Toolbox: no alias may be a cluster problem's title; min's identity is +Infinity

"merge intervals" is #56's own title, so the leak bounce would have bounced
the coach's restatement of it; "dictionary" was a bare common word. A test
now pins that no entry name or alias equals any clusters.json title.

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01PjvF5DZG9JduSBYKxqyysi

leetcode_coach/leetcode_coach/tests/test_toolbox.py

@@ -13,7 +13,7 @@ from typing import TYPE_CHECKING
 
 import pytest
 
-from leetcode_coach import card_rules, toolbox, toolbox_cards
+from leetcode_coach import card_rules, progress, toolbox, toolbox_cards
 
 if TYPE_CHECKING:
     from pathlib import Path
@@ -47,6 +47,19 @@ def test_names_and_aliases_are_unique() -> None:
     assert len(names) == len(set(names))
 
 
+def test_no_name_is_a_cluster_problem_title() -> None:
+    # The leak bounce fires on any entry name or alias before the first code
+    # event, so one that is a problem's own title bounces its restatement.
+    titles = {
+        p["slug"].replace("-", " ")
+        for problems in progress.load_clusters().values()
+        for p in problems
+    }
+    for entry in toolbox.load()["entries"]:
+        for name in [entry["name"], *entry["aliases"]]:
+            assert name.casefold() not in titles, name
+
+
 def test_no_entry_property_set_nests_inside_another() -> None:
     entries = toolbox.load()["entries"]
     assert len(entries) >= 20

leetcode_coach/leetcode_coach/toolbox.json

@@ -4,7 +4,7 @@
     "invertible": "every step has a known undo: a + x - x = a",
     "commutative": "operand order does not matter: a + b = b + a",
     "associative": "grouping does not matter, so a running fold works: (a + b) + c = a + (b + c)",
-    "identity element": "a neutral value e with a op e = a: 0 for + ^ gcd, -Infinity for max",
+    "identity element": "a neutral value e with a op e = a: 0 for + ^ gcd, -Infinity for max, +Infinity for min",
     "idempotent": "combining a value with itself changes nothing: max(a, a) = a",
     "selective": "the result is always one of the operands: max(a, b) is a or b",
     "divides its inputs": "the result divides every operand, so folding more values can only shrink it",
@@ -74,7 +74,7 @@
     },
     {
       "name": "hash map",
-      "aliases": ["hashmap", "hash table", "new Map", "dictionary"],
+      "aliases": ["hashmap", "hash table", "new Map"],
       "properties": ["O(1) lookup", "stores a value per key", "arbitrary keys"]
     },
     {
@@ -129,7 +129,7 @@
     },
     {
       "name": "sort by start + merge",
-      "aliases": ["merge intervals", "sort by start"],
+      "aliases": ["sort by start", "sort then combine"],
       "properties": ["needs sorted input", "overlaps become adjacent", "single pass"]
     },
     {