{
  "abstract": "[ESPA&Ntilde;OL]\n\nEste registro presenta la demostración anal&iacute;tico-espectral y la telemetr&iacute;a de verificación del Cálculo Dimensional Numérico (CDN) y del Cálculo de Cohomolog&iacute;a Topológica (CCT-Doble) aplicada al problema milenario de los n&uacute;meros perfectos impares y los n&uacute;meros falsos (spoof numbers de Descartes y pseudoprimos modulares de Carmichael). Se demuestra que la perfección aritmética es un isomorfismo de equilibrio termodinámico unitario que exige la paridad bimétrica base (p_0 = 2), mientras que el sector estrictamente impar se encuentra bloqueado por una barrera diofántica (gamma_paridad > 0) que proh&iacute;be la existencia de n&uacute;meros perfectos impares en el espacio f&iacute;sico libre de fantasmas (H_phys). Asimismo, mediante el Predictor de Radio Cr&iacute;tico (en resguardo bajo secreto industrial), se reconstruyen sin fuerza bruta los vórtices primos del n&uacute;cleo de Descartes (>99.94% de precisión) y se reporta el descubrimiento expl&iacute;cito de seis (6) nuevos n&uacute;meros perfectos falsos impares exactos (Sigma_F^*[N] = 2N, desde 21 hasta 134 d&iacute;gitos) emergentes en la variedad fibrada extendida (D+n), junto con su purga s&uacute;per-exponencial mediante el Filtro de Nash-Moser (||R_m|| < 1.08e-15) sobre una malla de Chebyshev-Gauss-Lobatto de N=128 nodos.\n\n[ENGLISH]\n\nThis repository presents the spectral-analytical proof and verification telemetry of the Numerical Dimensional Calculus (CDN) and Double Topological Cohomology Calculus (CCT-Doble) applied to the problem of odd perfect numbers and spoof/false numbers (Descartes spoof numbers and Carmichael modular pseudoprimes). We prove that arithmetic perfection is a unitary thermodynamic equilibrium isomorphism strictly requiring base bimetric parity (p_0 = 2), whereas the odd sector is governed by a strict Diophantine obstruction gap (gamma_parity > 0) forbidding odd perfect numbers in the ghost-free physical subspace (H_phys). Furthermore, using a proprietary Critical Vortex Radius Predictor (kept under industrial trade secret / black-box ring-fencing), we analytically reconstruct the prime vortices of Descartes' core without brute force (>99.94% accuracy) and report the explicit discovery of six (6) new exact odd spoof perfect numbers (Sigma_F^*[N] = 2N, ranging from 21 to 134 digits) in the extended fiber manifold (D+n), certified alongside their super-exponential Nash-Moser spectral purge (||R_m|| < 1.08e-15) on an N=128 Chebyshev-Gauss-Lobatto grid.",
  "abstract_shown": true,
  "affiliations": [
    "Topological Dimensional Calculus Framework, Independent Research"
  ],
  "article_type": null,
  "arxiv": null,
  "author_total": 1,
  "authors": [
    {
      "affs": [
        0
      ],
      "name": "J.I. Álvarez Valencia"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/42m0r2ypqn3sc.bib",
  "cited_by": 0,
  "doi": "10.5281/zenodo.23587938",
  "fulltext_url": null,
  "id": "42m0r2ypqn3sc",
  "issns": [],
  "landing_url": "https://zenodo.org/records/23587938",
  "language": "spa",
  "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/23587938/files/falsos_y_perfecto_impares%20v3.pdf/content",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-23",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/42m0r2ypqn3sc.ris",
  "sources": [
    {
      "first_seen": "2026-11-06T12:21:46Z",
      "native_id": "23587938",
      "source": "zenodo",
      "url": "https://zenodo.org/records/23587938"
    }
  ],
  "subjects": [],
  "title": "Arithmetic-Topological Falsifiability Framework (CDN / CCT-Doble): Spectral Exclusion of Odd Perfect Numbers, Ab Initio Vortex Reconstruction, and Discovery Catalog of New Spoof Perfect Numbers in the Extended Fiber (D+n)",
  "title_text": "Arithmetic-Topological Falsifiability Framework (CDN / CCT-Doble): Spectral Exclusion of Odd Perfect Numbers, Ab Initio Vortex Reconstruction, and Discovery Catalog of New Spoof Perfect Numbers in the Extended Fiber (D+n)",
  "type": "preprint",
  "updated_at": "2026-11-06T12:21:46Z",
  "url": "https://research.draconitic.com/paper/42m0r2ypqn3sc",
  "venue": "Zenodo",
  "versions": []
}