{
  "abstract": "Fracture networks control fluid flow, reservoir connectivity, and production performance in carbonate systems, yet their multiscale hierarchical organization remains difficult to characterize from heterogeneous geological and geophysical datasets. Here, we introduce physics-informed visio-numerical primitives that jointly encode numerical, visual, geometric, and topological attributes of complex fracture patterns. A SYM-Fractron is a computational pipeline that fuses these patterns through the Digital Transformer (DiT) framework, enabling positional visualization and classification of Big Geodata. The multisensor, multiscale metadata constitute the symbolic–numerical representations derived directly from physical measurements. Instead of textual tokenization, the proposed framework employs an effective number metric based on Diophantine, p-adic, and multifractal approximations to transform metadata into discrete integer-based tokens. These tokens are not interpretable as new physical observables. Instead, they are introduced as computational entities designed to preserve relevant structural, spatial, and statistical positional information from the original datasets, which is likely useful for floating-point multiscale data comparison. The framework integrates two complementary computational environments: Muuk’il Kaab (MIK) for multidimensional metadata fusion and Spatial Digital Twin construction, and SYM-Fractron for hybrid binary–symbolic image analysis. Digital Twins are virtual replicas of a system that can be digitized, while Spatial Digital Twins emphasize the geospatial aspects of the whole physics-informed positional metadata. We unified coupled visual and statistical numerical representations of geological system metadata with their computational counterparts, enabling interpretable fracture classification and supporting well-trajectory optimization, using dolomitized carbonate reservoirs as an example. We achieve quantitative comparison between fracture systems and their Digital Twins through topology-preserving and position encoding. The original physical measurements are preserved and remain traceable throughout the computational workflow of signal-to-image transformations and analyses. Integer-based representations and color maps, with a user-selected chromatic scale, are used for tokenization. Validation is supported by visual and statistical consistency between the original spatially encoded datasets and their corresponding Spatial Digital Twins, while preserving the cross-scale topological consistency often lost in conventional AI workflows.",
  "abstract_shown": true,
  "affiliations": [
    "Instituto de Geociencias, Campus UNAM Juriquilla, Universidad Nacional Autonoma de Mexico (UNAM), Blvd. Juriquilla 3001, Queretaro 76230, Mexico",
    "PEMEX Exploración y Extracción, Villahermosa 86010, Mexico",
    "International Center for Mathematical Modeling in Physics and Cognitive Sciences, Linnaeus University, 351 95 Växjö, Sweden",
    "School of Earth Sciences and Engineering, Sun Yat-sen University, Tangjiaway, Xiangzhou District, Zhuhai 519082, China"
  ],
  "article_type": null,
  "arxiv": null,
  "author_total": 9,
  "authors": [
    {
      "affs": [
        0
      ],
      "name": "Klaudia Oleshko",
      "orcid": "0000-0003-4683-8653"
    },
    {
      "affs": [
        1
      ],
      "name": "María de Jesús Correa López"
    },
    {
      "affs": [
        2
      ],
      "name": "Andrey Khrennikov"
    },
    {
      "affs": [
        3
      ],
      "name": "Qiuming Cheng",
      "orcid": "0000-0003-3122-5942"
    },
    {
      "affs": [
        1
      ],
      "name": "José Luis Landa"
    },
    {
      "affs": [
        0
      ],
      "name": "Ramiro Guillermo Paz Cruz"
    },
    {
      "affs": [
        0
      ],
      "name": "Alejandro Romero"
    },
    {
      "affs": [
        0
      ],
      "name": "Paulina Patiño"
    },
    {
      "affs": [
        1
      ],
      "name": "Yesica Guerrero Amador"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1tkcfxthpxjmm.bib",
  "cited_by": 0,
  "doi": "10.3390/fractalfract10100705",
  "fulltext_url": null,
  "id": "1tkcfxthpxjmm",
  "issns": [
    "2504-3110"
  ],
  "landing_url": "https://www.mdpi.com/2504-3110/10/10/705",
  "language": null,
  "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",
      "2210|Hydraulic Fracturing and Reservoir Analysis"
    ]
  ],
  "openalex": "W7153092123",
  "pdf_url": null,
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-08",
  "publisher": "MDPI AG",
  "ris": "https://research.draconitic.com/paper/1tkcfxthpxjmm.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:32Z",
      "native_id": "10.3390/fractalfract10100705",
      "source": "crossref",
      "url": "https://www.mdpi.com/2504-3110/10/10/705"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "issn:2504-3110",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Digital Transformer for Fracture Classification: SYM-Fractron, a Physics-Driven Hybrid Binary–Symbolic Computing Ecosystem",
  "title_text": "Digital Transformer for Fracture Classification: SYM-Fractron, a Physics-Driven Hybrid Binary–Symbolic Computing Ecosystem",
  "type": "peer-reviewed",
  "updated_at": "2026-10-30T12:18:32Z",
  "url": "https://research.draconitic.com/paper/1tkcfxthpxjmm",
  "venue": "Fractal and Fractional",
  "versions": []
}