From One to the Universe: The Infinite Halving Journey and the Villaber Framework of Unity (1 = 1/2 + 1/2)
Year: 2026
Type: preprint
Abstract: From One to the Universe: The Infinite Halving Journey and the Villaber Framework of Unity Author: Ruel Villaber Independent Researcher, Mandaluyong City, Philippines, 2026 ABSTRACT This work presents a conceptual and mathematical framework based on a simple principle of balance and unity: 1 = 1/2 + 1/2 1 - 1/2 - 1/2 = 0 The framework is developed through 14 related works that build from basic arithmetic to a general model of integration: 1. The Four Pillars of Unity for 1: - 3/4 + 1/4 = 1 - 1/2 + 1/2 = 1 - 2/4 + 1/4 + 1/4 = 1 - 1/4 + 1/4 + 1/4 + 1/4 = 1 2. Decimal equivalents: - 0.75 + 0.25 = 1 - 0.5 + 0.5 = 1 - 0.5 + 0.25 + 0.25 = 1 - 0.25 + 0.25 + 0.25 + 0.25 = 1 3. General Rule: If a1 + a2 + ... + an = 1, then 1 - a1 - a2 - ... - an = 0 4. Extension to Two: - 3/2 + 1/2 = 2 - 1 + 1 = 2 - 1 + 1/2 + 1/2 = 2 - 1/2 + 1/2 + 1/2 + 1/2 = 2 5. Infinite Halving Series: 1/2 + 1/4 + 1/8 + ... = 1 Sum from n=1 to infinity of (1/2)^n = 1 6. Binary Representation: 0.111... in base 2 = 1 in base 10 7. The Villaber Formula: Every idea is a half. Two halves make one whole idea. 1/2 + 1/2 = 1 8. Unified Theory Map: A 111-field map (00 to 110) organizing mathematics, physics, chemistry, biology, technology, society, philosophy, and speculative frameworks under the principle All = 1. CONTENT OF THIS DEPOSIT This deposit contains 14 works: - Four Pillars posters for 1 and 2 - Decimal and fraction versions - General Rule formulations - Villaber Formula - Unified Theory Map v1 and v2 (111 fields, 00-110) - From One to the Universe: The Infinite Halving Journey PURPOSE This is presented as an independent conceptual framework for integration, balance, and unity across disciplines. The arithmetic identities are standard and verifiable. The application of the principle to all fields of knowledge is proposed as a philosophical and integrative framework, not as a claim of a completed proof in mainstream physics. The author invites open review, correction, and collaboration.
Author: Villaber, Ruel
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7225661619
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