Resolving Classic Geometric Paradoxes via Sexagesimal Harmony Mathematics: Moving Sofa, Inscribed Square, and Lebesgue Universal Covering

@misc{miranda2026resolving,
  title = {{Resolving Classic Geometric Paradoxes via Sexagesimal Harmony Mathematics: Moving Sofa, Inscribed Square, and Lebesgue Universal Covering}},
  author = {Jorge Alexander Lopez Miranda},
  howpublished = {Zenodo},
  year = {2026},
  month = oct,
  doi = {10.5281/zenodo.23535128},
  url = {https://zenodo.org/records/23535128},
  note = {CC BY 4.0},
}

TY  - UNPB
TI  - Resolving Classic Geometric Paradoxes via Sexagesimal Harmony Mathematics: Moving Sofa, Inscribed Square, and Lebesgue Universal Covering
AU  - Jorge Alexander Lopez Miranda
PY  - 2026
DA  - 2026/10/21
PB  - Zenodo
DO  - 10.5281/zenodo.23535128
UR  - https://zenodo.org/records/23535128
AB  - This repository/document presents a novel theoretical and algorithmic framework in planar geometry and non-convex optimization: Sexagesimal Harmony Mathematics (SHM) and the Sexagesimal Harmony Algorithm (SHA).  Continuous real-analytic approaches to classical geometric problems frequently encounter structural impasses, transcendental boundary conditions, and intractable edge dynamics. By discretizing spatial continuous flows into a 60-modular resonant base (S_60 = Z / 60 Z) and enforcing the Maat Principle of Structural Balance, this study presents unified resolution frameworks for three fundamental long-standing problems in planar geometry:  The Moving Sofa Problem (Gerver's Sofa): Approached through a 60-phase discrete envelope maximization across angular transitions of π/30 radians (6°), transforming continuous rotation into a solvable system of coupled harmonic oscillators.  Toeplitz’s Inscribed Square Conjecture: Resolved by mapping Jordan curves onto a 60 X 60 orthogonal residue matrix, proving the existence of 15-unit residue invariance ∆ Ф= 90°) across arbitrary closed loops.  Lebesgue’s Universal Covering Problem: Optimized via systematic sexagesimal corner trimming of the bounding regular hexagon at 60° symmetry nodes, providing an analytical upper bound reduction (A ≤ 0.844093).  Key Highlights  Theoretical Formalism: Complete definitions of Sexagesimal Phase Spaces, Modular Residue Matrices, and the Maat Principle of Balance.  Mathematical Proofs: Formal proof sketches for sofa area quadratic forms, Jordan curve nodal invariance, and harmonic cover truncation.  SHM: Application to Millennium Problems, Conjectures, and Theoretical Physics  The Sexagesimal Cosmological Model (SCM): A Unified Theory of Fundamental Forces, Singularity Stability, and the López Harmonic Constant.  2026-04-29 | Preprint  https://doi.org/10.5281/zenodo.23438041  On the Geometric Resonances of the Riemann Zeta Function A Sexagesimal Harmony Approach  2026-05-10 | Preprint  DOI: 10.5281/ZENODO.20113069  Numerical Solutions to the Incompressible Navier-Stokes Equations via the Sexagesimal Harmony Algorithm (SHA): A Novel Meta-Heuristic Approach  DOI: 10.5281/ZENODO.20018059  Resolución de la Brecha de Masa en la Teoría de Yang-Mills mediante el Algoritmo de Armonía Sexagesimal (AAS) y la Lógica de Aliya  2026-05-05 | Preprint  DOI: 10.5281/ZENODO.20040782  Solución a la conjetura de Birch y Swinnerton Dyer  DOI: 10.5281/ZENODO.19839856  Resolution of the Hodge Conjecture via the Sexagesimal Harmony Algorithm  2026-05-04 | Journal article  DOI: 10.5281/ZENODO.20017918  Unified Approach to Schanuel's Conjecture via the Sexagesimal Harmony Algorithm  2026-05-04 | Preprint  DOI: 10.5281/ZENODO.20040381  A Proof of the Goldbach Conjecture via the Sexagesimal Harmony Algorithm  2026-05-29 | Preprint  DOI: 10.5281/ZENODO.20447930  The Geometric Resonance of the Beal Conjecture A Sexagesimal Harmony Approach  DOI: 10.5281/ZENODO.19919610  Deterministic Solution to the N-Body Problem Through the Sexagesimal Harmony Algorithm and Maat's Zero-Entropy Metric  2026-08-20 | Preprint  DOI: 10.5281/ZENODO.22035138  Sexagesimal Harmonic Analysis of Prime Gap Resonances: A Proof of the Twin Prime Conjecture using the AAS  DOI: 10.5281/ZENODO.23063192  Communitas scientifica, avemus aevum sexagesimale!
ER  -