A Finite-Range Induced Gravity Framework A Dark-Matter-Free Interpretation of Gravitational Phenomena (Sourced Gravity,SG)

(Notice on Version 3 / 版本更新说明): This version (V3) contains the identical theoretical core and mathematical derivations as the complete framework in Version 2. The update is purely a structural and presentation optimization, limited to the renumbering of certain sections and a rewritten Abstract for better readability,the theoretical abbreviation changed to LSG. The absolute chronological priority of the full LSG framework remains anchored to the original January 2026 file. (注意: 本版本(V3)所包含的理论核心与数学推导,与 V2 版完整手稿完全一致。本次更新纯属文本结构与呈现方式的优化,仅限于重排了部分章节的序号,并重写了摘要以提升可读性,理论简写变更为LSG。LSG 完整框架的绝对时间优先权依然完好锁死在 2026 年 1 月的原始文件上。) We dismantle the foundational postulate of infinite-range, absolute gravitation—a logical over-extrapolation that has forced the invention of non-physical "dark matter." We introduce the Local Sourced Gravity (LSG) framework, which defines gravity as an effective, finite-range induced interaction limited by the structural capacity of spacetime.By recognizing that gravity is a structural state of the induction domain rather than an instantaneous slave to mass, we provide a singular resolution to the field’s most persistent anomalies:1. Gravitational Hysteresis: The offset in merging clusters (e.g., the Bullet Cluster) is revealed as a dynamical induction lag, proving gravity’s nature as a spacetime accumulation effect.2. Galaxy Dynamics: Flat rotation curves emerge naturally as the gravitational induction undergoes a structural transition at galactic scales, leading to a significant and predictable departure from the Newtonian inverse-square decay.3. Cosmic Maturity: Early massive galaxies are predicted by the time-dependent efficiency of localized induction.4. The End of Singularities: Finite induction inherently prevents divergent potentials, rendering singularities non-existent.Within this framework, General Relativity and Quantum Field Theory are identified as flawed subsets resulting from foundational misinterpretations of induction boundaries. This work establishes the necessary macroscopic foundation for a singularity-free, logically closed cosmology.