What question did this study set out to answer?

The aim is to present a unified mathematical framework integrating various domains like physics and cryptography using the Brahim sequence.

January 27, 2026Open Access

A Mathematical Framework for Physics, Cryptography, Geospatial Encoding, and Network Protocols

Key Points

The aim is to present a unified mathematical framework integrating various domains like physics and cryptography using the Brahim sequence.
Introduced the Brahim sequence as a foundation for different mathematical and physical domains.
Developed a Brahim calculator to compute the fine structure constant and related constraints.
Formulated core algebraic constraints for cryptographic applications and spatial requirements in Brahim Sudoku.
Calculated planetary orbital periods using sequences derived from the Brahim system.
Identified 147 applications across 12 industrial sectors for the Brahim framework.
Achieved an accuracy of 2 parts per million for the fine structure constant with proposed relations.
Demonstrated 0% error margin in calculating Martian orbital resonance periods.

Abstract

Unified Brahim System: Technical Overview DOI: 10. 5281/zenodo. 18368980 Reference File: publications/UnifiedBrahimSystemIEEE. pdf (4 pages, 270KB) Document Structure Section Topic I Introduction - Brahim Sequence & Unification Theorem II Brahim Calculator - Physics constants (^-1 = 137. 036) III Wormhole Machines - Cryptography (² + 4 - 1 = 0) IV Brahim Sudoku - Constraint satisfaction V Brahim Geospacing - Cantor pairing coordinates VI Brahim Network Protocol - Geographic-aware networking VII Applications Taxonomy - 147 apps, 12 industries VIII Implementation - Kotlin reference IX Conclusion Key Theorems & Formulations 1. Unification Theorem Proposes that five distinct mathematical and physical domains are derived from a single underlying "Brahim Sequence. " 2. Fine Structure Constant The document defines the inverse fine structure constant (^-1) using the following relation: ^-1 = S² + 12² = 137. 036 Accuracy: Within 2 ppm (parts per million). 3. Self-Verification A core algebraic constraint for the system's cryptographic application: ² + 4 - 1 = 0 4. Mars Orbital Resonance Calculates the Martian orbital period (P) relative to the sequence S: P = 3S + 45 = 687 days Error Margin: 0%. 5. Mirror Constraint (Brahim Sudoku) Defines the spatial symmetry requirement for the constraint satisfaction grid: Celli, j + Cell11-i, 11-j = 214 Technical Scope Taxonomy: 147 specific applications identified. Industries: Impacting 12 distinct industrial sectors. Reference Code: Implemented in Kotlin.

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