PST – Prime, Second, Third Numerical Families, Modular Families, and the Order of Positive Natural Numbers

Abstract

Mathematics – Number Theory (math.NT) PST (Prime, Second, Third) is a theory of natural numbers based on the partitioning of the families of N and on a comprehensive modular study, extended to more than 1,500 fractions of the field. The theory coordinates two levels: the numerical family of the number treated as a point, and the modular family of the field within which that point is observed. The research originates from the observation of CPB chains and of the order assumed by Pg points in regular modules. Mod3inverter resolves the ambiguity between even Sg and Tg values and, in the modulo 12 field, transforms the apparent 4/6/2 reading into the 4/4/4 partition. The work presents, in the author's order, POWER, AB with D cycles, AT, PAU and PAU Library, grids and lanes, SERIES, Prime Test, hyperbolic and saddle research, reproducible results, and FAST Test. The declared scope is limited to the territory of positive natural numbers. The deposit includes the Italian authorial edition in PDF format, digitally signed and provided with a timestamp, together with the corresponding external SHA-256 report. The source files, ANC files, and further supplementary materials are not included in the deposit. Access to the files is restricted and subject to the author's approval.