Erdős–Straus Project Archive: Residual Divisor Shells, Quotient Surpluses, and Finite Verification

Abstract

This release consolidates the Erdős–Straus project under its existing concept DOI. The principal paper develops the residual divisor-shell equivalence and its origin counts, proves the Star–Kneser quotient-surplus theorem, and records the exact certificate at p = 12289 with R = 11, m = (3,6,3), and surplus profile (1,6,2,1). It also treats the divisor-complement involution, Wick-completed support coordinates, the mod-107 congruence package, and the Lorentz and circle-packing coordinate identities. The accompanying archives contain the complete LaTeX source, a research logbook, replayed symbolic and finite checks, a pinned Lean 4 development, the three preceding versions of this concept, earlier drafts with a correction guide, and a reviewed working corpus. DOI_LINEAGE.csv gives the earlier Erdős–Straus records and two related project lineages. The full Erdős–Straus conjecture remains open. A cyclic arithmetic C3 action remains an additional hypothesis. The correction guide marks earlier terminal claims whose arithmetic input was incomplete. Begin with 00_ERDOS_STRAUSS_Project_Reader.pdf. The remaining files supply sources, verification, history, and supporting artifacts.