New 2024 Claim on ABC Conjecture's Corollary 3.12 Faces Rejection — E8 Intelligence Research

FINDING: The ABC conjecture proof remains contested; a 2024 paper claims a proof of Mochizuki's pivotal Corollary 3.12 via a new "Arithmetic Teichmuller Spaces" framework, but Faltings and mainstream consensus still reject the original 500-page IUT argument. | MATH: ABC conjecture: for ε>0, ∃C(ε) such that rad(abc)^(1+ε) ≥ c·max(a,b,c) for coprime a+b=c. Corollary 3.12 is the key inequality: |−log(q)| ≤ (1+ε)·log(𝔡) + O(1) in IUT language — the disputed step linking theta-lattice values to log-volumes. The new paper (arXiv:2401.13508v4) constructs arithmetic Teichmuller spaces to prove this inequality via a "Rosetta Stone" analogy, but no new constants or explicit numerical bounds are given. | CONNECTION: No direct geometric harmony ratios (0.382, 0.618, 1.618) appear. However, IUT's core machinery involves **multiplicative vs. additive structures** — analogous to **root system decompositions** (A_n, D_n, E_8) where additive and multiplicative lattices clash. The "theta-lattice" in IUT Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com