Which conclusion?
I am not desperately hoping to find anything. I am just discussing the various “versions” of history.
Here is a list of books and articles that you might find interesting. Long story short tho, the field of papal and church history has stagnated for the most part. And where it hasn’t stagnated, it usually avoids the question of papal authority.
I also want to note the following however. Church history, especially regarding the authority of Rome, before the fifth century is very hard. There isn’t much evidence in the historical record to arrive at a conclusion for either side. Most of my suggestions will be stuff concerning the period between the 5th and 11th centuries. This list concerns the subject of specifically papal Rome and Western Christianity as a whole.
You don’t have to read in order, but you should at least read numbers 1 and 2 before deciding to skip around. I do suggest reading in order though.
1.) Noble, Thomas F. X. “The Christian Church as an Institution.” In The Cambridge History of Christianity, 3: Early Medieval Christianities, c. 600 - c. 1100, pgs. 249-274. Edited by Thomas Noble and Julia Smith. Cambridge: Cambridge University Press, 2008.
2.) Noble, Thomas F. X. “Morbidity and Vitality in the History of the Early Medieval Papacy.” The Catholic Historical Review 81, no. 4 (Oct. 1995), 505-540.
3.) Meyendorff, John. Imperial Unity and Christian Division: The Church, 450-680 A.D. Crestwood, NY: St. Valdimir’s Seminary Press, 1992.
4.) Democopoulos, George. The Invention of Peter: Apostolic Discourse and Papal Authority in Late Antiquity. Philadelphia: University of Pennsylvania Press, 2013.
5.) Brown, Peter. The Rise of Western Christendom: Triumph and Diversity, A.D. 200-1000. 3rd edition. Malden, MA: Wiley-Blackwell, 2013. (Note: Second edition is okay too, but don’t read the first edition.)
6.) Deliyannis, Deborah. “The Roman Liber Pontificalis, Papal Primacy, and the Acacian Schism.” Viator 45, no. 2 (2014): 1-16.
7.) Jong, Mayke de. “Hincmar, priests and Pseudo-Isidore: The Case of Trising in Context.” In Hincmar of Rheims: Life and Work, pgs. 268-280. Edited by Rachel Stone and Charles West. Manchester, MI: Manchester University Press, 2015.
8.) Noble, Thomas F. X. The Republic of St. Peter: The Birth of the Papal State, 680-825. Philadelphia: University of Pennsylvania Press, 1984.
9.) Dvornik, Francis. Byzantium and the Roman Primacy. New York: Fordham University Press, 1966. Corrected edition, 1979.
10.) Gallagher, Clarence. “Diversity in Unity: Approaches to Church Order in Rome and Byzantium.” Ecclesiastical Law Journal: The Journal of the Ecclesiastical Law Society 6, no. 30 (2002): 208-238.
11.) Herrin, Judith. “The Pentarchy: Theory and Reality in the Ninth Century.” In Cristianità d’Occidente e cristianità d’Oriente (secoli VI-XI) : 24-30 aprile 2003. Spoleto, Italy: Settimane di studio della Fondazione Centro italiano di studi sull’Alto Medioevo, 2004. 591-628.
12.) Runciman, Steven. The Eastern Schism: A Study of the Papacy and the Eastern Churches during the XIth and XIIth Cenuturies. Oxford: Clarendon Press, 1955.
13.) Grant, Ken. “A Divine Mandate: Pope Gregory VII’s Defense of Papal Authority.” In Authorities in the Middle Ages: Influence, Legitimacy, and Power in Medieval Society. Edited by Sini Kangas et al. 2013. 39-54. ISBN 978-3-11-029449-1