Sources

1) Source: The Henry Project . External Link
https://fasg.org/projects/henryproject/data/pepin000.htm. Reference: Pépin (Carloman) (Questionable reliability of evidence)
2) Source: Carolingian Chronicles: Royal Frankish Annals and Nithard's Histories "812... the emperor sent his grandson Bernard, son of Pepin, to Italy.". Reference: RFA (Data from secondary evidence)
3) Source: Vita Hludovici Imperatoris "Ipso eodemque anno Bernhardus, filius Pippini ex concubina natus". Reference: 22 (Data from direct source)
4) Source: Carolingian Chronicles: Royal Frankish Annals and Nithard's Histories "810... that his son Pepin, the King of Italy, had died on July 8". Reference: RFA (Data from secondary evidence)
5) Source: Vita Hludovici Imperatoris "Anno regni eius quadragesimo secundo obiit Pippinus filius eius, anno aetatis suae XXXIII. Sequenti vero anno Karolus, primogenitus filius eius ex regina supradicta Hiltigarda, obiit. Solus Hludowicus ad regni gubernacula remansit.". Reference: 5 (Data from secondary evidence)
6) Source: Carolingian Chronicles: Royal Frankish Annals and Nithard's Histories "Oct 840... When Pepin, son of Bernard, king of the Lombards, and others saw this treachery...". Reference: Nithard's Histories (Data from secondary evidence)
7) Source: The Henry Project . External Link
https://fasg.org/projects/henryproject/data/berna000.htm. Reference: Bernard (Questionable reliability of evidence)
8) Source: Carolingian Chronicles: Royal Frankish Annals and Nithard's Histories "818... a few days after Holy Easter... the king with them, were condemned to death". Reference: RFA (Data from secondary evidence)
9) Source: Vita Hludovici Imperatoris "Tertio die post amissionem luminum Bernhardus obiit. ". Reference: 23 (Data from direct source)