The Framework I mentioned previously is now within your message. That's a great first step toward finding common ground.
Any reference to Arbitration does not apply in this case. I highlighted in red those references. The Inter-American Convention on Extra-Territorial Validity of Foreign Judgements does not apply as the U.S. is not a Signatory so that is also noted in red font. Brazil has no Convention on Recognition and Enforcement, just Service.
Thank you for acknowledging that Recognition and Enforcement are separate steps.
The remaining portion broadly states elements of the Recognition phase.
I never said the Bro's could challenge the merits of the U.S. case. They can challenge the viability of the Judgement based on allowable conditions in Brazil--such as working against Brazil's Public Policy. I've noted these previously.
They must be served within Brazil. That process flows through the Brazil Court and happens after the Brazil Court receives the documents you mention. The Bros must be served the Judgement. They then have a voice in the Recognition phase and their counsel can bring to light the reasons the Court can do just what you mentioned: Approve, Partially Approve, or Disapprove the Judgement. This is not a quick process. Thus, the 30-60 day comment on Service. GDSIs Judgement will be in a work queue in line with other Court filings needing to be reviewed by their Central Court. A separate hearing may be scheduled during the Recognition phase.
The law links in my Stickie are fairly recent. These are composed by experienced International lawyers working in Brazil. They say it can take a year. I won't diss their information. I'm going to watch this unfold. I think they're spot on.