The core grammatical component of the phrase is a noun. Specifically, "holiday" functions as the head noun, which is the main point or subject of the phrase. The other words, "september 11" and "public," act as modifiers that describe and specify this particular noun.
In a detailed grammatical analysis, the entire phrase constitutes a noun phrase. The word "holiday" is the simple subject. It is modified by the adjective "public," which defines its type (i.e., for the general populace). The term "september 11" is a compound noun adjunct, where a proper noun and a number collectively function as an adjective to specify which public holiday is being referenced. This structure demonstrates how nouns can serve an attributive role to modify other nouns.
Understanding that "holiday" is the grammatical anchor is crucial for constructing syntactically correct sentences and maintaining thematic clarity. This determination dictates subject-verb agreement (e.g., "The september 11 public holiday is..." not "are"). It ensures that the article's focus remains on the concept of a formal day of observance, rather than on the date itself or the adjective "public," thereby providing a precise and stable subject for discussion.