Sorry, I still don't see the smoking gun, that tells us we are dealing with the right person. And I don't see the Iowa Death Index with DOB or DOD?
The fifth column in Peter Frederik Christensens birth record asks:
Name of the parents, their rank, handling, and residence.
In Danish:
Ugift Inger Johanne
Pedersen, Ulhuse
hos faderen Peder
Frederiksen i Bagterp
24 Aar, og udlagt
Barf. Ungk. Peder
Christensen
In English
Unmarried Inger Johanne Pedersen in Ulhuse at her father Peder Frederiksen in Bagterp, 24 years old, and alleged father of the child bachelor Peder Christensen.