For researching very new appellate & supreme court decisions it's helpful to know that similar to the statutes publication system,
Opinions are published in three phases (similar to statutes):
1. Slip Opinions– new opinions appear on the court’s website the day they are announced.
Supreme Court website: https://www.supremecourt.gov/opinions/slipopinion/23
2. The second phase of publication for an opinion is called Advance sheets or preliminary print.
It takes more than four years for an opinion to reach this stage of preliminary print. These are Available on:
3. And finally they are bound into the published volumes of US Reports – which are the final, official version of Supreme Court decisions.
They include preface text called a syllabus which summarizes the case and the holding. as well as a listing of Justices and officers of the Court during the Term. These are available online through the supreme court website.