In advanced English syntax and determiner systems, the distribution of articles (definite, indefinite, and zero) and quantifying determiners is governed by intricate semantic constraints, countability distinctions, and idiomatic fixed structures. Consider the following four complex propositions regarding articles and determiners: I. When an uncountable noun or a plural countable noun is used in a specific, referentially restricted context known to both speaker and listener (e.g., *'The water in this reservoir is contaminated'* or *'The books on the top shelf belong to the professor's private collection'*), the definite article 'the' is obligatory, whereas generic uses of the same nouns take the zero article. II. The indefinite article 'a/an' can be used before a proper noun when the proper noun denotes an unspecified or unknown member of a family or is used metaphorically to represent a person possessing characteristic qualities of a well-known figure (e.g., *'A Mr. Henderson called for you while you were out'* or *'He fancies himself a regular Einstein'*), functioning essentially as a nominalizer. III. When two or more adjectives modify different nouns or distinct entities coordinated in a single noun phrase, the definite article must be repeated before each adjective to signal separate referents (e.g., *'The black and the white cat were sleeping on the rug'* denotes two distinct felines), whereas a single shared article indicates a single entity possessing multiple attributes. IV. The quantifying determiners 'many a' and 'more than one' are syntactically and semantically plural, requiring a plural noun head and a plural verb agreement across all formal registers in standard English (e.g., *'Many a student were penalized for late submission'*). Identify the option that correctly evaluates the grammatical and syntactic validity of propositions I, II, III, and IV.