Final answer:
The effective date of the mechanic's lien in this scenario is July 1st, which is the date when the building supply company first provided materials for the construction of the patio.
Step-by-step explanation:
The question pertains to the effective date of a mechanic's lien. In legal terms, the effective date of a mechanic's lien is typically the date when the labor, services, or materials were first provided by the contractor or supplier. In this scenario, the building supply company delivered bricks on July 1st for the construction of a patio, which establishes the commencement of the work. Thus, notwithstanding the bankruptcy filing on September 1st and the filing of the mechanic's lien on September 5th, the effective date of the lien relates back to the date when the materials were first supplied, which is July 1st.