Adds Input With Missing Required Fields

spec/Section 4 -- Composition.md

@@ -14,6 +14,80 @@ run in sequence to produce the composite execution schema.
 
 ### Pre Merge Validation
 
+#### **Input With Missing Required Fields**
+
+**Error Code:** 
+
+REQUIRED_INPUT_FIELD_MISSING_IN_SOME_SUBGRAPH
+
+**Severity:** 
+
+ERROR
+
+**Formal Specification:**
+
+- Let {typeNames} be the set of all input object types from all source schemas that are not declared as `@inaccessible`.
+- For each {typeName} in {typeNames}:
+  - Let `{types}` be the list of all input object types from different source schemas with the name {typeName}.
+  - `{AreTypesConsistent(types)}` must be true.
+
+**Function Definition:**
+
+`AreTypesConsistent(inputs):`
+
+- Let `{requiredFields}` be the intersection of all required field names across all input objects in `{inputs}`.
+- For each `{input}` in `{inputs}`:
+  - Let `{inputFields}` be the set of all field names in of required fields in `{input}`.
+  - `{inputFields}` must equal `{requiredFields}`.
+
+**Explanatory Text**
+
+Input types are merged by intersection, meaning that the merged input type will have all fields that are present in all input types with the same name.
+This rule ensures that input object types with the same name across different subgraphs share a consistent set of required fields. 
+
+When an input object is defined across multiple subgraphs, this rule ensures that any required field present in one subgraph is present in all others defining the input object. 
+This allows for reliable usage of input objects in queries across subgraphs.
+
+### Examples
+
+**Valid Example:**
+
+If all subgraphs define `Input1` with the required field `field1`, the rule is satisfied:
+
+```graphql
+# Subgraph 1
+input Input1 {
+  field1: String!
+  field2: String
+}
+
+# Subgraph 2
+input Input1 {
+  field1: String!
+  field3: Int
+}
+```
+
+**Invalid Example:**
+
+If `field1` is required in one subgraph but missing in another, this violates the rule:
+
+```graphql
+# Subgraph 1
+input Input1 {
+  field1: String!
+  field2: String
+}
+
+# Subgraph 2
+input Input1 {
+  field2: String
+  field3: Int
+}
+```
+
+In this invalid case, `field1` is mandatory in `Subgraph 1` but not defined in `Subgraph 2`, causing inconsistency in required fields across subgraphs.
+
 ### Merge
 
 ### Post Merge Validation