Critique the conceptual definitions and legal precedents defining secularism within the Indian Republic:
1. The indigenous framework enforces a strict, impenetrable wall of separation isolating all state mechanisms from religious institutions.
2. The philosophical model is defined as a 'positive' concept, empowering the state to execute principled interventions within religious domains.
3. The judicial branch formally cemented the doctrine of secularism as an immutable element of the Constitution's basic structure.