Step 1: Lengthiest written constitution: The Indian Constitution is the longest written constitution of any sovereign country in the world, originally containing 395 articles in 22 parts and 8 schedules (now expanded further through amendments).
Step 2: Sovereign, socialist, secular, democratic republic: As declared in its Preamble, India is a sovereign (independent in decision-making), socialist (committed to social and economic equality), secular (no state religion, equal treatment of all faiths), democratic (government elected by the people) republic (head of state is elected, not hereditary).
Step 3: Blend of rigidity and flexibility: It is partly rigid and partly flexible — some provisions can be amended by a simple parliamentary majority, while others (like federal provisions) need a special majority plus ratification by half the state legislatures.
Step 4: Fundamental Rights, Directive Principles, and federal structure with a unitary bias: It guarantees Fundamental Rights (justiciable, enforceable in court) alongside non-justiciable Directive Principles of State Policy (guiding governance); it establishes a federal structure dividing powers between Centre and States, but leans unitary in emergencies, giving the Centre stronger powers when needed.
Final Answer: The Indian Constitution is the world's lengthiest written constitution, establishing a sovereign, socialist, secular, democratic republic with a Centre-leaning federal structure, a blend of rigid/flexible amendment procedures, and both Fundamental Rights and Directive Principles.