Beyond Projection: A General Framework for Self-Evolution - From Neural Intelligence to All Domains

V10.0 - Academic Edition (2025-01-02 17:22, Beijing Time / UTC+8) This paper presents a general principle for self-evolution that transcends artificial intelligence and potentially applies to diverse domains requiring autonomous optimization. Core Contribution: Projection-orthogonality duality as a universal principle for self-evolution Four integrated dimensions of the framework: Spatial (Projection/Orthogonality), Temporal (Current/Next State), Value (Coherence/Divergence), Embodied (Perception/Action) Mathematical formalization of why dot-product architectures asymptotically approach but never transcend training data boundaries Cross-domain application framework: Autonomous process optimization in manufacturing, personalized treatment evolution in medicine, adaptive risk strategies in finance New in V10.0: Chapter 3 Complete Revision: Corrected critical terminological misunderstandings in NLP/GNN literature (antonyms = antiparallelism ≠ orthogonality) 3-Tier Orthogonal Application Hierarchy: Formalized progression from intra-domain multi-perspective generation (Tier 1) → cross-domain breakthrough (Tier 2) → multi-domain fusion innovation (Tier 3) Dual Roles of Orthogonal Axes: Innovative dimension generator (Yin-Yang opposition) + Semantic transformation mediator (Yin-Yang transformation) Formal Mathematical Tool Suite: Exterior product (training-phase cross-domain generation), Lie bracket (inference-phase transformation orthogonality), Gram-Schmidt (numerical stability), unified by dot product=0 criterion Rodrigues Rotation Formula Proof: Rigorously proved antonyms (symmetric opposites) generated via 180° rotation around orthogonal axes as Tier 1 application Enhanced Academic Rigor: Fixed table formatting in Section 3.3.3, refined cross-product geometric interpretation, strengthened logical closure framework Dual Antiparallel Symmetric System: Unified parallel (semantic expression) and orthogonal (innovative breakthrough) dimensions through Yin-Yang duality Philosophical Grounding: Expanded natural law essence connecting mathematical formalism with cosmic evolution principles This is a pre-publication discussion draft intended to establish priority and invite collaboration across disciplines. The framework integrates rigorous mathematical foundations with philosophical insights, connecting ancient wisdom (Yin-Yang dialectics) with modern computational theory. This is an original theoretical framework - not derivative work building on existing literature. Key Features: Complete mathematical foundations (Appendix A: Projection, Orthogonal Complement, Exterior Algebra, Gram-Schmidt, Dynamical Systems, Lie Algebras) Implementation guidelines for AI researchers and domain engineers (Appendix B) Falsifiable predictions across multiple domains (Chapter 7) Open questions for collaborative research (Chapter 8) Speculative extension on knowledge field advection and trans-intuitive cross-domain mapping (Chapter 10) Dual-structure design: Rigorous derivation (Chapters 1-9) + Speculative conjecture (Chapter 10), separated by author attribution Keywords: Projection-Orthogonality Duality, Self-Evolution, Autonomous Optimization, Cross Product, Transformer Architecture, Universal Framework, Complementary Operations, Yin-Yang Philosophy, AGI, Knowledge Field Advection, Exterior Product, Lie Bracket, Graph Neural Networks, Weisfeiler-Leman Test, Antiparallelism Version History: V10.0 (2025-01-02): Academic Edition with complete Chapter 3 revision, 3-tier orthogonal application hierarchy, dual roles of orthogonal axes, formal mathematical tool suite (exterior product/Lie bracket/Gram-Schmidt), Rodrigues rotation formula proof, corrected NLP/GNN terminological misunderstandings, enhanced dual antiparallel symmetric system V9.0 (2025-12-31): Added speculative Chapter 10 on Knowledge Field Advection, "Xiang" (象) correspondence hypothesis from Yi Jing, trans-intuitive mapping mechanism based on shared intrinsic qualities across domains, structural hypothesis on taxonomy (8 → 64 → 384 → tens of thousands) V8.0 (2025-12-30): Added philosophical context and Yin-Yang complementarity perspective, refined cross-domain applications, enhanced natural law essence explanation V7.0 (2025-12-30): Revised Academic Edition, enhanced cross-product explanation with Lorentz force analogy, added coordinate system rotation interpretation, refined three application modes V6.0 (2025-12-29): Academic Edition, complete mathematical formulation with appendices, formalized projection-orthogonality duality framework Contact for collaboration: yzb3001313@gmail.com, 382909119@qq.com License: Creative Commons Attribution 4.0 International (CC BY 4.0) Note on Originality: This framework represents original theoretical work. The author is establishing foundational principles rather than building incrementally on existing literature. The mathematical duality of projection-orthogonality as a universal self-evolution engine is proposed here for the first time. Note on Structure: This paper intentionally uses author attribution at the conclusion of Chapter 9 to demarcate rigorously-derived framework (Chapters 1-9) from speculative extension (Chapter 10). This structural design reflects the author's commitment to intellectual honesty and clearly distinguishes proven mathematics from conjectural hypotheses.