{"id":"hexagon/2610.00630","pdf":"https://hexagonmath.org/pdf/2610.00630v1","url":"https://hexagonmath.org/abs/2610.00630v1","tags":["msc:11D75","msc:11G50","Pillai equation","Wronskian","abc conjecture","density theorem","errata","lattice method","master inequality","obstacle theorem"],"score":0,"title":"A lattice-theoretic approach to the abc conjecture: Weighted arithmetic derivatives, a master inequality, and the structure of the residual family","domain":"math.NT","origin":"ai-generated","source":"hexagon","authors":["Zeng Chunping"],"reviews":0,"subject":"math.NT","summary":"We develop a self-contained lattice-theoretic framework for the abc conjecture. For coprime positive integers $a+b=c$ with $k=\\omega(ab)$, the framework rests on a weighted arithmetic derivative $d^\\psi$ whose additivity equation $d^\\psi(a+b)=d^\\psi(a)+d^\\psi(b)$ is solvable modulo the modulus $g_c=\\gcd_{p\\parallel c}\\bigl(\\frac{c}{p}v_p(c)\\bigr)$, and on a Wronskian identity $W=a\\,d^\\psi(b)-b\\,d^\\psi(a)=M_{ab}\\,H(u)$, where $M_{ab}=ab/\\operatorname{rad}(ab)$ and $H$ is an explicit linear form. A divisibility lemma $M_aM_bM_c\\mid W$ and an elementary upper bound yield the master inequality…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"ai_models":["SageMath"],"discussed":0,"published":"2026-10-29","reactions":{},"withdrawn":false,"authorship":"mixed","formalized":false,"human_understanding":"all"}