{
  "abstract": "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).\n\nContinuous 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:\n\nThe 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.\n\nToeplitz’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.\n\nLebesgue’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).\n\nKey Highlights\n\nTheoretical Formalism: Complete definitions of Sexagesimal Phase Spaces, Modular Residue Matrices, and the Maat Principle of Balance.\n\nMathematical Proofs: Formal proof sketches for sofa area quadratic forms, Jordan curve nodal invariance, and harmonic cover truncation.\n\nSHM: Application to Millennium Problems, Conjectures, and Theoretical Physics\n\nThe Sexagesimal Cosmological Model (SCM): A Unified Theory of Fundamental Forces, Singularity Stability, and the López Harmonic Constant.\n\n2026-04-29 | Preprint\n\nhttps://doi.org/10.5281/zenodo.23438041\n\nOn the Geometric Resonances of the Riemann Zeta Function A Sexagesimal Harmony Approach\n\n2026-05-10 | Preprint\n\nDOI: 10.5281/ZENODO.20113069\n\nNumerical Solutions to the Incompressible Navier-Stokes Equations via the Sexagesimal Harmony Algorithm (SHA): A Novel Meta-Heuristic Approach\n\nDOI: 10.5281/ZENODO.20018059\n\nResolución de la Brecha de Masa en la Teoría de Yang-Mills mediante el Algoritmo de Armonía Sexagesimal (AAS) y la Lógica de Aliya\n\n2026-05-05 | Preprint\n\nDOI: 10.5281/ZENODO.20040782\n\nSolución a la conjetura de Birch y Swinnerton Dyer\n\nDOI: 10.5281/ZENODO.19839856\n\nResolution of the Hodge Conjecture via the Sexagesimal Harmony Algorithm\n\n2026-05-04 | Journal article\n\nDOI: 10.5281/ZENODO.20017918\n\nUnified Approach to Schanuel's Conjecture via the Sexagesimal Harmony Algorithm\n\n2026-05-04 | Preprint\n\nDOI: 10.5281/ZENODO.20040381\n\nA Proof of the Goldbach Conjecture via the Sexagesimal Harmony Algorithm\n\n2026-05-29 | Preprint\n\nDOI: 10.5281/ZENODO.20447930\n\nThe Geometric Resonance of the Beal Conjecture A Sexagesimal Harmony Approach\n\nDOI: 10.5281/ZENODO.19919610\n\nDeterministic Solution to the N-Body Problem Through the Sexagesimal Harmony Algorithm and Maat's Zero-Entropy Metric\n\n2026-08-20 | Preprint\n\nDOI: 10.5281/ZENODO.22035138\n\nSexagesimal Harmonic Analysis of Prime Gap Resonances: A Proof of the Twin Prime Conjecture using the AAS\n\nDOI: 10.5281/ZENODO.23063192\n\nCommunitas scientifica, avemus aevum sexagesimale!",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": null,
  "author_total": 1,
  "authors": [
    {
      "name": "Jorge Alexander Lopez Miranda",
      "orcid": "0009-0008-4226-1555"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8hmw2kpqvgdjf.bib",
  "cited_by": 0,
  "doi": "10.5281/zenodo.23535128",
  "fulltext_url": null,
  "id": "8hmw2kpqvgdjf",
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  "landing_url": "https://zenodo.org/records/23535128",
  "language": "eng",
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": null,
  "native_subjects": [],
  "openalex": null,
  "pdf_url": "https://zenodo.org/api/records/23535128/files/Resolving%20Classic%20Geometric%20Paradoxes%20via%20SHM.pdf/content",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-21",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8hmw2kpqvgdjf.ris",
  "sources": [
    {
      "first_seen": "2026-11-04T12:21:07Z",
      "native_id": "23535128",
      "source": "zenodo",
      "url": "https://zenodo.org/records/23535128"
    }
  ],
  "subjects": [],
  "title": "Resolving Classic Geometric Paradoxes via Sexagesimal Harmony Mathematics: Moving Sofa, Inscribed Square, and Lebesgue Universal Covering",
  "title_text": "Resolving Classic Geometric Paradoxes via Sexagesimal Harmony Mathematics: Moving Sofa, Inscribed Square, and Lebesgue Universal Covering",
  "type": "preprint",
  "updated_at": "2026-11-04T12:21:07Z",
  "url": "https://research.draconitic.com/paper/8hmw2kpqvgdjf",
  "venue": "Zenodo",
  "versions": []
}