No. The US Supreme Court hears most cases under appellate jurisdiction, and does not listen to witness testimony. In fact, appellate courts may not retry cases, but must accept the factual determination of the lower court and/or trial jury.
The US Supreme Court's role in the appellate process is to determine whether the petitioner/plaintiff's constitutional rights were violated by a law or the legal process, not to determine a defendant's guilt or innocence.
For more information, see Related Questions, below.
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You don't 'submit evidence' to the Supreme Court. The Supreme Court only rules on cases which have already been litigated, and does not hear witnesses or view evidence.
US Supreme Court decisions are called "Opinions."
A supreme court is the highest court within the hierarchy of many legal jurisdictions. Other descriptions for such courts include court of last resort, instance court, judgment court, apex court, and highest court of appeal. Broadly speaking, the decisions of a supreme court are not subject to further review by any other court.
Chief Justice
The explanation for the US Supreme Court's decision is called the opinion.