In most environments in Arm., PIE t eventually became tH (in different environments t or d (or 0 between V)). However, if tr >Tr and tt > Tt with interdental th, with further changes later, it would help explain some odd correspondences.
The new th > f and then all other changes as in p > f ( > h/0/w/etc. ) in most environments. This would explain all these correspondences:
(all this likely opt. for t > th in at least some environments)
pater patr- L; hayr (n) hawr (g) Arm;
from
*patrós > *faTrós > *xWaxWrós > *xWawrós > etc.
and the same in other “family” words.
trees G; erekH Ar; tráyas S; 3
merging with pr- below instead of tr- > VrtH- expected from other dental clusters as:
pr- > fr- > hr- > r- > ër- > etc.
pri:scus = antique / of olden times L; ere:cH = elder Arm;
pro:któs = anus G; erastan-kH = buttocks Arm;
*wid+ = see > gtanem = find Arm;
*widtí+ > giwt -i- = finding / invention; git -i- = finding / gift Arm;
aM-vitti- = not finding S; an-giwt = not found Arm;
showing opt. Tt > tt > t (note lack of t > tH in -ti- suffix as opt. for other t after fric., making a stage with th more likely).
Probably also tl > Tl in:
*dweitló+ > erkiwL = fear Arm; dvaetha:- = menace Av; [e:>e ?] bellum L;
*dweitló+ / *dweiló+ ?? > deilós = cowardly G;
and perhaps also in a word with unknown etym.:
*pedtró+ >
*pedtló+ >
or
*pedró+ >
*pedló+ >
etc.
fezzil, fezzera OHG; fetel(s) = belt, feter = shackle/etc OE; fetter E; pHiwlake: = prison Arm;