diff --git a/dist/chunk-DRJX3OJG.js b/dist/chunk-DRJX3OJG.js
index 6e5aedb..ce4bdb4 100644
--- a/dist/chunk-DRJX3OJG.js
+++ b/dist/chunk-DRJX3OJG.js
@@ -86,6 +86,18 @@ var BaseSchema = class {
   or(other) {
     return k.union([this, other]);
   }
+  optional() {
+    return new KOptional(this);
+  }
+  nullable() {
+    return this.or(k.null());
+  }
+  nullish() {
+    return this.nullable().optional();
+  }
+  default(defaultValue) {
+    return new KDefault(this, defaultValue);
+  }
   example(example) {
     if (example === void 0) {
       return this.def.example;
@@ -99,6 +111,74 @@ var BaseSchema = class {
     return this.clone({ description });
   }
 };
+var KOptional = class extends BaseSchema {
+  schema;
+  constructor(schema) {
+    super({});
+    this.schema = schema;
+  }
+  serialize(value) {
+    if (value === void 0) {
+      return void 0;
+    }
+    return this.schema.serialize(value);
+  }
+  toOpenAPI() {
+    return this.schema.toOpenAPI();
+  }
+  parseSafe(json) {
+    if (json === void 0) {
+      return { success: true, result: void 0 };
+    }
+    return this.schema.parseSafe(json);
+  }
+  parse(json) {
+    const result = this.parseSafe(json);
+    if (!result.success) {
+      throw new SchemaError(result.issues);
+    }
+    return result.result;
+  }
+  visit(visitor) {
+    visitor(this.schema);
+    this.schema.visit(visitor);
+  }
+};
+var KDefault = class extends BaseSchema {
+  schema;
+  defaultValue;
+  constructor(schema, defaultValue) {
+    super({});
+    this.schema = schema;
+    this.defaultValue = defaultValue;
+  }
+  serialize(value) {
+    return this.schema.serialize(value === void 0 ? this.defaultValue : value);
+  }
+  toOpenAPI() {
+    return {
+      ...this.schema.toOpenAPI(),
+      default: this.schema.serialize(this.defaultValue)
+    };
+  }
+  parseSafe(json) {
+    if (json === void 0) {
+      return { success: true, result: this.defaultValue };
+    }
+    return this.schema.parseSafe(json);
+  }
+  parse(json) {
+    const result = this.parseSafe(json);
+    if (!result.success) {
+      throw new SchemaError(result.issues);
+    }
+    return result.result;
+  }
+  visit(visitor) {
+    visitor(this.schema);
+    this.schema.visit(visitor);
+  }
+};
 var STRING_FORMAT_REGEXES = {
   uuid: /^[0-9a-fA-F]{8}\b-[0-9a-fA-F]{4}\b-[0-9a-fA-F]{4}\b-[0-9a-fA-F]{4}\b-[0-9a-fA-F]{12}$/i,
   email: /^(?!\.)(?!.*\.\.)([A-Z0-9_'+\-\.]*)[A-Z0-9_+-]@([A-Z0-9][A-Z0-9\-]*\.)+[A-Z]{2,}$/i,
@@ -406,6 +486,22 @@ var KNumber = class _KNumber extends BaseSchema {
   visit() {
   }
 };
+var KCoercedNumber = class extends KNumber {
+  static create = () => new KCoercedNumber({});
+  parseSafe(json) {
+    if (typeof json === "string") {
+      if (json.trim() === "") {
+        return { success: false, issues: /* @__PURE__ */ new Set([{ message: "Expected number", path: [] }]) };
+      }
+      const coerced = Number(json);
+      if (!Number.isFinite(coerced)) {
+        return { success: false, issues: /* @__PURE__ */ new Set([{ message: "Expected number", path: [] }]) };
+      }
+      return super.parseSafe(coerced);
+    }
+    return super.parseSafe(json);
+  }
+};
 var KBoolean = class _KBoolean extends BaseSchema {
   static create = () => new _KBoolean({});
   serialize(value) {
@@ -545,6 +641,9 @@ var KObject = class _KObject extends BaseSchema {
       if (Object.prototype.hasOwnProperty.call(this.def.shape, key)) {
         const fieldValue = value[key];
         if (fieldValue === void 0) {
+          if (this.def.shape[key] instanceof KOptional) {
+            continue;
+          }
           throw new Error(`Missing required property: ${key}`);
         }
         result[key] = this.def.shape[key].serialize(fieldValue);
@@ -563,7 +662,7 @@ var KObject = class _KObject extends BaseSchema {
           return [key, value.toOpenAPI()];
         })
       ),
-      required: Object.keys(this.def.shape)
+      required: Object.entries(this.def.shape).filter(([, value]) => !(value instanceof KOptional) && !(value instanceof KDefault)).map(([key]) => key)
     };
   }
   parseSafe(json) {
@@ -574,11 +673,7 @@ var KObject = class _KObject extends BaseSchema {
       const result = {};
       for (const key in this.def.shape) {
         if (Object.prototype.hasOwnProperty.call(this.def.shape, key)) {
-          const value = json[key];
-          if (value === void 0) {
-            return ctx.addIssue(`Missing required property: ${key}`, [key]);
-          }
-          const parseResult = this.def.shape[key].parseSafe(value);
+          const parseResult = this.def.shape[key].parseSafe(json[key]);
           if (!parseResult.success) {
             return ctx.addIssues(parseResult.issues, [key]);
           }
@@ -621,10 +716,7 @@ var KObjectFromURLSearchParams = class _KObjectFromURLSearchParams extends KObje
       const result = {};
       for (const key in this.def.shape) {
         if (Object.prototype.hasOwnProperty.call(this.def.shape, key)) {
-          const value = json.get(key);
-          if (value === null) {
-            return ctx.addIssue(`Missing required property: ${key}`, [key]);
-          }
+          const value = json.get(key) ?? void 0;
           const parseResult = this.def.shape[key].parseSafe(value);
           if (!parseResult.success) {
             return ctx.addIssues(parseResult.issues, [key]);
@@ -644,6 +736,9 @@ var KRef = class _KRef extends BaseSchema {
       if (Object.prototype.hasOwnProperty.call(this.def.shape, key)) {
         const fieldValue = value[key];
         if (fieldValue === void 0) {
+          if (this.def.shape[key] instanceof KOptional) {
+            continue;
+          }
           throw new Error(`Missing required property: ${key}`);
         }
         result[key] = this.def.shape[key].serialize(fieldValue);
@@ -675,11 +770,7 @@ var KRef = class _KRef extends BaseSchema {
       const result = {};
       for (const key in this.def.shape) {
         if (Object.prototype.hasOwnProperty.call(this.def.shape, key)) {
-          const value = json[key];
-          if (value === void 0) {
-            return ctx.addIssue(`Missing required property: ${key}`, [key]);
-          }
-          const parseResult = this.def.shape[key].parseSafe(value);
+          const parseResult = this.def.shape[key].parseSafe(json[key]);
           if (!parseResult.success) {
             return ctx.addIssues(parseResult.issues, [key]);
           }
@@ -951,6 +1042,9 @@ var KLazy = class _KLazy extends BaseSchema {
 var k = {
   string: KString.create,
   number: KNumber.create,
+  coerce: {
+    number: KCoercedNumber.create
+  },
   boolean: KBoolean.create,
   array: KArray.create,
   null: KNull.create,
diff --git a/dist/index.cjs b/dist/index.cjs
index 98f0764..47390b8 100644
--- a/dist/index.cjs
+++ b/dist/index.cjs
@@ -247,6 +247,18 @@ var BaseSchema = class {
   or(other) {
     return k.union([this, other]);
   }
+  optional() {
+    return new KOptional(this);
+  }
+  nullable() {
+    return this.or(k.null());
+  }
+  nullish() {
+    return this.nullable().optional();
+  }
+  default(defaultValue) {
+    return new KDefault(this, defaultValue);
+  }
   example(example) {
     if (example === void 0) {
       return this.def.example;
@@ -260,6 +272,74 @@ var BaseSchema = class {
     return this.clone({ description });
   }
 };
+var KOptional = class extends BaseSchema {
+  schema;
+  constructor(schema) {
+    super({});
+    this.schema = schema;
+  }
+  serialize(value) {
+    if (value === void 0) {
+      return void 0;
+    }
+    return this.schema.serialize(value);
+  }
+  toOpenAPI() {
+    return this.schema.toOpenAPI();
+  }
+  parseSafe(json) {
+    if (json === void 0) {
+      return { success: true, result: void 0 };
+    }
+    return this.schema.parseSafe(json);
+  }
+  parse(json) {
+    const result = this.parseSafe(json);
+    if (!result.success) {
+      throw new SchemaError(result.issues);
+    }
+    return result.result;
+  }
+  visit(visitor) {
+    visitor(this.schema);
+    this.schema.visit(visitor);
+  }
+};
+var KDefault = class extends BaseSchema {
+  schema;
+  defaultValue;
+  constructor(schema, defaultValue) {
+    super({});
+    this.schema = schema;
+    this.defaultValue = defaultValue;
+  }
+  serialize(value) {
+    return this.schema.serialize(value === void 0 ? this.defaultValue : value);
+  }
+  toOpenAPI() {
+    return {
+      ...this.schema.toOpenAPI(),
+      default: this.schema.serialize(this.defaultValue)
+    };
+  }
+  parseSafe(json) {
+    if (json === void 0) {
+      return { success: true, result: this.defaultValue };
+    }
+    return this.schema.parseSafe(json);
+  }
+  parse(json) {
+    const result = this.parseSafe(json);
+    if (!result.success) {
+      throw new SchemaError(result.issues);
+    }
+    return result.result;
+  }
+  visit(visitor) {
+    visitor(this.schema);
+    this.schema.visit(visitor);
+  }
+};
 var STRING_FORMAT_REGEXES = {
   uuid: /^[0-9a-fA-F]{8}\b-[0-9a-fA-F]{4}\b-[0-9a-fA-F]{4}\b-[0-9a-fA-F]{4}\b-[0-9a-fA-F]{12}$/i,
   email: /^(?!\.)(?!.*\.\.)([A-Z0-9_'+\-\.]*)[A-Z0-9_+-]@([A-Z0-9][A-Z0-9\-]*\.)+[A-Z]{2,}$/i,
@@ -567,6 +647,22 @@ var KNumber = class _KNumber extends BaseSchema {
   visit() {
   }
 };
+var KCoercedNumber = class extends KNumber {
+  static create = () => new KCoercedNumber({});
+  parseSafe(json) {
+    if (typeof json === "string") {
+      if (json.trim() === "") {
+        return { success: false, issues: /* @__PURE__ */ new Set([{ message: "Expected number", path: [] }]) };
+      }
+      const coerced = Number(json);
+      if (!Number.isFinite(coerced)) {
+        return { success: false, issues: /* @__PURE__ */ new Set([{ message: "Expected number", path: [] }]) };
+      }
+      return super.parseSafe(coerced);
+    }
+    return super.parseSafe(json);
+  }
+};
 var KBoolean = class _KBoolean extends BaseSchema {
   static create = () => new _KBoolean({});
   serialize(value) {
@@ -706,6 +802,9 @@ var KObject = class _KObject extends BaseSchema {
       if (Object.prototype.hasOwnProperty.call(this.def.shape, key)) {
         const fieldValue = value[key];
         if (fieldValue === void 0) {
+          if (this.def.shape[key] instanceof KOptional) {
+            continue;
+          }
           throw new Error(`Missing required property: ${key}`);
         }
         result[key] = this.def.shape[key].serialize(fieldValue);
@@ -724,7 +823,7 @@ var KObject = class _KObject extends BaseSchema {
           return [key, value.toOpenAPI()];
         })
       ),
-      required: Object.keys(this.def.shape)
+      required: Object.entries(this.def.shape).filter(([, value]) => !(value instanceof KOptional) && !(value instanceof KDefault)).map(([key]) => key)
     };
   }
   parseSafe(json) {
@@ -735,11 +834,7 @@ var KObject = class _KObject extends BaseSchema {
       const result = {};
       for (const key in this.def.shape) {
         if (Object.prototype.hasOwnProperty.call(this.def.shape, key)) {
-          const value = json[key];
-          if (value === void 0) {
-            return ctx.addIssue(`Missing required property: ${key}`, [key]);
-          }
-          const parseResult = this.def.shape[key].parseSafe(value);
+          const parseResult = this.def.shape[key].parseSafe(json[key]);
           if (!parseResult.success) {
             return ctx.addIssues(parseResult.issues, [key]);
           }
@@ -782,10 +877,7 @@ var KObjectFromURLSearchParams = class _KObjectFromURLSearchParams extends KObje
       const result = {};
       for (const key in this.def.shape) {
         if (Object.prototype.hasOwnProperty.call(this.def.shape, key)) {
-          const value = json.get(key);
-          if (value === null) {
-            return ctx.addIssue(`Missing required property: ${key}`, [key]);
-          }
+          const value = json.get(key) ?? void 0;
           const parseResult = this.def.shape[key].parseSafe(value);
           if (!parseResult.success) {
             return ctx.addIssues(parseResult.issues, [key]);
@@ -805,6 +897,9 @@ var KRef = class _KRef extends BaseSchema {
       if (Object.prototype.hasOwnProperty.call(this.def.shape, key)) {
         const fieldValue = value[key];
         if (fieldValue === void 0) {
+          if (this.def.shape[key] instanceof KOptional) {
+            continue;
+          }
           throw new Error(`Missing required property: ${key}`);
         }
         result[key] = this.def.shape[key].serialize(fieldValue);
@@ -836,11 +931,7 @@ var KRef = class _KRef extends BaseSchema {
       const result = {};
       for (const key in this.def.shape) {
         if (Object.prototype.hasOwnProperty.call(this.def.shape, key)) {
-          const value = json[key];
-          if (value === void 0) {
-            return ctx.addIssue(`Missing required property: ${key}`, [key]);
-          }
-          const parseResult = this.def.shape[key].parseSafe(value);
+          const parseResult = this.def.shape[key].parseSafe(json[key]);
           if (!parseResult.success) {
             return ctx.addIssues(parseResult.issues, [key]);
           }
@@ -1112,6 +1203,9 @@ var KLazy = class _KLazy extends BaseSchema {
 var k = {
   string: KString.create,
   number: KNumber.create,
+  coerce: {
+    number: KCoercedNumber.create
+  },
   boolean: KBoolean.create,
   array: KArray.create,
   null: KNull.create,
@@ -1312,7 +1406,7 @@ var KaitoRouter = class _KaitoRouter {
             })
           );
           const sseHeaders = new Headers(head.touched ? head.headers : void 0);
-          sseHeaders.set("Content-Type", "text/event-stream");
+          sseHeaders.set("Content-Type", "text/event-stream; charset=utf-8");
           sseHeaders.set("Cache-Control", "no-cache");
           sseHeaders.set("Connection", "keep-alive");
           return new Response(stringStream, {
diff --git a/dist/index.js b/dist/index.js
index 7e4c4ff..f74b9c5 100644
--- a/dist/index.js
+++ b/dist/index.js
@@ -245,7 +245,7 @@ var KaitoRouter = class _KaitoRouter {
             })
           );
           const sseHeaders = new Headers(head.touched ? head.headers : void 0);
-          sseHeaders.set("Content-Type", "text/event-stream");
+          sseHeaders.set("Content-Type", "text/event-stream; charset=utf-8");
           sseHeaders.set("Cache-Control", "no-cache");
           sseHeaders.set("Connection", "keep-alive");
           return new Response(stringStream, {
diff --git a/dist/schema/schema.cjs b/dist/schema/schema.cjs
index 26cebbd..5568fe9 100644
--- a/dist/schema/schema.cjs
+++ b/dist/schema/schema.cjs
@@ -129,6 +129,18 @@ var BaseSchema = class {
   or(other) {
     return k.union([this, other]);
   }
+  optional() {
+    return new KOptional(this);
+  }
+  nullable() {
+    return this.or(k.null());
+  }
+  nullish() {
+    return this.nullable().optional();
+  }
+  default(defaultValue) {
+    return new KDefault(this, defaultValue);
+  }
   example(example) {
     if (example === void 0) {
       return this.def.example;
@@ -142,6 +154,74 @@ var BaseSchema = class {
     return this.clone({ description });
   }
 };
+var KOptional = class extends BaseSchema {
+  schema;
+  constructor(schema) {
+    super({});
+    this.schema = schema;
+  }
+  serialize(value) {
+    if (value === void 0) {
+      return void 0;
+    }
+    return this.schema.serialize(value);
+  }
+  toOpenAPI() {
+    return this.schema.toOpenAPI();
+  }
+  parseSafe(json) {
+    if (json === void 0) {
+      return { success: true, result: void 0 };
+    }
+    return this.schema.parseSafe(json);
+  }
+  parse(json) {
+    const result = this.parseSafe(json);
+    if (!result.success) {
+      throw new SchemaError(result.issues);
+    }
+    return result.result;
+  }
+  visit(visitor) {
+    visitor(this.schema);
+    this.schema.visit(visitor);
+  }
+};
+var KDefault = class extends BaseSchema {
+  schema;
+  defaultValue;
+  constructor(schema, defaultValue) {
+    super({});
+    this.schema = schema;
+    this.defaultValue = defaultValue;
+  }
+  serialize(value) {
+    return this.schema.serialize(value === void 0 ? this.defaultValue : value);
+  }
+  toOpenAPI() {
+    return {
+      ...this.schema.toOpenAPI(),
+      default: this.schema.serialize(this.defaultValue)
+    };
+  }
+  parseSafe(json) {
+    if (json === void 0) {
+      return { success: true, result: this.defaultValue };
+    }
+    return this.schema.parseSafe(json);
+  }
+  parse(json) {
+    const result = this.parseSafe(json);
+    if (!result.success) {
+      throw new SchemaError(result.issues);
+    }
+    return result.result;
+  }
+  visit(visitor) {
+    visitor(this.schema);
+    this.schema.visit(visitor);
+  }
+};
 var STRING_FORMAT_REGEXES = {
   uuid: /^[0-9a-fA-F]{8}\b-[0-9a-fA-F]{4}\b-[0-9a-fA-F]{4}\b-[0-9a-fA-F]{4}\b-[0-9a-fA-F]{12}$/i,
   email: /^(?!\.)(?!.*\.\.)([A-Z0-9_'+\-\.]*)[A-Z0-9_+-]@([A-Z0-9][A-Z0-9\-]*\.)+[A-Z]{2,}$/i,
@@ -449,6 +529,22 @@ var KNumber = class _KNumber extends BaseSchema {
   visit() {
   }
 };
+var KCoercedNumber = class extends KNumber {
+  static create = () => new KCoercedNumber({});
+  parseSafe(json) {
+    if (typeof json === "string") {
+      if (json.trim() === "") {
+        return { success: false, issues: /* @__PURE__ */ new Set([{ message: "Expected number", path: [] }]) };
+      }
+      const coerced = Number(json);
+      if (!Number.isFinite(coerced)) {
+        return { success: false, issues: /* @__PURE__ */ new Set([{ message: "Expected number", path: [] }]) };
+      }
+      return super.parseSafe(coerced);
+    }
+    return super.parseSafe(json);
+  }
+};
 var KBoolean = class _KBoolean extends BaseSchema {
   static create = () => new _KBoolean({});
   serialize(value) {
@@ -588,6 +684,9 @@ var KObject = class _KObject extends BaseSchema {
       if (Object.prototype.hasOwnProperty.call(this.def.shape, key)) {
         const fieldValue = value[key];
         if (fieldValue === void 0) {
+          if (this.def.shape[key] instanceof KOptional) {
+            continue;
+          }
           throw new Error(`Missing required property: ${key}`);
         }
         result[key] = this.def.shape[key].serialize(fieldValue);
@@ -606,7 +705,7 @@ var KObject = class _KObject extends BaseSchema {
           return [key, value.toOpenAPI()];
         })
       ),
-      required: Object.keys(this.def.shape)
+      required: Object.entries(this.def.shape).filter(([, value]) => !(value instanceof KOptional) && !(value instanceof KDefault)).map(([key]) => key)
     };
   }
   parseSafe(json) {
@@ -617,11 +716,7 @@ var KObject = class _KObject extends BaseSchema {
       const result = {};
       for (const key in this.def.shape) {
         if (Object.prototype.hasOwnProperty.call(this.def.shape, key)) {
-          const value = json[key];
-          if (value === void 0) {
-            return ctx.addIssue(`Missing required property: ${key}`, [key]);
-          }
-          const parseResult = this.def.shape[key].parseSafe(value);
+          const parseResult = this.def.shape[key].parseSafe(json[key]);
           if (!parseResult.success) {
             return ctx.addIssues(parseResult.issues, [key]);
           }
@@ -664,10 +759,7 @@ var KObjectFromURLSearchParams = class _KObjectFromURLSearchParams extends KObje
       const result = {};
       for (const key in this.def.shape) {
         if (Object.prototype.hasOwnProperty.call(this.def.shape, key)) {
-          const value = json.get(key);
-          if (value === null) {
-            return ctx.addIssue(`Missing required property: ${key}`, [key]);
-          }
+          const value = json.get(key) ?? void 0;
           const parseResult = this.def.shape[key].parseSafe(value);
           if (!parseResult.success) {
             return ctx.addIssues(parseResult.issues, [key]);
@@ -687,6 +779,9 @@ var KRef = class _KRef extends BaseSchema {
       if (Object.prototype.hasOwnProperty.call(this.def.shape, key)) {
         const fieldValue = value[key];
         if (fieldValue === void 0) {
+          if (this.def.shape[key] instanceof KOptional) {
+            continue;
+          }
           throw new Error(`Missing required property: ${key}`);
         }
         result[key] = this.def.shape[key].serialize(fieldValue);
@@ -718,11 +813,7 @@ var KRef = class _KRef extends BaseSchema {
       const result = {};
       for (const key in this.def.shape) {
         if (Object.prototype.hasOwnProperty.call(this.def.shape, key)) {
-          const value = json[key];
-          if (value === void 0) {
-            return ctx.addIssue(`Missing required property: ${key}`, [key]);
-          }
-          const parseResult = this.def.shape[key].parseSafe(value);
+          const parseResult = this.def.shape[key].parseSafe(json[key]);
           if (!parseResult.success) {
             return ctx.addIssues(parseResult.issues, [key]);
           }
@@ -994,6 +1085,9 @@ var KLazy = class _KLazy extends BaseSchema {
 var k = {
   string: KString.create,
   number: KNumber.create,
+  coerce: {
+    number: KCoercedNumber.create
+  },
   boolean: KBoolean.create,
   array: KArray.create,
   null: KNull.create,
diff --git a/dist/schema/schema.d.cts b/dist/schema/schema.d.cts
index a174a17..ed9d9da 100644
--- a/dist/schema/schema.d.cts
+++ b/dist/schema/schema.d.cts
@@ -60,6 +60,10 @@ declare abstract class BaseSchema<Input extends JSONValue, Output, Def extends B
     protected clone(def: Partial<Def>): this;
     protected constructor(def: Def);
     or<OtherInput extends JSONValue, OtherOutput, Def extends BaseSchemaDef<OtherInput>>(other: BaseSchema<OtherInput, OtherOutput, Def>): KUnion<(this | BaseSchema<OtherInput, OtherOutput, Def>)["_input"], (this | BaseSchema<OtherInput, OtherOutput, Def>)["_output"]>;
+    optional(): BaseSchema<Input, Output | undefined, BaseSchemaDef<Input>>;
+    nullable(): BaseSchema<Input | null, Output | null, BaseSchemaDef<Input | null>>;
+    nullish(): BaseSchema<Input | null, Output | null | undefined, BaseSchemaDef<Input | null>>;
+    default(defaultValue: Output): BaseSchema<Input, Exclude<Output, undefined>, BaseSchemaDef<Input>>;
     example(example: Input): this;
     example(): Input | undefined;
     description(description: string): this;
@@ -365,6 +369,9 @@ declare class KLazy<Input extends JSONValue, Output> extends BaseSchema<Input, O
 declare const k: {
     string: () => KString;
     number: () => KNumber;
+    coerce: {
+        number: () => KNumber;
+    };
     boolean: () => KBoolean;
     array: <ItemsInput extends JSONValue, ItemsOutput, Def extends BaseSchemaDef<ItemsInput>>(items: BaseSchema<ItemsInput, ItemsOutput, Def>) => KArray<ItemsInput, ItemsOutput>;
     null: () => KNull;
diff --git a/dist/schema/schema.d.ts b/dist/schema/schema.d.ts
index a174a17..ed9d9da 100644
--- a/dist/schema/schema.d.ts
+++ b/dist/schema/schema.d.ts
@@ -60,6 +60,10 @@ declare abstract class BaseSchema<Input extends JSONValue, Output, Def extends B
     protected clone(def: Partial<Def>): this;
     protected constructor(def: Def);
     or<OtherInput extends JSONValue, OtherOutput, Def extends BaseSchemaDef<OtherInput>>(other: BaseSchema<OtherInput, OtherOutput, Def>): KUnion<(this | BaseSchema<OtherInput, OtherOutput, Def>)["_input"], (this | BaseSchema<OtherInput, OtherOutput, Def>)["_output"]>;
+    optional(): BaseSchema<Input, Output | undefined, BaseSchemaDef<Input>>;
+    nullable(): BaseSchema<Input | null, Output | null, BaseSchemaDef<Input | null>>;
+    nullish(): BaseSchema<Input | null, Output | null | undefined, BaseSchemaDef<Input | null>>;
+    default(defaultValue: Output): BaseSchema<Input, Exclude<Output, undefined>, BaseSchemaDef<Input>>;
     example(example: Input): this;
     example(): Input | undefined;
     description(description: string): this;
@@ -365,6 +369,9 @@ declare class KLazy<Input extends JSONValue, Output> extends BaseSchema<Input, O
 declare const k: {
     string: () => KString;
     number: () => KNumber;
+    coerce: {
+        number: () => KNumber;
+    };
     boolean: () => KBoolean;
     array: <ItemsInput extends JSONValue, ItemsOutput, Def extends BaseSchemaDef<ItemsInput>>(items: BaseSchema<ItemsInput, ItemsOutput, Def>) => KArray<ItemsInput, ItemsOutput>;
     null: () => KNull;