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If the Supreme Court is the final authority, where does the authority of future Supreme Courts come from, to overturn prior results? Wouldn't past and future courts be of equal authority?

If the Supreme Court is the final authority

The Supreme court is not the final authority. The Supreme Court is the court of last resort, but that does not prevent its case law from possibly being superseded or invalidated by constitutional amendments or the enactment of legislation.

Wouldn't past and future courts be of equal authority

No. Whether in the form of statutes or court decisions, laws are supposed to preserve ordered liberty. That entails the need to keep up-to-date with the state or evolution of civilization.

If the Supreme Court case law --aka authorities-- were deemed inexorably perpetual, the entire judicial system would become imminently useless due to its inability to respond to new challenges [in the civilization] which are (1) encompassed by prior SC authorities, and yet (2) not properly assessed therein.

The general rule is that a governmental institution cannot bind future versions of itself. Thus a legislature can pass a law, but a later session of that same legislature can amend or repeal it, and the legislature cannot make it unamedable. Similarly, a President can issue an executive order, but later that same President, or a different one, can cancel or modify it.

A court can, in a proper case, issue a decision. This will tend to form a rule for future cases in the same court, and may form an absolute rule for courts subordinate to the original court, if there are any. But in a later case, the court can issue a decision that conflicts with the earlier decision, thereby partly or fully overruling it. This is not something unique to the US Supreme Court, but is an inherent power of all courts.

Courts generally prefer not to overrule previous decisions, particularly long-established ones, if they have any other choice. But if the previous decision is later found to be incorrect or unjust, sometimes it will be overruled. Some courts are more willing to do this than others. The US Supreme Court is perhaps more willing than the highest courts of some other countries, but that is a matter of style and judgment, and will vary with the current makeup of the court. Some US Justices have felt more strongly about precedent and stare decisis than others.

The general reason for the rule is that the later (more recent) actions of a body or office must be considered to overrule earlier actions. Otherwise mistakes could not be corrected, changes of policy could not be implemented, and changing conditions could not be allowed for.

See also the Wikipedia article on Precedent