The Complete Conquest of the Seven Millennium Problems — Version 3.0: Mathematical and Geometric Derivation/千禧年七大難題的完整攻克 — Version 3.0:數學與幾何推導

Description — English Version 3.0 develops a unified framework for mathematical and geometric derivation across the seven Millennium Prize Problems. It extends the series through explicit mathematical derivations, literature alignment, numerical experiments where applicable, and clearly identified unresolved mathematical gaps. Each problem is organized through definitions, known mathematical results, geometric structures, physical mappings, engineering correspondences, verification methods, and explicit derivation sections. Structural correspondences are classified using an evidentiary grading framework to distinguish rigorous mathematical relationships from structural mappings and analogies. This work does not claim a proof of any of the seven Millennium Prize Problems. Of the seven, only the Poincaré Conjecture has been solved, by Grigori Perelman. The remaining six problems remain open. Numerical agreement is not treated as a theorem, structural mapping is not treated as physical law, and physical correspondence is not treated as mathematical proof. Version 3.0 further includes numerical experiments, PCS analysis, formula chains, a cross-problem handoff matrix, and explicit statements of the remaining mathematical boundaries. https://alvin-lin-pcs.uranusastudio.chatgpt.site/https://planetarycommonstate.org/PCS_OBSERVATORY/https://orcid.org/0009-0006-8999-8293 描述 — 中文 Version 3.0 建立千禧年七大難題的「數學與幾何推導」架構,從問題原始定義與核心公式出發,依序整理幾何結構、物理映射、工程對應、驗證方法與數學推演,並明確標示尚未跨越的數學缺口。 本稿透過一致的模組化架構處理七大題,並建立結構對齊的證據分級,使嚴格數學關係、結構映射、物理對應與類比能夠被分開記錄與檢查。後段加入公式鏈、PCS 分析、數值實驗、跨題交接矩陣與數學邊界。 本研究不宣稱證明七大難題中的任何一題。 七題之中只有 Poincaré 猜想已由 Grigori Perelman 解決,其餘六題仍為未解問題。數值一致不等於數學定理,結構對齊不等於物理定律,物理映射亦不等於數學證明。https://alvin-lin-pcs.uranusastudio.chatgpt.site/https://planetarycommonstate.org/PCS_OBSERVATORY/https://orcid.org/0009-0006-8999-8293