Unified Maxwell equations derived from spacetime geometry

Statement of Changes and Attribution This document is an updated and extended working paper based on the original article published in Scientific Reports (Nature Portfolio). Note that all derivations and main conclusions remain unchanged. Original Article Citation: Baoxia Su, "Extended Maxwell equations derived from spacetime geometry", Scientific Reports, vol. 16, no. 1, article no. 27682, 2026, DOI: 10.1038/s41598-026-57062-8. (Note: The title of this updated version has been revised to avoid overlap with existing literature.) Detailed List of Revisions: The main revisions compared to the Version of Record (VoR) are listed below: 1. Two diagrams have been added to visualize the defined sets (Sec. 2.4) and the inference structure (Sec. 4.4). 2. A table and extended discussions on the unified charge system (UCS) have been added (Sec. 4.5). 3. Terminology updates: "quasi-charge conditions" -> "standard charge conditions", "inverse operation" -> "paired operation". Misused term correction: "Helmholtz equation" -> "wave equation". 4. The last property regarding groups has been removed in Sec. 2.2.3, because a required condition was missing. Since this property was originally intended for future extensions, its removal does not affect any subsequent content. 5. Two equations (Eqs. (3) and (7)), which are straightforward to derive and were omitted from the original paper for brevity, have been added in Sec. 2.3 of this extended version for readers’ convenience. 6. The Matrix Θ has been replaced by Υ−1 in Eq. (2) to facilitate future extensions. 7. The language in the Abstract, Introduction, and Summary sections has been refined for better readability. 8. The article title has been revised to avoid overlap with existing literature. 9. The original published article has been added to the reference list [1] to ensure proper version tracking. License: The original article is licensed under a Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/). In accordance with this license, changes are indicated above. This updated version is also distributed under the CC BY 4.0 license. Related Preprint: An earlier preprint version of this work was hosted on Preprints.org (DOI: 10.20944/preprints202512.2006.v1)