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An unsolved problem of Italic historical phonology is the explanation of the Oscan adverbial form πεhεδ (Lu 13) ‘piously’, as well as of the related words in Sabellian and Latin (the Oscan word and the other forms are given according to Helmut Rix’s edition): Paelignian pes (Pg 10), peo[i]s (Pg 11), Marrucinian peoi/pioi (MV 1) ‘pious’, Umbrian pihaner (e.g. Iguvine Tables VIa 19), pehaner (Iguvine Tables VIa 20), peihaner (Iguvine Tables VIa 8) ‘to be propitiated’, Oscan piíhiúí (Sa 1), Volscian pihom (VM 2), Latin pius ‘pious’. Nicholas Zair points out that it is difficult to reconstruct a single protoform because of the variation in the first syllable, arguing that the vowel in Oscan πεhεδ, Marrucinian peoi/pioi and the Umbrian forms may represent *-i-, *-ē– or *-e-, while in Volscian pihom and Latin pius it may stand for *-ī– or *-i-. He rejects the explanation put forward by Dinu Adamesteanu and Michel Lejeune, which derives Oscan πεhεδ from a root *pi-, both because such a root cannot explain Oscan piíhiúí and Paelignian pes and because it goes against the commonly accepted theory that explains Latin pius as going back to pīus < *pū–jo– by Thurneysen’s law (also known as the pius Gesetz) and connects it to Latin pūrus. Zair finds Françoise Bader’s theory problematic, since it has the disadvantage of tracing the words for ‘pious’ back to two different protoforms (*pī–o– and *pi–jo-) from the same root *peh2(j)- ‘to protect’. Zair doubts Gerhard Meiser’s account, which reconstructs a change *pū–jo– > *pī–jo– followed by the lowering of –ī– to –ē– before a back vowel, because we find /i:/ before a back vowel in Oscan píihiúí, but /e:/ before a front vowel in Oscan πεhεδ, and i (representing either ī or i) before a front vowel in Volscian pihom. Finally, he rules out Loretta Del Tutto Palma’s explanation, which reconstructs *pjē–jo-, because, even though this root would yield all the Italic forms, this scenario rejects the connection with Latin pūrus and derives all the words from two different formations.
Considering that the h is a hiatus-marker, a close look at the spelling of the relevant material reveals that, taken together, the digraph íi and the i in Oscan píihiúí represent ī and the glide immediately following the vowel (that is, a sequence īj), while the oscillating spelling <i>/<e>/<ei> in the Umbrian forms (pihaner, pehaner, peihaner) constitutes an attempt to represent the short mid-front vowel į (itself resulting from the merger of the short high vowel i with the long mid-vowel ē though the Sabellian vowel shift), for which Umbrian, unlike Oscan, did not develop a distinct sign. Moreover, I think that the i in Volscian pihom most probably represents ī, as is shown by the fact the in the Tabula Veliterna i is consistently used to indicate long i (e.g. bim, vesclis, vinu), in contrast to the use of e for short i (e.g. se, covehriu, sepu). The presence of a short mid-front vowel may also be inferred from the spelling variation e/i in the first vowel of the related words attested in the minor dialects (Marrucinian peoi/pioi, Volscian pihom, Paelignian pes) and in Oscan (πεhεδ). On the basis of the available evidence, we can therefore conclude that it is impossibile to reconstruct a single protoform that could have given rise to the historically attested words, since Oscan píihiúí and Volscian pihom clearly point to *pīj-, while the other forms undoubtedly reflect *pi-. In view of the fact that first-syllable long i shortened before another vowel in Latin, it may be suggested that the original Proto-Sabellian form for ‘pious’ was *pī-, whose vowel retained its length in Oscan píihiúí (with the insertion of a glide) and Volscian pihom, but underwent shortening in the other forms.
A final issue I would like to discuss is the etymology of the aforementioned words. In my view, the most convincing solution is that put forward by Maria Luisa Porzio Gernia. She sees Latin pius as a religious term borrowed from Umbrian going back to the root *kwei– ‘to pay the penalty’, which is widely attested in the Indo-European languages: Middle Irish cin ‘fault, liability’, Lithuanian kaina ‘cost, price’, Old Church Slavonic cěna ‘reward’, Greek atimazw ‘to dishonour’, poinh ‘retribution, penalty’, timh ‘price, value, honour’, tinw ‘to atone for, pay the price’, Avestan čikayat̰ ‘to atone for’, kaēnā ‘punishment, revenge’, Sanskrit cayate ‘to avenge, punish’. If this etymology is correct, then the p must be secondary, that is the regular reflex of the labiovelar kw in Sabellian (for further details see Nicholas Zair, Oscan in the Greek alphabet, Cambridge 2016; Helmut Rix, Sabellische Texte. Die Texte des Oskischen, Umbrischen und Südpikenischen, 2002; Gerhard Meiser, Lautgeschichte der umbrischen Sprache, Innsbruck 1986; Helmut Rix, Zur Entstehung der lateinischen Perfektparadigmas, in Latein und Indogermanisch: Akten des Kolloquiums der Indogermanischen Gesellschaft, Salzburg, 23-26 September 1986, pp. 221-240 (O. Panagl-T. Krisch edd.), Innsbruck 1992; Michael Weiss, Outline of the historical and comparative grammar of Latin, Ann Arbor-New York 2009; Rafael Jiménez Zamudio, Estudio de dialecto peligno y su entorno lingüístico, Salamanca 1986; Michel Lejeune, Phonologie osque et graphie grecque. Revue des Études Anciennes 72, pp. 271-315, 1970; Michel Lejeune, Méfitis d’après les dédicaces lucaniennes de Rossano di Vaglio, Louvain-la-neuve 1990; Dinu Adamesteanu-Michel Lejeune, Il santuario lucano di Macchia di Rossano di Vaglio. Atti dell’Accademia nazionale dei Lincei. Memorie. Classe di scienze morali, storiche e filologiche, 8, 16, pp. 39-83; Michiel de Vaan, Etymological dictionary of Latin and the other Italic languages, Leiden-Boston 2008; Françoise Bader, De ‘protéger’ a ‘razzier’ au néolithique indo-européen: phraséologie, étymologies, civilisation. Bulletin de la Societé de Linguistique de Paris 73, pp. 101-219; Loretta Del Tutto Palma, Grafia e scrittura nella Tavola di Agnone, in La Tavola di Agnone nel contesto italico. Convegno di studio, Agnone, 13-15 aprile 1994, pp. 413-433 (Loretta Del Tutto Palma ed.), Firenze 1996; Karin Tikkanen, A Sabellian case grammar, Heidelberg 2011; Maria Luisa Porzio Gernia, Rapporti tra il lessico sacrale osco e latino, in Archivio Glottologico Italiano, 46, pp. 97-138, 1961; Maria Luisa Porzio Gernia, Il latino e le lingue indoeuropee dell’Italia antica, in Atti del Convegno della Società italiana di Glottologia ‘Alle origini del latino’, Pisa 7-9 dicembre 1980, pp. 11-26, Pisa 1982; Maria Luisa Porzio Gernia, Tra storia e preistoria linguistica. Il valore concettuale della radice *PAC- nell’Italia antica, Historical phonology. Greek, Latin and Romance. Papers in honor of Oswald Szemerényi II, pp. 267-292; https://lrc.la.utexas.edu/lex/master/1088).