR); dy <= Math.ceil(maxR); dy++) {
      for (let dx = -Math.ceil(maxR); dx <= Math.ceil(maxR); dx++) {
        const d = Math.hypot(dx, dy);
        if (d < minR || d > maxR) continue;
        const x = city.x + dx;
        const y = city.y + dy;
        if (!inside(x, y)) continue;
        const i = indexOf(x, y);
        if (sea[i] || !prefectureMask[i] || elevation[i] > 0.82) continue;
        const score = plain[i] * 0.7 + midDensityAffinity(x, y) * 0.32 + densityValue(x, y) * 0.2 - slope[i] * 1.15 - Math.max(0, elevation[i] - 0.58) * 0.88 - Math.abs(d - targetRadius) * 0.02 + hash2(x, y, seed + 7555) * 0.06;
        candidates.push({ x, y, score, angle: Math.atan2(dy, dx), kind: "flexible ring anchor", parent: city });
      }
    }
    return pickEntities(candidates, { max: maxAnchors, minDistance: 5, threshold: -1, seed: seed + city.x * 83 + city.y * 89 })
      .sort((a, b) => a.angle - b.angle);
  }

  function addLooseEnvironmentalRing(city, bucket, baseCost, targetRadius) {
    let anchors = ringAnchorCandidates(city, "road", targetRadius, 6);
    if (anchors.length < 3) anchors = flexibleRingAnchors(city, targetRadius, 6);
    if (anchors.length < 2) return 0;
    let made = 0;
    for (let i = 0; i < anchors.length; i++) {
      const a = anchors[i];
      const b = anchors[(i + 1) % anchors.length];
      const path = aStar(a, b, (x, y, cx, cy) => {
        const base = baseCost(x, y, cx, cy);
        if (base >= INF) return INF;
        const d = Math.hypot(x - city.x, y - city.y);
        const band = Math.max(0, targetRadius * 0.42 - d) * 0.22 + Math.max(0, d - targetRadius * 1.7) * 0.14 + Math.abs(d - targetRadius) * 0.012;
        return Math.max(0.3, base + band);
      });
      if (path.length >= 4 && path.length <= targetRadius * 9.0) {
        bucket.push(path);
        made++;
      }
    }
    return made;
  }

  const mediumRingCities = modernCities.filter((c) => (c.population || 0) >= 130000).slice(0, 6);
  for (const city of mediumRingCities) {
    const radius = clamp(8 + Math.sqrt(city.population || 100000) / 170, 10, 22);
    addEnvironmentalRing(city, "road", ringRoads, roadCost, [...nationalRoads, ...railways, ...branchRailways], radius);
  }
  const largeRingCities = modernCities.filter((c) => (c.population || 0) >= 900000).slice(0, 1);
  for (const city of largeRingCities) {
    const roadRadius = clamp(10 + Math.sqrt(city.population || 400000) / 155, 13, 28);
    const expressRadius = roadRadius + 3 + rand(seed, city.x * 71 + city.y * 73) * 3;
    const railRadius = Math.max(8, roadRadius - 4);
    addEnvironmentalRing(city, "road", ringRoads, roadCost, [...nationalRoads, ...expressways, ...railways, ...branchRailways], roadRadius);
    // Expressway rings are intentionally disabled; expressways stay as sparse interurban corridors.
    const railRingSegments = addEnvironmentalRing(city, "rail", ringRailways, railCost, [...railways, ...branchRailways, ...nationalRoads, ...expressways], railRadius);
    // Expressway rings should be rare; do not force a fallback ring when terrain rejects it.
    if (railRingSegments === 0) addLooseEnvironmentalRing(city, ringRailways, softRingRailCost, railRadius);
  }
  ringExpressways.length = 0;
  compactPathArray(ringRoads, { minLength: 8, maxOverlap: 0.32, maxCount: 18 });
  compactPathArray(ringRailways, { minLength: 8, maxOverlap: 0.26, maxCount: 8 });

  const gatewayCandidates = [];
  for (let x = 0; x < MAP_W; x++) for (const y of [0, MAP_H - 1]) { const i = indexOf(x, y); if (!sea[i]) gatewayCandidates.push({ x, y, side: y === 0 ? "N" : "S", score: plain[i] + agriculture[i] + (1 - slope[i]) * 0.5 + coastalLowland[i] * 0.2 - Math.max(0, elevation[i] - 0.56) * 1.6 - ridgeField[i] * 0.35 }); }
  for (let y = 0; y < MAP_H; y++) for (const x of [0, MAP_W - 1]) { const i = indexOf(x, y); if (!sea[i]) gatewayCandidates.push({ x, y, side: x === 0 ? "W" : "E", score: plain[i] + agriculture[i] + (1 - slope[i]) * 0.5 + coastalLowland[i] * 0.2 - Math.max(0, elevation[i] - 0.56) * 1.6 - ridgeField[i] * 0.35 }); }

  let externalGateways = pickEntities(gatewayCandidates, {
    max: 2 + Math.floor(rand(seed, 1201) * 3),
    minDistance: 28,
    threshold: 0.4,
    seed: seed + 1201,
  }).map((p) => ({ ...p, kind: "External Gateway" }));

  function externalRoadCost(goal) {
    return (x, y) => {
      const i = indexOf(x, y);
      if (sea[i]) return INF;
      const barrier = mountainBarrierPenalty(x, y, "road");
      if (barrier >= INF) return INF;
      const borderPenalty = nearMapEdge(x, y, 1) && !(Math.abs(x - goal.x) <= 2 && Math.abs(y - goal.y) <= 2) ? 7 : nearMapEdge(x, y, 3) ? 1.5 : 0;
      const density = densityValue(x, y);
      const nodeAvoid = distanceToNearest(townAvoidNodes, x, y) < 2.2 ? 2.0 : 0;
      return Math.max(0.35, 1 + slope[i] * 13 + barrier + Math.max(0, elevation[i] - 0.54) * 7.5 + nodeAvoid + (river[i] > 0.45 ? 0.9 : 0) + floodplain[i] * 0.24 - density * 0.3 - plain[i] * 0.24 + borderPenalty + hash2(x, y, seed + 333) * 0.06);
    };
  }
  function externalExpresswayCost(goal) {
    return (x, y) => {
      const i = indexOf(x, y);
      if (sea[i]) return INF;
      const barrier = mountainBarrierPenalty(x, y, "express");
      if (barrier >= INF) return INF;
      const borderPenalty = nearMapEdge(x, y, 1) && !(Math.abs(x - goal.x) <= 2 && Math.abs(y - goal.y) <= 2) ? 7 : nearMapEdge(x, y, 3) ? 1.5 : 0;
      const density = densityValue(x, y);
      const cityDistance = distanceToNearest(modernCities, x, y);
      const cityAvoid = cityDistance < 5 ? 22.0 : cityDistance < 9 ? 11.0 : cityDistance < 13 ? 4.0 : distanceToNearest(markets, x, y) < 4 ? 3.2 : 0;
      const densityPenalty = density > 0.66 ? (density - 0.66) * 9.5 : density < 0.08 ? (0.08 - density) * 2.4 : 0;
      return Math.max(0.42, 1 + slope[i] * 19 + barrier + cityAvoid + densityPenalty + (river[i] > 0.45 ? 1 : 0) + floodplain[i] * 0.2 - midDensityAffinity(x, y) * 0.7 - plain[i] * 0.12 + borderPenalty + hash2(x, y, seed + 444) * 0.05);
    };
  }
  function externalRailCost(goal) {
    return (x, y) => {
      const i = indexOf(x, y);
      if (sea[i]) return INF;
      const barrier = mountainBarrierPenalty(x, y, "rail");
      if (barrier >= INF) return INF;
      const borderPenalty = nearMapEdge(x, y, 1) && !(Math.abs(x - goal.x) <= 2 && Math.abs(y - goal.y) <= 2) ? 9 : nearMapEdge(x, y, 3) ? 1.8 : 0;
      const density = densityValue(x, y);
      return Math.max(0.42, 1 + slope[i] * 22 + barrier + Math.max(0, elevation[i] - 0.52) * 14 + (river[i] > 0.45 ? 1.2 : 0) + borderPenalty - density * 1.0 - plain[i] * 0.28 + hash2(x, y, seed + 222) * 0.05);
    };
  }

  const externalRoads = [];
  const externalExpressways = [];
  const externalRailways = [];

  function selectExternalStart(pool, gate, degreeMap, maxDegree = 2) {
    const sorted = pool
      .filter(Boolean)
      .map((p) => ({ ...p, d: Math.hypot(p.x - gate.x, p.y - gate.y), degree: getDegree(degreeMap, p) }))
      .sort((a, b) => a.d + a.degree * 16 + (a.degree >= maxDegree ? 30 : 0) - (b.d + b.degree * 16 + (b.degree >= maxDegree ? 30 : 0)));
    return sorted.find((p) => p.degree < maxDegree) || sorted[0] || capital;
  }

  externalGateways.forEach((gate, idx) => {
    const makeExpressLink = idx === 0 || rand(seed, 1210 + idx) > 0.4;
    const roadStartRaw = selectExternalStart([...roadCore, ...modernCities, ...ports, ...markets], gate, roadDegree, 3);
    const roadStart = routePoint(roadStartRaw, makeExpressLink ? "express" : "road", gate.x * 53 + gate.y * 59);
    const roadExisting = [...nationalRoads, ...expressways, ...externalRoads, ...externalExpressways, ...railways, ...branchRailways];
    const roadBaseCost = makeExpressLink ? externalExpresswayCost(gate) : externalRoadCost(gate);
    const roadPath = aStar(roadStart, gate, makeTransportCost(roadBaseCost, roadExisting, roadHubs, [roadStart, gate], makeExpressLink ? 4 : 3, makeExpressLink ? 8.2 : 6.2, townAvoidNodes, makeExpressLink ? 5.4 : 3.2, makeExpressLink ? 7.8 : 5.6));
    if (roadPath.length > 6) {
      if (makeExpressLink) {
        externalExpressways.push(roadPath);
        incrementDegree(expressDegree, roadStartRaw);
        incrementDegree(expressDegree, gate);
        expressCore.push(gate);
      } else {
        externalRoads.push(roadPath);
        incrementDegree(roadDegree, roadStartRaw);
        incrementDegree(roadDegree, gate);
      }
    }
    if ((idx === 0 || rand(seed, 1220 + idx) > 0.5) && modernCities.length > 0) {
      const railStartRaw = selectExternalStart([...railCore, ...modernCities, ...ports], gate, railDegree, 2);
      const railStart = routePoint(railStartRaw, "rail", gate.x * 61 + gate.y * 67);
      const railExisting = [...railways, ...branchRailways, ...externalRailways, ...nationalRoads, ...expressways, ...externalExpressways];
      const railPath = aStar(railStart, gate, makeTransportCost(externalRailCost(gate), railExisting, railHubs, [railStart, gate], 4, 8.2, townAvoidNodes, 2.5, 4.4));
      if (railPath.length > 6) {
        externalRailways.push(railPath);
        incrementDegree(railDegree, railStartRaw);
        incrementDegree(railDegree, gate);
      }
    }
  });

  function pruneHighMountainTransport(paths, threshold = 0.82) {
    for (let i = paths.length - 1; i >= 0; i--) {
      if (paths[i].some(([x, y]) => elevation[indexOf(x, y)] > threshold)) paths.splice(i, 1);
    }
  }
  for (const paths of [railways, branchRailways, ringRailways, externalRailways, expressways, externalExpressways]) pruneHighMountainTransport(paths, 0.82);

  const expressInfluence = influenceFromPaths([...expressways, ...externalExpressways], 6);
  const roadInfluence = influenceFromPaths([...nationalRoads, ...ringRoads, ...expressways, ...externalRoads, ...externalExpressways], 4);

  const icCandidates = [];
  for (const path of [...expressways, ...externalExpressways]) {
    icCandidates.push(...samplePath(path, 11 + Math.floor(rand(seed, path.length + 333) * 5)).map((p) => ({ ...p, score: 0.62 + plain[indexOf(p.x, p.y)] * 0.24 + midDensityAffinity(p.x, p.y) * 0.16, kind: "Interchange" })));
    for (const city of modernCities) {
      let best = null;
      let bestDistance = 999;
      for (const [x, y] of path) {
        const d = Math.hypot(x - city.x, y - city.y);
        if (d < bestDistance) { bestDistance = d; best = { x, y }; }
      }
      if (best && bestDistance > 4 && bestDistance < 18) icCandidates.push({ ...best, score: 0.8 + city.score * 0.1, kind: "Urban Interchange" });
    }
  }

  let interchanges = pickEntities(icCandidates, { max: 14 + Math.floor(rand(seed, 1130) * 18), minDistance: 7, threshold: 0.44, seed: seed + 1130 });

  const icAccessRoads = [];
  const nationalRoadAccessPoints = nationalRoads.flatMap((path) => samplePath(path, 8));
  for (const ic of interchanges) {
    const accessTargets = [
      ...industrialZones.map((p) => ({ ...p, score: 0.95 / (1 + Math.hypot(p.x - ic.x, p.y - ic.y) / 7) })),
      ...modernCities.map((p) => ({ ...routePoint(p, "road", 8200 + p.x * 7 + p.y), score: 0.72 / (1 + Math.hypot(p.x - ic.x, p.y - ic.y) / 10) })),
      ...nationalRoadAccessPoints.map((p) => ({ ...p, score: 0.62 / (1 + Math.hypot(p.x - ic.x, p.y - ic.y) / 6), kind: "National Road Access" })),
    ];
    const target = pickEntities(accessTargets, { max: 1, minDistance: 1, threshold: 0, seed: seed + 1134 + ic.x * 3 + ic.y })[0];
    if (!target || Math.hypot(target.x - ic.x, target.y - ic.y) > 22) continue;
    const path = aStar(ic, target, roadCost);
    if (path.length > 2 && path.length < 36) icAccessRoads.push(path);
  }

  const logisticsScore = new Float32Array(SIZE);
  for (let y = 4; y < MAP_H - 4; y++) {
    for (let x = 4; x < MAP_W - 4; x++) {
      const i = indexOf(x, y);
      if (sea[i]) continue;
      const nearIC = 1 / (1 + distanceToNearest(interchanges, x, y) / 3);
      const cityPenalty = distanceToNearest(modernCities, x, y) < 5 ? 0.28 : 0;
      logisticsScore[i] = clamp(nearIC * 0.56 + plain[i] * 0.24 + roadInfluence[i] * 0.22 + expressInfluence[i] * 0.16 - slope[i] * 0.32 - cityPenalty);
    }
  }

  let logisticsParks = pickPoints(logisticsScore, {
    threshold: 0.32 + rand(seed, 1141) * 0.1,
    max: 3 + Math.floor(rand(seed, 1142) * 13),
    minDistance: 9,
    seedOffset: 1140,
    predicate: (x, y, i) => !sea[i],
  }).map((p) => ({ ...p, kind: "Logistics Park" }));

  const cityInfluence = influenceFromPoints(modernCities, 34, (p) => p.urbanWeight || 1.2);
  const cityCoreInfluence = influenceFromPoints(urbanCenters, 11, (p) => p.parent?.coreRadius ? 1.35 + p.parent.coreRadius / 5 : 1.2);
  const stationInfluence = influenceFromPoints(stations, 10, () => 1);
  const railInfluence2 = influenceFromPaths([...railways, ...branchRailways, ...ringRailways, ...externalRailways], 6);
  const satelliteScore = new Float32Array(SIZE);
  const largeCitiesForSatellites = modernCities.filter((c) => (c.population || 0) >= 320000);
  for (let y = 4; y < MAP_H - 4; y++) {
    for (let x = 4; x < MAP_W - 4; x++) {
      const i = indexOf(x, y);
      if (sea[i] || !prefectureMask[i]) continue;
      let ringPull = 0;
      let parent = null;
      for (const city of largeCitiesForSatellites) {
        const d = Math.hypot(city.x - x, city.y - y);
        const ideal = clamp(11 + Math.sqrt(city.population || 320000) / 150, 13, 27);
        const v = clamp(1 - Math.abs(d - ideal) / 9);
        if (v > ringPull) { ringPull = v; parent = city; }
      }
      if (!parent) continue;
      const railPull = Math.max(railInfluence2[i], stationInfluence[i] * 0.84);
      const separated = distanceToNearest(modernCities, x, y) > 7 ? 1 : 0;
      satelliteScore[i] = clamp(ringPull * 0.42 + railPull * 0.38 + populationDensity[i] * 0.14 + plain[i] * 0.2 + basinField[i] * 0.08 + agriculture[i] * 0.05 - slope[i] * 0.86 - ridgeField[i] * 0.34 - Math.max(0, elevation[i] - 0.56) * 0.72 + separated * 0.1 + hash2(x, y, seed + 1160) * 0.035);
    }
  }
  let satelliteCities = pickPoints(satelliteScore, {
    threshold: 0.43 + rand(seed, 1161) * 0.07,
    max: Math.min(14, 2 + largeCitiesForSatellites.length * 4 + Math.floor(rand(seed, 1162) * 4)),
    minDistance: 8,
    seedOffset: 1160,
    predicate: (x, y, i) => !sea[i] && prefectureMask[i],
  }).map((p, n) => {
    const parent = largeCitiesForSatellites.slice().sort((a, b) => Math.hypot(a.x - p.x, a.y - p.y) - Math.hypot(b.x - p.x, b.y - p.y))[0];
    const basePop = parent ? parent.population * (0.045 + rand(seed, 1165 + n) * 0.11) : 42000 + rand(seed, 1165 + n) * 90000;
    return { ...p, kind: "Satellite City", parentCityIndex: parent ? modernCities.indexOf(parent) : -1, population: Math.round(basePop / 1000) * 1000, urbanRadius: 5 + Math.sqrt(basePop) / 135, coreRadius: 1.5 + Math.sqrt(basePop) / 420, urbanWeight: 0.55 + Math.sqrt(basePop) / 720 };
  });
  const satelliteInfluence = influenceFromPoints(satelliteCities, 16, (p) => p.urbanWeight || 0.8);
  const oldCoreInfluence = influenceFromPoints([...castleTowns, ...markets, ...ports], 12, () => 1);
  const industrialInfluence = influenceFromPoints(industrialZones, 9, () => 1);
  const logisticsInfluence = influenceFromPoints(logisticsParks, 9, () => 1);
  const interchangeInfluence = influenceFromPoints(interchanges, 8, () => 1);
  const premodernInfluence = influenceFromPaths(premodernRoads, 4);
  const villageInfluence = influenceFromPoints(villages, 7, () => 1);

  const newTownScore = new Float32Array(SIZE);
  for (let y = 4; y < MAP_H - 4; y++) {
    for (let x = 4; x < MAP_W - 4; x++) {
      const i = indexOf(x, y);
      if (sea[i]) continue;
      const dCity = distanceToNearest(modernCities, x, y);
      const ring = dCity > 8 && dCity < 22 ? 1 : 0;
      const uplandTerrace = elevation[i] > 0.36 && elevation[i] < 0.58 && slope[i] < 0.34 && ridgeField[i] < 0.34 ? 0.24 : 0;
      newTownScore[i] = clamp(ring * 0.34 + stationInfluence[i] * 0.24 + roadInfluence[i] * 0.08 + railInfluence2[i] * 0.1 + plain[i] * 0.14 + uplandTerrace + agriculture[i] * 0.06 - slope[i] * 0.72 - ridgeField[i] * 0.22 - floodplain[i] * 0.22 - satelliteInfluence[i] * 0.18);
    }
  }

  let newTowns = pickPoints(newTownScore, {
    threshold: 0.32 + rand(seed, 1151) * 0.1,
    max: 2 + Math.floor(rand(seed, 1152) * 10),
    minDistance: 11,
    seedOffset: 1150,
    predicate: (x, y, i) => !sea[i],
  }).map((p) => ({ ...p, kind: "New Town" }));

  const minorRoads = [];
  const trunkNodes = [...markets, ...modernCities, ...stations.slice(0, 24), ...crossings.slice(0, 16)];
  const roadNetInfluence = influenceFromPaths([...nationalRoads, ...ringRoads, ...expressways, ...ringExpressways, ...externalRoads, ...externalExpressways, ...premodernRoads], 3);

  function minorRoadCost(x, y) {
    const i = indexOf(x, y);
    if (sea[i] || elevation[i] > 0.72) return INF;
    const barrier = mountainBarrierPenalty(x, y, "minor");
    if (barrier >= INF) return INF;
    return Math.max(0.3, 1 + slope[i] * 8.4 + barrier * 0.55 + Math.max(0, elevation[i] - 0.58) * 4.4 + floodplain[i] * 0.18 + (river[i] > 0.5 ? 1.0 : 0.18 * river[i]) - plain[i] * 0.24 - valleyField[i] * 0.36 - coastalLowland[i] * 0.12 + ridgeField[i] * 0.58 - roadNetInfluence[i] * 0.35 + normalEdgePenalty(x, y) + hash2(x, y, seed + 555) * 0.15);
  }

  const connectedPairs = new Set();
  function addMinorRoad(a, b) {
    const key = `${a.x},${a.y}|${b.x},${b.y}`;
    if (connectedPairs.has(key)) return;
    connectedPairs.add(key);
    const path = aStar(a, b, minorRoadCost);
    if (path.length > 2 && path.length < 90) minorRoads.push(path);
  }

  for (const village of villages) {
    if (rand(seed, village.x * 13 + village.y * 17) < 0.42) {
      const target = pickEntities(trunkNodes.map((p) => ({ ...p, score: 1 / (1 + Math.hypot(p.x - village.x, p.y - village.y)) })), { max: 1, minDistance: 1, threshold: 0 })[0];
      if (target && Math.hypot(target.x - village.x, target.y - village.y) < 28) addMinorRoad(village, target);
    }
  }
  for (const market of markets) {
    const localVillages = pickEntities(villages.map((v) => ({ ...v, score: 1 / (1 + Math.hypot(v.x - market.x, v.y - market.y)) })), { max: 3, minDistance: 1, threshold: 0 });
    for (const v of localVillages) addMinorRoad(market, v);
  }
  for (const pass of passes.slice(0, 8)) {
    const target = pickEntities([...markets, ...villages].map((p) => ({ ...p, score: 1 / (1 + Math.hypot(p.x - pass.x, p.y - pass.y)) })), { max: 1, minDistance: 1, threshold: 0 })[0];
    if (target) addMinorRoad(pass, target);
  }

  const newTownInfluence = influenceFromPoints(newTowns, 8, () => 1);
  const landuse = new Uint8Array(SIZE);
  for (let y = 0; y < MAP_H; y++) {
    for (let x = 0; x < MAP_W; x++) {
      const i = indexOf(x, y);
      if (sea[i]) continue;
      const mountain = elevation[i] > 0.62 || slope[i] > 0.46 || ridgeField[i] > 0.64;
      const farm = agriculture[i] > 0.26 && (plain[i] > 0.2 || valleyField[i] > 0.32 || basinField[i] > 0.25);
      let nearestCity = null;
      let nearestCityDistance = INF;
      for (const city of modernCities) {
        const d = Math.hypot(city.x - x, city.y - y);
        if (d < nearestCityDistance) { nearestCityDistance = d; nearestCity = city; }
      }
      const dCity = nearestCityDistance;
      const populationScale = nearestCity ? clamp(Math.log10(Math.max(10000, nearestCity.population)) - 4, 0.25, 2.2) : 0.5;
      const normalizedUrbanDistance = nearestCity ? dCity / Math.max(6, nearestCity.urbanRadius) : 99;
      const cityClusterBoost = nearestCity ? clamp(1 - normalizedUrbanDistance) * (0.18 + populationScale * 0.16) : 0;
      const density = populationDensity[i];
      const oldTownScore = oldCoreInfluence[i] * 0.64 + premodernInfluence[i] * 0.32 + plain[i] * 0.12 + density * 0.08;
      const terrainUrbanPenalty = slope[i] * 1.02 + ridgeField[i] * 0.55 + Math.max(0, elevation[i] - 0.56) * 0.56;
      const nodeCausalPull = Math.max(stationInfluence[i] * 0.18, premodernInfluence[i] * 0.13, coastalLowland[i] * river[i] * 0.12, valleyField[i] * 0.08);
      const satelliteEnvelope = satelliteInfluence[i] * 0.54;
      const urbanEnvelope = cityInfluence[i] * 0.58 + cityCoreInfluence[i] * 0.3 + satelliteEnvelope + density * 0.47 + stationInfluence[i] * 0.18 + oldCoreInfluence[i] * 0.14 + newTownInfluence[i] * 0.12 + cityClusterBoost + nodeCausalPull - terrainUrbanPenalty;
      const coreScore = cityCoreInfluence[i] * 0.74 + urbanEnvelope * 0.3 + density * 0.36 + satelliteInfluence[i] * 0.16 + stationInfluence[i] * 0.06 + railInfluence2[i] * 0.04 - slope[i] * 0.82 - ridgeField[i] * 0.28;
      const suburbScore = urbanEnvelope * 0.54 + density * 0.14 + satelliteInfluence[i] * 0.22 + stationInfluence[i] * 0.09 + roadInfluence[i] * 0.05 + railInfluence2[i] * 0.05 + plain[i] * 0.16 + valleyField[i] * 0.04 + populationScale * 0.05 + (coreScore < 0.58 ? 0.05 : 0) - slope[i] * 0.76 - ridgeField[i] * 0.22;
      const roadsideScore = interchangeInfluence[i] * 0.54 + logisticsInfluence[i] * 0.18 + roadInfluence[i] * 0.1 + plain[i] * 0.1 - cityInfluence[i] * 0.02;
      const isolatedCorridor = roadInfluence[i] > 0.22 && cityInfluence[i] < 0.08 && stationInfluence[i] < 0.08 && interchangeInfluence[i] < 0.18;
      const ruralScore = villageInfluence[i] * 0.3 + agriculture[i] * 0.38 + plain[i] * 0.18 - slope[i] * 0.08;

      if (mountain) landuse[i] = 9;
      else if (industrialInfluence[i] > 0.44) landuse[i] = 5;
      else if (logisticsInfluence[i] > 0.42) landuse[i] = 6;
      else if (newTownInfluence[i] > 0.42 && urbanEnvelope > 0.16) landuse[i] = 7;
      else if (coreScore > 0.68 && density > 0.48 && stationInfluence[i] > 0.05 && slope[i] < 0.24 && ridgeField[i] < 0.36) landuse[i] = 3;
      else if (oldTownScore > 0.49) landuse[i] = 2;
      else if (suburbScore > 0.235 && !isolatedCorridor && slope[i] < 0.32 && ridgeField[i] < 0.48 && (normalizedUrbanDistance < 1.42 || satelliteInfluence[i] > 0.24)) landuse[i] = 4;
      else if (roadsideScore > 0.5 && plain[i] > 0.18 && slope[i] < 0.34 && ridgeField[i] < 0.5 && !isolatedCorridor && (interchangeInfluence[i] > 0.24 || logisticsInfluence[i] > 0.16 || cityInfluence[i] > 0.09)) landuse[i] = 8;
      else if (farm) landuse[i] = 1;
      else if (ruralScore > 0.3) landuse[i] = 0;
      else landuse[i] = 0;
    }
  }

  function hasUrbanNeighborCluster(x, y, radius = 2, minUrban = 7) {
    let urban = 0;
    for (let dy = -radius; dy <= radius; dy++) {
      for (let dx = -radius; dx <= radius; dx++) {
        const nx = x + dx;
        const ny = y + dy;
        if (!inside(nx, ny)) continue;
        const lu = landuse[indexOf(nx, ny)];
        if (lu === 2 || lu === 3 || lu === 4 || lu === 7 || lu === 8) urban++;
      }
    }
    return urban >= minUrban;
  }

  function removeIsolatedUrbanPatches(maxCells = 22) {
    const seen = new Uint8Array(SIZE);
    const namedCenters = [...modernCities, ...(satelliteCities || []), ...markets, ...ports, ...newTowns, ...stations];
    const queue = [];
    for (let i = 0; i < SIZE; i++) {
      if (seen[i] || !prefectureMask[i] || sea[i]) continue;
      const lu0 = landuse[i];
      if (!(lu0 >= 2 && lu0 <= 8)) continue;
      const component = [];
      let maxDensity = 0;
      queue.length = 0;
      queue.push(i);
      seen[i] = 1;
      for (let q = 0; q < queue.length; q++) {
        const cur = queue[q];
        component.push(cur);
        maxDensity = Math.max(maxDensity, populationDensity[cur]);
        const [x, y] = xyOf(cur);
        for (const [nx, ny] of neighbors8(x, y)) {
          const ni = indexOf(nx, ny);
          if (seen[ni] || !prefectureMask[ni] || sea[ni]) continue;
          if (!(landuse[ni] >= 2 && landuse[ni] <= 8)) continue;
          seen[ni] = 1;
          queue.push(ni);
        }
      }
      if (component.length > maxCells) continue;
      let hasAnchor = false;
      for (const ci of component) {
        const [x, y] = xyOf(ci);
        if (distanceToNearest(namedCenters, x, y) <= 5.8) {
          hasAnchor = true;
          break;
        }
      }
      if (!hasAnchor) {
        for (const ci of component) landuse[ci] = agriculture[ci] > 0.34 ? 1 : 0;
      }
    }
  }

  for (let pass = 0; pass < 2; pass++) removeIsolatedUrbanPatches(36);

  // CBD is no longer a marker. It is a DID-like contiguous high-density core:
  // first remove isolated core cells, then grow connected high-density cells
  // from each urban center according to population scale.
  for (let y = 1; y < MAP_H - 1; y++) {
    for (let x = 1; x < MAP_W - 1; x++) {
      const i = indexOf(x, y);
      if (landuse[i] === 3 && !hasUrbanNeighborCluster(x, y, 2, 8)) landuse[i] = 4;
    }
  }

  function growDidCore(center, city, salt) {
    if (!center || !city) return 0;
    const start = indexOf(center.x, center.y);
    if (sea[start] || !prefectureMask[start]) return 0;
    if ((city.population || 0) < 220000) return 0;
    const targetCells = Math.round(clamp(2 + Math.sqrt(city.population || 80000) / 74, 4, 22));
    const maxRadius = clamp((city.coreRadius || 3) * 2.4 + Math.sqrt(city.population || 80000) / 260, 6, 16);
    const selected = new Set();
    const queued = new Set([start]);
    const heap = new MinHeap();
    heap.push({ i: start, f: -10 });
    let made = 0;

    while (heap.length > 0 && made < targetCells) {
      const cur = heap.pop();
      if (!cur || selected.has(cur.i)) continue;
      const [x, y] = xyOf(cur.i);
      const i = cur.i;
      const d = Math.hypot(x - center.x, y - center.y);
      const support = populationDensity[i] * 1.18 + cityInfluence[i] * 0.22 + stationInfluence[i] * 0.18 + plain[i] * 0.12 - slope[i] * 1.24 - ridgeField[i] * 0.54 - Math.max(0, elevation[i] - 0.58) * 0.50 - floodplain[i] * 0.08 - d / maxRadius * 0.22;
      if (d > maxRadius || support < 0.44 || sea[i] || !prefectureMask[i]) continue;
      if (!(landuse[i] === 2 || landuse[i] === 3 || landuse[i] === 4 || landuse[i] === 7 || populationDensity[i] > 0.22 || stationInfluence[i] > 0.14)) continue;

      selected.add(i);
      landuse[i] = 3;
      made++;

      for (const [nx, ny] of neighbors8(x, y)) {
        const ni = indexOf(nx, ny);
        if (queued.has(ni) || selected.has(ni) || sea[ni] || !prefectureMask[ni]) continue;
        const nd = Math.hypot(nx - center.x, ny - center.y);
        if (nd > maxRadius + 1) continue;
        const score = populationDensity[ni] * 1.24 + cityInfluence[ni] * 0.22 + stationInfluence[ni] * 0.18 + plain[ni] * 0.12 - slope[ni] * 1.25 - ridgeField[ni] * 0.54 - nd / maxRadius * 0.22 + hash2(nx, ny, seed + salt) * 0.03;
        queued.add(ni);
        heap.push({ i: ni, f: -score });
      }
    }
    return made;
  }

  urbanCenters.forEach((center, n) => growDidCore(center, center.parent || modernCities[n], 9400 + n * 17));
  for (let pass = 0; pass < 3; pass++) removeIsolatedUrbanPatches(42);
  for (let y = 1; y < MAP_H - 1; y++) {
    for (let x = 1; x < MAP_W - 1; x++) {
      const i = indexOf(x, y);
      if (landuse[i] === 3 && !hasUrbanNeighborCluster(x, y, 2, 8)) landuse[i] = 4;
    }
  }

  const prefectureArea = prefectureMask.reduce((sum, v) => sum + (v ? 1 : 0), 0);
  const municipalityCandidates = [];
  for (let y = 2; y < MAP_H - 2; y++) {
    for (let x = 2; x < MAP_W - 2; x++) {
      const i = indexOf(x, y);
      if (!prefectureMask[i] || sea[i]) continue;
      const urbanBias = landuse[i] === 3 ? 0.62 : landuse[i] === 2 ? 0.56 : landuse[i] === 4 ? 0.5 : landuse[i] === 1 ? 0.4 : 0.28;
      const score = urbanBias + settlementScore[i] * 0.22 + roadInfluence[i] * 0.08 + railInfluence2[i] * 0.05 + villageInfluence[i] * 0.04 - slope[i] * 0.18 - ridgeField[i] * 0.06 + hash2(x, y, seed + 1300) * 0.025;
      if (score > 0.40) municipalityCandidates.push({ x, y, score });
    }
  }
  const majorMunicipalSeeds = modernCities
    .filter((city) => (city.population || 0) >= 220000 && prefectureMask[indexOf(city.x, city.y)])
    .map((city) => ({ x: city.x, y: city.y, score: 1.55 + (city.population || 0) / 700000, protectedCity: city }));
  const filteredMunicipalityCandidates = municipalityCandidates.filter((p) => {
    const nearMajor = majorMunicipalSeeds.some((city) => Math.hypot(city.x - p.x, city.y - p.y) < clamp(12 + Math.sqrt(city.protectedCity.population || 300000) / 130, 14, 28));
    const nearSmallUrban = modernCities.some((city) => (city.population || 0) < 260000 && Math.hypot(city.x - p.x, city.y - p.y) < 8 && p.x !== city.x && p.y !== city.y);
    return !nearMajor && !nearSmallUrban;
  });
  const satelliteMunicipalSeeds = (satelliteCities || [])
    .filter((city) => prefectureMask[indexOf(city.x, city.y)])
    .map((city) => ({ x: city.x, y: city.y, score: 1.05 + (city.population || 40000) / 260000, protectedSatellite: city }));
  let adminCentersRaw = [
    ...majorMunicipalSeeds,
    ...satelliteMunicipalSeeds,
    ...pickEntities(filteredMunicipalityCandidates.filter((p) => satelliteMunicipalSeeds.every((s) => Math.hypot(s.x - p.x, s.y - p.y) >= 6)), {
      max: Math.min(20, Math.max(10, Math.floor(prefectureArea / 950) + 6 + Math.floor(rand(seed, 1301) * 3))),
      minDistance: 9 + Math.floor(rand(seed, 1302) * 3),
      threshold: 0.40,
      seed: seed + 1300,
      jitter: 0.025,
    }),
  ];
  if (adminCentersRaw.length < 12) {
    const fallback = [...modernCities, ...satelliteCities, ...markets, ...newTowns, ...stations, ...villages]
      .filter((p) => prefectureMask[indexOf(p.x, p.y)])
      .map((p) => ({ x: p.x, y: p.y, score: p.score || 0.5 }));
    adminCentersRaw = pickEntities(fallback, { max: 12, minDistance: 8, threshold: 0, seed: seed + 1303 });
  }
  if (adminCentersRaw.length < 10) {
    const extra = pickEntities(municipalityCandidates, { max: 10 - adminCentersRaw.length, minDistance: 8, threshold: 0.32, seed: seed + 1304 });
    adminCentersRaw.push(...extra.filter((p) => adminCentersRaw.every((q) => Math.hypot(p.x - q.x, p.y - q.y) >= 6)));
  }
  const adminId = generateAdminRegions(adminCentersRaw, prefectureMask, sea, elevation, slope, river, ridgeField, valleyField, populationDensity, landuse);
  smoothAdminRegionsTerrainAware(adminId, prefectureMask, sea, elevation, slope, river, ridgeField, valleyField, populationDensity, landuse, 7);

  function lockUrbanClusterToMunicipality(city, radius, allowSuburban = true) {
    if (!city || !prefectureMask[indexOf(city.x, city.y)]) return;
    let bestAdmin = -1;
    let bestD = INF;
    adminCentersRaw.forEach((center, id) => {
      const d = Math.hypot(center.x - city.x, center.y - city.y);
      if (d < bestD) { bestD = d; bestAdmin = id; }
    });
    if (bestAdmin < 0) return;
    const r = Math.ceil(radius);
    for (let dy = -r; dy <= r; dy++) {
      for (let dx = -r; dx <= r; dx++) {
        const x = city.x + dx;
        const y = city.y + dy;
        if (!inside(x, y)) continue;
        const i = indexOf(x, y);
        if (!prefectureMask[i] || sea[i]) continue;
        const d = Math.hypot(dx, dy);
        if (d > radius) continue;
        const urban = landuse[i] === 2 || landuse[i] === 3 || (allowSuburban && (landuse[i] === 4 || landuse[i] === 7 || landuse[i] === 8));
        if (urban || populationDensity[i] > 0.22) adminId[i] = bestAdmin;
      }
    }
  }
  for (const city of modernCities) {
    const radius = (city.population || 0) >= 500000
      ? clamp(17 + Math.sqrt(city.population) / 120, 20, 38)
      : clamp(5 + Math.sqrt(city.population || 70000) / 210, 6, 11);
    lockUrbanClusterToMunicipality(city, radius, true);
  }
  // Satellite cities should remain independent municipalities, not swallowed by the parent core city.
  for (const sat of satelliteCities || []) {
    if (!prefectureMask[indexOf(sat.x, sat.y)]) continue;
    let bestAdmin = -1;
    let bestD = INF;
    adminCentersRaw.forEach((center, id) => {
      const d = Math.hypot(center.x - sat.x, center.y - sat.y);
      if (d < bestD) { bestD = d; bestAdmin = id; }
    });
    if (bestAdmin >= 0) {
      const r = 5;
      for (let dy = -r; dy <= r; dy++) {
        for (let dx = -r; dx <= r; dx++) {
          const x = sat.x + dx;
          const y = sat.y + dy;
          if (!inside(x, y)) continue;
          const i = indexOf(x, y);
          if (!prefectureMask[i] || sea[i] || Math.hypot(dx, dy) > r) continue;
          if ((landuse[i] >= 2 && landuse[i] <= 4) || landuse[i] === 7 || populationDensity[i] > 0.18) adminId[i] = bestAdmin;
        }
      }
    }
  }
  lockSmallUrbanComponentsToMunicipality(adminId, prefectureMask, sea, landuse, populationDensity, 520);
  lockSmallUrbanComponentsToMunicipality(adminId, prefectureMask, sea, landuse, populationDensity, 620);
  mergeTinyMunicipalities(adminId, prefectureMask, sea, populationDensity, [...modernCities, ...satelliteCities], 260);
  removeMunicipalExclaves(adminId, prefectureMask, sea, adminCentersRaw, [...modernCities, ...satelliteCities], 180);
  applyLandscapeUnitAdminPartition(adminId, prefectureMask, sea, elevation, slope, river, ridgeField, valleyField, basinField, coastalLowland, flowAccum, plain, agriculture, populationDensity, landuse, adminCentersRaw);
  snapAdminBoundariesToTerrain(adminId, prefectureMask, sea, elevation, slope, river, ridgeField, valleyField, flowAccum, populationDensity, landuse, adminCentersRaw, [...modernCities, ...satelliteCities, ...ports, ...industrialZones, ...logisticsParks], 5);
  removeMunicipalExclaves(adminId, prefectureMask, sea, adminCentersRaw, [...modernCities, ...satelliteCities], 360);
  mergeTinyMunicipalities(adminId, prefectureMask, sea, populationDensity, [...modernCities, ...satelliteCities], 220);
  const adminBorders = extractAdminBorderSegments(adminId, prefectureMask);

  // Final population pass after land-use cleanup, satellite municipality locking, and isolated urban deletion.
  // This keeps population figures proportional to the actually rendered urbanized area.
  recalculatePopulationAfterLanduse(modernCities, satelliteCities, populationDensity, landuse, prefectureMask, sea, stationInfluence, roadInfluence, railInfluence2);
  for (const city of modernCities) {
    if (city.isPrefecturalCapital) continue;
    const cap = cityPopulationCap(city);
    if (cap < INF && (city.population || 0) > cap) {
      city.population = Math.round(cap / 1000) * 1000;
      city.urbanRadius = clamp(5.0 + Math.sqrt(city.population) / 100, 6, 16);
      city.coreRadius = clamp(1.8 + Math.sqrt(city.population) / 400, 2.2, 5.2);
      city.urbanWeight = clamp(0.72 + Math.log10(Math.max(10000, city.population)) * 0.30, 1.0, 2.0);
    }
  }

  function makeHarborWorks(ports) {
    const out = [];
    for (const port of ports) {
      const parts = [];
      const limit = port.portClass === "major" ? 5 : port.portClass === "regional" ? 3 : 1;
      for (const [dx, dy] of [[1,0],[-1,0],[0,1],[0,-1],[1,1],[-1,1],[1,-1],[-1,-1]]) {
        const sx = port.x + dx;
        const sy = port.y + dy;
        if (!inside(sx, sy) || !sea[indexOf(sx, sy)]) continue;
        parts.push([[port.x, port.y], [sx, sy]]);
        const wx = sx + dx;
        const wy = sy + dy;
        if (port.portClass === "major" && inside(wx, wy) && sea[indexOf(wx, wy)] && rand(seed, sx * 101 + sy * 103) > 0.22) parts.push([[sx, sy], [wx, wy]]);
        if (parts.length >= limit) break;
      }
      if (parts.length) out.push({ port, segments: parts, kind: port.portClass === "major" ? "Major Harbor Works" : "Harbor Works" });
    }
    return out;
  }

  // Bridge and tunnel icon systems were removed from the visual model.
  // Arrays remain empty for backward-compatible tests and downstream code.
  const bridges = [];
  const tunnels = [];
  const harborWorks = makeHarborWorks(ports);
  const abandonedRailways = branchRailways.filter((_, i) => i % 3 === 0);
  let castleRuins = castles.filter((_, i) => i % 2 === 1).map((c) => ({ ...c, kind: "Castle Ruins" }));
  const preservedOldRoads = premodernRoads.filter((_, i) => i % 2 === 0);
  const nameFields = { elevation, slope, sea, river, plain, agriculture, ridgeField, valleyField, basinField, coastalLowland };
  const usedNames = new Set(Object.values(CUSTOM_NAMES));

  villages = attachIdsAndNames(tagInsidePrefecture(villages, prefectureMask), "village", seed, null, nameFields, usedNames);
  ports = attachIdsAndNames(tagInsidePrefecture(ports, prefectureMask), "port", seed, null, nameFields, usedNames);
  crossings = attachIdsAndNames(tagInsidePrefecture(crossings, prefectureMask), "crossing", seed, null, nameFields, usedNames);
  passes = attachIdsAndNames(tagInsidePrefecture(passes, prefectureMask), "pass", seed, null, nameFields, usedNames);
  markets = attachIdsAndNames(tagInsidePrefecture(markets, prefectureMask), "market", seed, null, nameFields, usedNames);
  castles = attachIdsAndNames(tagInsidePrefecture(castles, prefectureMask), "castle", seed, null, nameFields, usedNames);
  castleTowns = attachIdsAndNames(tagInsidePrefecture(castleTowns, prefectureMask), "castleTown", seed, null, nameFields, usedNames);
  modernCities = attachIdsAndNames(tagInsidePrefecture(modernCities, prefectureMask), "city", seed, null, nameFields, usedNames);
  stations = attachIdsAndNames(tagInsidePrefecture(stations, prefectureMask), "station", seed, null, nameFields, usedNames);
  industrialZones = attachIdsAndNames(tagInsidePrefecture(industrialZones, prefectureMask), "industrial", seed, null, nameFields, usedNames);
  interchanges = attachIdsAndNames(tagInsidePrefecture(interchanges, prefectureMask), "interchange", seed, null, nameFields, usedNames);
  logisticsParks = attachIdsAndNames(tagInsidePrefecture(logisticsParks, prefectureMask), "logistics", seed, null, nameFields, usedNames);
  satelliteCities = attachIdsAndNames(tagInsidePrefecture(satelliteCities, prefectureMask), "satellite", seed, null, nameFields, usedNames);
  newTowns = attachIdsAndNames(tagInsidePrefecture(newTowns, prefectureMask), "newtown", seed, null, nameFields, usedNames);
  castleRuins = attachIdsAndNames(tagInsidePrefecture(castleRuins, prefectureMask), "castleRuin", seed, null, nameFields, usedNames);
  externalGateways = attachIdsAndNames(tagInsidePrefecture(externalGateways, prefectureMask), "gateway", seed, "External Gateway", nameFields, usedNames);
  const adminCenters = attachIdsAndNames(tagInsidePrefecture(adminCentersRaw, prefectureMask), "admin", seed, "Municipal Center", nameFields, usedNames);

  const entitiesForNames = [
    ...modernCities,
    ...ports,
    ...markets,
    ...castles,
    ...stations,
    ...industrialZones,
    ...interchanges,
    ...logisticsParks,
    ...satelliteCities,
    ...newTowns,
    ...passes,
    ...crossings,
    ...externalGateways,
  ].filter((p) => p.insidePrefecture || p.kind === "External Gateway");

  return applyOutputOptions({
    width: MAP_W,
    height: MAP_H,
    cellSize: CELL_SIZE,
    prefectureMask,
    prefectureBorder,
    prefectureRegionId,
    regionalPrefectureBorders,
    elevation,
    moisture,
    slope,
    sea,
    river,
    floodplain,
    plain,
    agriculture,
    settlementCluster,
    ridgeField,
    valleyField,
    basinField,
    coastalLowland,
    flowAccum,
    erosionField,
    depositionField,
    villages,
    ports,
    crossings,
    passes,
    markets,
    castles,
    castleTowns,
    premodernRoads,
    minorRoads,
    modernCities,
    prefecturalCapital: modernCities.find((city) => city.isPrefecturalCapital && prefectureMask[indexOf(city.x, city.y)]) || null,
    totalPopulation: [...modernCities, ...satelliteCities].reduce((sum, city) => sum + (city.population || 0), 0),
    populationDensity,
    railways,
    branchRailways,
    ringRailways,
    externalRailways,
    stations,
    industrialZones,
    nationalRoads,
    ringRoads,
    expressways,
    ringExpressways,
    icAccessRoads,
    externalRoads,
    externalExpressways,
    interchanges,
    logisticsParks,
    satelliteCities,
    newTowns,
    bridges,
    tunnels,
    harborWorks,
    landuse,
    adminCenters,
    adminId,
    adminBorders,
    abandonedRailways,
    castleRuins,
    preservedOldRoads,
    riverPaths,
    mainRivers,
    tributaryRivers,
    smallStreams,
    externalGateways,
    entitiesForNames,
  }, options);
}