Examine the logical coherence between the following administrative entities and their classification under Article 12:
1. Evidence 1: A village Panchayat enforces localized administrative rules regarding water distribution. Inference 1: Because it operates at the lowest tier of governance, the Panchayat is excluded from the Article 12 definition of the 'State'.
2. Evidence 2: The Life Insurance Corporation (LIC) is a statutory authority established by an act of Parliament. Inference 2: Consequently, LIC is bound by the provisions of Part III as it falls under the definition of 'other authorities' in Article 12.
3. Evidence 3: A private security firm is contracted by the government to manage a federal prison facility. Inference 3: As an instrumentality performing state functions, this private firm is legally considered the 'State' under Article 12.