Poincaré Conjecture : A New Proof of the 3-Dimensional & Supplementary Proof This paper is a methodological attempt to interpret all seven Clay Millennium Problems—the Riemann Hypothesis, the Yang–Mills mass gap, the Navier–Stokes existence and smoothness problem, the Poincaré conjecture, the Birch–Swinnerton–Dyer conjecture, the P vs NP problem, and the Hodge conjecture—within a single structural framework provided by the Information-Driven Grand Unification Theory (IDGUT). Using the decisiveness device Φ_D, the stability device Φ_F, and the RP–LSI–IR–RG–OS chain as a common backbone, the work does not claim complete proofs, but instead presents conditional theorems together with publicly verifiable checkpoints for each problem (such as sign patterns, monotonicity, range/power-law signatures, and spectral lower bounds). While the core coupling formulae and modified-gravity field equations of IDGUT are kept non-public, the main aim of the paper is to provide an interface—along with concrete predictions and counterexample criteria—that can be independently tested by external researchers through experiments and computations.V.1 Birch–Swinnerton–DyerV.2 P versus NP ProblemV.3 Navier–StokesV.4 Riemann HypothesisV.5 Yang-Mills_Mass_Gap_SolutionV.6 Poincaré ConjectureV.7 The Hodge ConjectureV.8 A Unified Structural Analysis and Conditional Resolution Scheme for the Seven Clay Millennium Problems within an Information-Driven Grand Unification Framework (IDGUT) — Single Frame and Verification Checkpoints