Lucius Pinarius is likely the closest male heir (either him or Quintus Pedius) NOT Octavius who was heir of Caesar’s younger sister. WITHOUT Caesar’s will and adoption Gaius Octavian is an adolescent nobody who would NEVER get Caesar’s inheritance or support from the troops.
If Caesar’s heir can be a male relative from the female line then Pinarius (or Pedius) is the heir as senior descendant of Caesar’s father. If Caesar‘s heir must be from the male line and the line of Caesar‘s grandfather is extinct then Lucius Julius Caesar would get the inheritance. And that Lucius Caesar is Mark Antony’s maternal uncle NOT his father-in-law (Antony right now is married to Fulvia and was married to his paternal cousin Antonia before her )
You cant say that. There is so little known about either or about the order of Julia Major's marriages to say anything for sure. Aurelia is born in c120, her third child is Caesar born in 100. The latest Julia Major could be born is c103. Pedius is born in 92. We have almost no knowledge of Pinarius.
To be the mother of Pedius the assumption is that two girls get pregnant and carry to term in the age range 12 -14. Possible but not probable.
What we do know is how Octavian, Pedius and Pinarus behaved and what their contemporaries thought of of them. Pinarius serves with Anthony until Actium when he is sent to Cyrene and mints money, until one of Octavian's generals, who happens to be of the Equestrian Order the Pinarii are patrician senatorials, turns up when he hand over his legions to Octavian and is reapponted to his Governership and mints money for Augustus.
Pedius fails in election to Aedile. but seems to be a competent aide to Caesar who gets him a Praetorship, appoints him Legate where he does well. He immediately cleaves to Octavian and runs his political operation in Rome until his early death, serving alongside him as Consul.
Octavian gives the Funeral oration for his Grandmother at age 12 is appointed one of 16 Pontifex by Caesar, appointed Praefectus Urbi by Caesar, Attends numerous social engagements with Caesar, marches in Caesar's Triumphs and is accorded ( underserved) military honours by Caesar, serves as an intermediary between Caesar and favour seekers which would include Caesars clients, spends a year serving with Caesar in administering Spain, travels back to Rome is Elevated to Patrician status by Caesar, appointed Master of Horse for 43 bc by Caesar and seems to have been the advance party commander of 5 legions destined for the Parthian war when Caesar is assassinated and then he goes to Brundisium where the rest of the army acclaims him. At age 19.
There is only one person in this who clearly has Caesar's favour and trust and confidence and inherits his Auctoritas. He does not need a piece of paper to do this. It helps but is really not needed.