diff --git a/rules/jsonschema-2019-09-to-2020-12.json b/rules/jsonschema-2019-09-to-2020-12.json
index 7e94865..a7c85b7 100644
--- a/rules/jsonschema-2019-09-to-2020-12.json
+++ b/rules/jsonschema-2019-09-to-2020-12.json
@@ -10,7 +10,8 @@
         "required": [ "$schema" ],
         "properties": {
           "$schema": {
-            "const": "https://json-schema.org/draft/2019-09/schema"
+            "type": "string",
+            "pattern": "^http[s]?://json-schema.org/draft/2019-09/schema[#]?$"
           }
         }
       },
diff --git a/rules/jsonschema-draft3-to-draft4.json b/rules/jsonschema-draft3-to-draft4.json
index 281247e..615c298 100644
--- a/rules/jsonschema-draft3-to-draft4.json
+++ b/rules/jsonschema-draft3-to-draft4.json
@@ -10,7 +10,8 @@
         "required": [ "$schema" ],
         "properties": {
           "$schema": {
-            "const": "http://json-schema.org/draft-03/schema#"
+            "type": "string",
+            "pattern": "^http[s]?://json-schema.org/draft-03/schema[#]?$"
           }
         }
       },
diff --git a/rules/jsonschema-draft4-to-draft6.json b/rules/jsonschema-draft4-to-draft6.json
index 9f76891..28ce4f5 100644
--- a/rules/jsonschema-draft4-to-draft6.json
+++ b/rules/jsonschema-draft4-to-draft6.json
@@ -10,7 +10,8 @@
         "required": [ "$schema" ],
         "properties": {
           "$schema": {
-            "const": "http://json-schema.org/draft-04/schema#"
+            "type": "string",
+            "pattern": "^http[s]?://json-schema.org/draft-04/schema[#]?$"
           }
         }
       },
diff --git a/rules/jsonschema-draft6-to-draft7.json b/rules/jsonschema-draft6-to-draft7.json
index 63d7fd8..e7e1a4c 100644
--- a/rules/jsonschema-draft6-to-draft7.json
+++ b/rules/jsonschema-draft6-to-draft7.json
@@ -10,7 +10,8 @@
         "required": [ "$schema" ],
         "properties": {
           "$schema": {
-            "const": "http://json-schema.org/draft-06/schema#"
+            "type": "string",
+            "pattern": "^http[s]?://json-schema.org/draft-06/schema[#]?$"
           }
         }
       },
diff --git a/rules/jsonschema-draft7-to-2019-09.json b/rules/jsonschema-draft7-to-2019-09.json
index 81f7bd9..2a8d7f2 100644
--- a/rules/jsonschema-draft7-to-2019-09.json
+++ b/rules/jsonschema-draft7-to-2019-09.json
@@ -10,7 +10,8 @@
         "required": [ "$schema" ],
         "properties": {
           "$schema": {
-            "const": "http://json-schema.org/draft-07/schema#"
+            "type": "string",
+            "pattern": "^http[s]?://json-schema.org/draft-07/schema[#]?$"
           }
         }
       },
diff --git a/test/rules/jsonschema-2019-09-to-2020-12.json b/test/rules/jsonschema-2019-09-to-2020-12.json
index 6c2b0d3..9c0d65b 100644
--- a/test/rules/jsonschema-2019-09-to-2020-12.json
+++ b/test/rules/jsonschema-2019-09-to-2020-12.json
@@ -10,6 +10,28 @@
       "type": "object"
     }
   },
+  {
+    "name": "2019-09 official $schema to 2020-12 with http scheme",
+    "schema": {
+      "$schema": "http://json-schema.org/draft/2019-09/schema",
+      "type": "object"
+    },
+    "expected": {
+      "$schema": "https://json-schema.org/draft/2020-12/schema",
+      "type": "object"
+    }
+  },
+  {
+    "name": "2019-09 official $schema to 2020-12 with an empty fragment",
+    "schema": {
+      "$schema": "https://json-schema.org/draft/2019-09/schema#",
+      "type": "object"
+    },
+    "expected": {
+      "$schema": "https://json-schema.org/draft/2020-12/schema",
+      "type": "object"
+    }
+  },
   {
     "name": "items array to prefixItems",
     "schema": {
diff --git a/test/rules/jsonschema-draft4-to-2019-09.json b/test/rules/jsonschema-draft4-to-2019-09.json
index 086f972..f5630fc 100644
--- a/test/rules/jsonschema-draft4-to-2019-09.json
+++ b/test/rules/jsonschema-draft4-to-2019-09.json
@@ -8,6 +8,24 @@
       "$schema": "https://json-schema.org/draft/2019-09/schema"
     }
   },
+  {
+    "name": "draft4 $schema with https scheme",
+    "schema": {
+      "$schema": "https://json-schema.org/draft-04/schema#"
+    },
+    "expected": {
+      "$schema": "https://json-schema.org/draft/2019-09/schema"
+    }
+  },
+  {
+    "name": "draft4 $schema without an empty fragment",
+    "schema": {
+      "$schema": "http://json-schema.org/draft-04/schema"
+    },
+    "expected": {
+      "$schema": "https://json-schema.org/draft/2019-09/schema"
+    }
+  },
   {
     "name": "draft4 id to $id",
     "schema": {
diff --git a/test/rules/jsonschema-draft4-to-2020-12.json b/test/rules/jsonschema-draft4-to-2020-12.json
index a2af82a..8c73dc6 100644
--- a/test/rules/jsonschema-draft4-to-2020-12.json
+++ b/test/rules/jsonschema-draft4-to-2020-12.json
@@ -8,6 +8,24 @@
       "$schema": "https://json-schema.org/draft/2020-12/schema"
     }
   },
+  {
+    "name": "draft4 $schema with https scheme",
+    "schema": {
+      "$schema": "http://json-schema.org/draft-04/schema#"
+    },
+    "expected": {
+      "$schema": "https://json-schema.org/draft/2020-12/schema"
+    }
+  },
+  {
+    "name": "draft4 $schema without an empty fragment",
+    "schema": {
+      "$schema": "http://json-schema.org/draft-04/schema"
+    },
+    "expected": {
+      "$schema": "https://json-schema.org/draft/2020-12/schema"
+    }
+  },
   {
     "name": "draft4 id to $id",
     "schema": {
diff --git a/test/rules/jsonschema-draft4-to-draft6.json b/test/rules/jsonschema-draft4-to-draft6.json
index 2dbf04c..d387929 100644
--- a/test/rules/jsonschema-draft4-to-draft6.json
+++ b/test/rules/jsonschema-draft4-to-draft6.json
@@ -8,6 +8,24 @@
       "$schema": "http://json-schema.org/draft-06/schema#"
     }
   },
+  {
+    "name": "draft4 $schema with https scheme",
+    "schema": {
+      "$schema": "http://json-schema.org/draft-04/schema#"
+    },
+    "expected": {
+      "$schema": "http://json-schema.org/draft-06/schema#"
+    }
+  },
+  {
+    "name": "draft4 $schema without an empty fragment",
+    "schema": {
+      "$schema": "http://json-schema.org/draft-04/schema"
+    },
+    "expected": {
+      "$schema": "http://json-schema.org/draft-06/schema#"
+    }
+  },
   {
     "name": "draft4 id to $id",
     "schema": {
diff --git a/test/rules/jsonschema-draft4-to-draft7.json b/test/rules/jsonschema-draft4-to-draft7.json
index cca8d1b..6b7ad36 100644
--- a/test/rules/jsonschema-draft4-to-draft7.json
+++ b/test/rules/jsonschema-draft4-to-draft7.json
@@ -8,6 +8,24 @@
       "$schema": "http://json-schema.org/draft-07/schema#"
     }
   },
+  {
+    "name": "draft4 $schema with https scheme",
+    "schema": {
+      "$schema": "http://json-schema.org/draft-04/schema#"
+    },
+    "expected": {
+      "$schema": "http://json-schema.org/draft-07/schema#"
+    }
+  },
+  {
+    "name": "draft4 $schema without an empty fragment",
+    "schema": {
+      "$schema": "http://json-schema.org/draft-04/schema"
+    },
+    "expected": {
+      "$schema": "http://json-schema.org/draft-07/schema#"
+    }
+  },
   {
     "name": "draft4 id to $id",
     "schema": {
diff --git a/test/rules/jsonschema-draft6-to-2019-09.json b/test/rules/jsonschema-draft6-to-2019-09.json
index 205294b..e75c8be 100644
--- a/test/rules/jsonschema-draft6-to-2019-09.json
+++ b/test/rules/jsonschema-draft6-to-2019-09.json
@@ -8,6 +8,24 @@
       "$schema": "https://json-schema.org/draft/2019-09/schema"
     }
   },
+  {
+    "name": "draft6 $schema witgh https scheme",
+    "schema": {
+      "$schema": "https://json-schema.org/draft-06/schema#"
+    },
+    "expected": {
+      "$schema": "https://json-schema.org/draft/2019-09/schema"
+    }
+  },
+  {
+    "name": "draft6 $schema without an empty fragment",
+    "schema": {
+      "$schema": "http://json-schema.org/draft-06/schema"
+    },
+    "expected": {
+      "$schema": "https://json-schema.org/draft/2019-09/schema"
+    }
+  },
   {
     "name": "draft6 $id with # to $anchor",
     "schema": {
diff --git a/test/rules/jsonschema-draft6-to-2020-12.json b/test/rules/jsonschema-draft6-to-2020-12.json
index 6226beb..bfa8bfc 100644
--- a/test/rules/jsonschema-draft6-to-2020-12.json
+++ b/test/rules/jsonschema-draft6-to-2020-12.json
@@ -8,6 +8,24 @@
       "$schema": "https://json-schema.org/draft/2020-12/schema"
     }
   },
+  {
+    "name": "draft6 $schema with https scheme",
+    "schema": {
+      "$schema": "https://json-schema.org/draft-06/schema#"
+    },
+    "expected": {
+      "$schema": "https://json-schema.org/draft/2020-12/schema"
+    }
+  },
+  {
+    "name": "draft6 $schema without an empty fragment",
+    "schema": {
+      "$schema": "http://json-schema.org/draft-06/schema"
+    },
+    "expected": {
+      "$schema": "https://json-schema.org/draft/2020-12/schema"
+    }
+  },
   {
     "name": "draft6 $id with # to $anchor",
     "schema": {
diff --git a/test/rules/jsonschema-draft6-to-draft7.json b/test/rules/jsonschema-draft6-to-draft7.json
index 5ecde0b..3ac517d 100644
--- a/test/rules/jsonschema-draft6-to-draft7.json
+++ b/test/rules/jsonschema-draft6-to-draft7.json
@@ -8,6 +8,24 @@
       "$schema": "http://json-schema.org/draft-07/schema#"
     }
   },
+  {
+    "name": "draft6 $schema wituh https scheme",
+    "schema": {
+      "$schema": "http://json-schema.org/draft-06/schema#"
+    },
+    "expected": {
+      "$schema": "http://json-schema.org/draft-07/schema#"
+    }
+  },
+  {
+    "name": "draft6 $schema without an empty fragment",
+    "schema": {
+      "$schema": "http://json-schema.org/draft-06/schema"
+    },
+    "expected": {
+      "$schema": "http://json-schema.org/draft-07/schema#"
+    }
+  },
   {
     "name": "true no metaschema",
     "schema": {},
diff --git a/test/rules/jsonschema-draft7-to-2019-09.json b/test/rules/jsonschema-draft7-to-2019-09.json
index d63e87b..b1c1d02 100644
--- a/test/rules/jsonschema-draft7-to-2019-09.json
+++ b/test/rules/jsonschema-draft7-to-2019-09.json
@@ -8,6 +8,24 @@
       "$schema": "https://json-schema.org/draft/2019-09/schema"
     }
   },
+  {
+    "name": "draft7 $schema with https scheme",
+    "schema": {
+      "$schema": "https://json-schema.org/draft-07/schema#"
+    },
+    "expected": {
+      "$schema": "https://json-schema.org/draft/2019-09/schema"
+    }
+  },
+  {
+    "name": "draft7 $schema without an empty fragment",
+    "schema": {
+      "$schema": "http://json-schema.org/draft-07/schema"
+    },
+    "expected": {
+      "$schema": "https://json-schema.org/draft/2019-09/schema"
+    }
+  },
   {
     "name": "draft7 $id with # to $anchor",
     "schema": {
diff --git a/test/rules/jsonschema-draft7-to-2020-12.json b/test/rules/jsonschema-draft7-to-2020-12.json
index 85e6206..8b49bf8 100644
--- a/test/rules/jsonschema-draft7-to-2020-12.json
+++ b/test/rules/jsonschema-draft7-to-2020-12.json
@@ -8,6 +8,24 @@
       "$schema": "https://json-schema.org/draft/2020-12/schema"
     }
   },
+  {
+    "name": "draft7 $schema with https scheme",
+    "schema": {
+      "$schema": "https://json-schema.org/draft-07/schema#"
+    },
+    "expected": {
+      "$schema": "https://json-schema.org/draft/2020-12/schema"
+    }
+  },
+  {
+    "name": "draft7 $schema without an empty fragment",
+    "schema": {
+      "$schema": "http://json-schema.org/draft-07/schema"
+    },
+    "expected": {
+      "$schema": "https://json-schema.org/draft/2020-12/schema"
+    }
+  },
   {
     "name": "draft7 $id with # to $anchor",
     "schema": {