diff --git a/core/src/PotionCatalog.cpp b/core/src/PotionCatalog.cpp
index fd2d16d..a25383d 100644
--- a/core/src/PotionCatalog.cpp
+++ b/core/src/PotionCatalog.cpp
@@ -155,3 +155,156 @@ int PotionCatalog::variantTicks(const PotionItem& potion) const {
     if (!row.carriesEffect()) return 0;
     if (row.instant) return 1;
 
+    int ticks = row.normalTicks;
+    if (potion.upgraded && row.acceptsGlowstone()) {
+        ticks = row.upgradedTicks;
+    } else if (potion.extended && row.acceptsRedstone()) {
+        ticks = row.extendedTicks;
+    }
+
+    if (potion.form == PotionItem::Form::Splash) {
+        return static_cast<int>(std::floor(static_cast<float>(ticks) * splashDurationScale));
+    }
+    if (potion.form == PotionItem::Form::Lingering) {
+        return static_cast<int>(std::floor(static_cast<float>(ticks) * lingeringDoseScale));
+    }
+    return ticks;
+}
+
+int PotionCatalog::cloudTicks(const PotionItem& potion) const {
+    if (potion.form != PotionItem::Form::Lingering) return 0;
+    if (!entry(potion.kind).carriesEffect()) return 0;
+    return lingeringCloudTicks;
+}
+
+const PotionCatalog& potionCatalog() {
+    static const PotionCatalog catalog;
+    return catalog;
+}
+
+int blazePowderForBrews(int brewCount) {
+    if (brewCount <= 0) return 0;
+    return (brewCount + brewsPerBlazePowder - 1) / brewsPerBlazePowder;
+}
+
+PotionItem catalogBrewStep(const PotionItem& base, Ingredient ingredient, bool& changed) {
+    changed = false;
+    if (base.form == PotionItem::Form::Lingering) return base;
+    if (ingredient == Ingredient::DragonBreath) {
+        if (base.form != PotionItem::Form::Splash) return base;
+        PotionItem lingering = base;
+        lingering.form = PotionItem::Form::Lingering;
+        changed = true;
+        return lingering;
+    }
+    return brewResult(base, ingredient, changed);
+}
+
+int BrewGraph::stateCount() { return potionKindCount * potionFormCount * potionModifierCount; }
+
+int BrewGraph::stateIndex(const PotionItem& potion) {
+    int kind = static_cast<int>(potion.kind);
+    int form = static_cast<int>(potion.form);
+    return (kind * potionFormCount + form) * potionModifierCount + modifierIndex(potion);
+}
+
+PotionItem BrewGraph::stateAt(int index) {
+    PotionItem potion;
+    int modifier = index % potionModifierCount;
+    int rest = index / potionModifierCount;
+    potion.form = static_cast<PotionItem::Form>(rest % potionFormCount);
+    potion.kind = static_cast<PotionKind>(rest / potionFormCount);
+    potion.upgraded = modifier == 1;
+    potion.extended = modifier == 2;
+    return potion;
+}
+
+BrewGraph::BrewGraph(const PotionCatalog& source) : catalog(&source), nodes(stateCount()) {
+    int start = stateIndex(PotionItem{});
+    nodes[static_cast<std::size_t>(start)].depth = 0;
+
+    std::deque<int> frontier;
+    frontier.push_back(start);
+    while (!frontier.empty()) {
+        int current = frontier.front();
+        frontier.pop_front();
+        PotionItem bottle = stateAt(current);
+
+        for (int step = 1; step < static_cast<int>(Ingredient::Count); ++step) {
+            Ingredient ingredient = static_cast<Ingredient>(step);
+            bool changed = false;
+            PotionItem brewed = catalogBrewStep(bottle, ingredient, changed);
+            if (!changed) continue;
+
+            int next = stateIndex(brewed);
+            Node& node = nodes[static_cast<std::size_t>(next)];
+            if (node.depth >= 0) continue;
+            node.depth = nodes[static_cast<std::size_t>(current)].depth + 1;
+            node.previous = current;
+            node.via = ingredient;
+            frontier.push_back(next);
+        }
+    }
+}
+
+int BrewGraph::depthOf(const PotionItem& potion) const {
+    return nodes[static_cast<std::size_t>(stateIndex(potion))].depth;
+}
+
+bool BrewGraph::reachable(const PotionItem& potion) const { return depthOf(potion) >= 0; }
+
+BrewPath BrewGraph::shortestPath(const PotionItem& target) const {
+    BrewPath path;
+    path.target = target;
+
+    int index = stateIndex(target);
+    if (nodes[static_cast<std::size_t>(index)].depth < 0) return path;
+
+    path.reachable = true;
+    while (nodes[static_cast<std::size_t>(index)].previous >= 0) {
+        const Node& node = nodes[static_cast<std::size_t>(index)];
+        path.steps.push_back(node.via);
+        if (node.via == Ingredient::BlazePowder) ++path.blazePowderIngredient;
+        index = node.previous;
+    }
+    std::reverse(path.steps.begin(), path.steps.end());
+    path.blazePowderFuel = blazePowderForBrews(path.stepCount());
+    path.totalTicks = path.stepCount() * brewDurationTicks;
+    return path;
+}
+
+BrewPath BrewGraph::shortestPath(PotionKind kind) const {
+    PotionItem bottle;
+    bottle.kind = kind;
+    return shortestPath(bottle);
+}
+
+int BrewGraph::reachableStateCount() const {
+    int total = 0;
+    for (const Node& node : nodes) {
+        if (node.depth >= 0) ++total;
+    }
+    return total;
+}
+
+std::vector<PotionItem> BrewGraph::statesAtDepth(int steps) const {
+    std::vector<PotionItem> found;
+    for (int index = 0; index < stateCount(); ++index) {
+        if (nodes[static_cast<std::size_t>(index)].depth != steps) continue;
+        found.push_back(stateAt(index));
+    }
+    return found;
+}
+
+std::vector<BrewPath> BrewGraph::drinkablePaths() const {
+    std::vector<BrewPath> paths;
+    for (const PotionEntry& row : catalog->entries()) paths.push_back(shortestPath(row.kind));
+    return paths;
+}
+
+const BrewGraph& brewGraph() {
+    static const BrewGraph graph(potionCatalog());
+    return graph;
+}
+
+} // namespace vf