v25: Complete restructuring - Math first, unified narrative thread
MAJOR RESTRUCTURING: * Document flow reversed: Mathematical proof → Philosophy → AI collaboration * Reduced from 29 pages to 14 pages through better organization * Clear thread: discovery of simple truth hidden for 100 years New document structure: * Abstract: Rewritten to present F = ℏ²/(γmr³) = ke²/r² upfront * Introduction: Explicitly states why physics/philosophy/AI are mixed * Section 2: Mathematical identity (moved from later sections) * Section 3: Philosophical considerations (consolidated all journey content) * Section 4: Human-AI collaboration (unchanged from v24) * Section 5: Discussion and conclusions Content reorganization: * All philosophical content moved to Section 3: - Crisis and lying on ground - "I think therefore I am an electron" - Standing on hydrogen atom thought experiment - Dog walk story - Spacetime from 3D rotation * Mathematical proof now standalone in Section 2 * Parameters defined inline on first appearance * Removed redundant content from multiple sections Key improvements: * Clearer narrative: Math truth → How we got there → What it means * More direct: "This paper presents a mathematical identity..." * Emphasizes discovery over theory building * Structured from most to least objective Title changed to: "The Electromagnetic Force as Three-Dimensional Geometric Necessity: A Mathematical Identity" 14 pages total (from 29) - more focused and direct
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\newcommand{\xmark}{\ding{55}} % ✗
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% Document version
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\newcommand{\docversion}{v24}
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\newcommand{\docversion}{v25}
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\newcommand{\docdate}{June 2025}
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\newcommand{\doctitle}{The Electromagnetic Force as Three-Dimensional Geometric Necessity: A Mathematical Identity}
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@ -74,4 +74,4 @@ We intentionally combine rigorous physics, philosophical reasoning, and document
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We could sanitize this story, presenting only the final mathematical result. But that would miss the larger truth: breakthrough insights often emerge from unconventional paths. A human who learned to question everything, AI systems that confidently reported imaginary results, and the collision between them that revealed a mathematical fact hiding in plain sight.
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What follows is structured from most to least objective. Section 2 presents the mathematical proof—verifiable by anyone with a calculator. Section 3 explores the philosophical journey that led to asking the right question. Section 4 documents the messy reality of human-AI collaboration. Each section could stand alone, but together they tell the complete story of how humanity discovered that electromagnetic force is not a fundamental interaction but a geometric requirement of existing in three-dimensional space.
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What follows is structured from most to least objective. Section 2 presents the mathematical proof—verifiable by anyone with a calculator. Section 3 explores the philosophical journey that led to asking the right question. Section 4 documents the messy reality of human-AI collaboration. Each section could stand alone, but together they tell the complete story of how humanity discovered that electromagnetic force is not a fundamental interaction but a geometric requirement of existing in three-dimensional space.
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