{
  "schema": "connectedness-atlas/publications/v1",
  "updated": "2026-10-02",
  "items": [
    {
      "id": "4d-connectedness-2026",
      "title": "Connectedness Loci for Pairs of Planar Similarities",
      "titleStatus": "provisional",
      "authors": [
        "Bernat Espigulé"
      ],
      "status": "Manuscript in preparation · provisional title",
      "publicationState": "in-preparation",
      "date": "2026-10-02",
      "dateMeaning": "Announcement updated",
      "description": "Connectedness loci in the four real parameters of pairs of planar similarities, with topology, contact criteria and exact families. The PDF will be posted after author review and approval.",
      "url": "https://complextrees.com/4D/publication/#flagship",
      "links": [
        {
          "label": "Manuscript announcement",
          "url": "https://complextrees.com/4D/publication/#flagship"
        },
        {
          "label": "BibTeX and LaTeX citations",
          "url": "https://complextrees.com/4D/publication/#citations"
        }
      ],
      "citation": {
        "text": "Bernat Espigulé. Connectedness Loci for Pairs of Planar Similarities. Manuscript in preparation, 2026. Provisional title.",
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      },
      "scope": "Pairs of nonzero strict planar contractions, organized by their direct and reversing orientations.",
      "pdfAvailable": false,
      "featured": true
    },
    {
      "id": "4d-research-companion-2026",
      "title": "Connectedness Loci for Pairs of Planar Similarities: Contact Families, Sections and Landmarks",
      "titleStatus": "provisional",
      "authors": [
        "Bernat Espigulé"
      ],
      "status": "Research companion in preparation · provisional title",
      "publicationState": "in-preparation",
      "date": "2026-10-02",
      "dateMeaning": "Announcement updated",
      "description": "Contact families, exact landmarks, two-dimensional slices and their placement in three-dimensional sections of the four-dimensional parameter space. The PDF will be posted after author review and approval.",
      "url": "https://complextrees.com/4D/publication/#companion",
      "links": [
        {
          "label": "Companion announcement",
          "url": "https://complextrees.com/4D/publication/#companion"
        },
        {
          "label": "BibTeX and LaTeX citations",
          "url": "https://complextrees.com/4D/publication/#citations"
        }
      ],
      "citation": {
        "text": "Bernat Espigulé. Connectedness Loci for Pairs of Planar Similarities: Contact Families, Sections and Landmarks. Research companion in preparation, 2026. Provisional title.",
        "bibtex": "@unpublished{Espigule2026ContactFamilies,\n  author = {Espigul{\\'e}, Bernat},\n  title = {Connectedness Loci for Pairs of Planar Similarities: Contact Families, Sections and Landmarks},\n  year = {2026},\n  note = {Research companion in preparation; provisional title},\n  url = {https://complextrees.com/4D/publication/#companion}\n}"
      },
      "pdfAvailable": false,
      "featured": true
    },
    {
      "id": "bmd-poster-2026",
      "title": "Four-Dimensional Mandelbrot Sets for Binary Self-Similar Sets of the Plane",
      "authors": [
        "Bernat Espigulé"
      ],
      "status": "BMD 2026 · submitted poster",
      "publicationState": "conference-poster",
      "date": "2026-09-27",
      "dateMeaning": "Submitted",
      "description": "The submitted 70 × 140 cm poster: the equal-contraction atlas, collinear, mirror-symmetric, Fibonacci–Mandelbrot and quarter-turn slices, with exact S and U landmarks.",
      "url": "https://complextrees.com/4D/publication/poster.pdf",
      "links": [
        {
          "label": "Submitted poster PDF · 70 × 140 cm",
          "url": "https://complextrees.com/4D/publication/poster.pdf"
        },
        {
          "label": "Poster preview",
          "url": "https://complextrees.com/4D/publication/#poster"
        }
      ],
      "citation": {
        "text": "Bernat Espigulé. Four-Dimensional Mandelbrot Sets for Binary Self-Similar Sets of the Plane. Poster for Barcelona Mathematical Days 2026, submitted 27 September 2026.",
        "bibtex": "@misc{Espigule2026BMDPoster,\n  author = {Espigul{\\'e}, Bernat},\n  title = {Four-Dimensional Mandelbrot Sets for Binary Self-Similar Sets of the Plane},\n  year = {2026},\n  note = {Poster for Barcelona Mathematical Days 2026; submitted 27 September 2026},\n  url = {https://complextrees.com/4D/publication/poster.pdf}\n}"
      },
      "featured": true
    },
    {
      "id": "doctoral-thesis-2026",
      "title": "Collinear Fractals and Connectedness Loci: Topology, Finite Capture, and Restricted Polynomial Roots",
      "authors": [
        "Bernat Espigulé Pons"
      ],
      "status": "Doctoral thesis · deposited",
      "publicationState": "deposited-thesis",
      "date": "2026-09-09",
      "description": "The collinear foundations: topology of connectedness loci, finite capture and restricted polynomial roots. Deposited at the Universitat de Girona; the linked page identifies the available edition.",
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      "links": [
        {
          "label": "Thesis and edition information",
          "url": "https://complextrees.com/research/thesis/"
        }
      ],
      "citation": {
        "text": "Bernat Espigulé Pons. Collinear Fractals and Connectedness Loci: Topology, Finite Capture, and Restricted Polynomial Roots. Doctoral thesis, Universitat de Girona, deposited 9 September 2026.",
        "bibtex": "@phdthesis{Espigule2026Thesis,\n  author = {Espigul{\\'e} Pons, Bernat},\n  title = {Collinear Fractals and Connectedness Loci: Topology, Finite Capture, and Restricted Polynomial Roots},\n  school = {Universitat de Girona},\n  year = {2026},\n  note = {Deposited 9 September 2026},\n  url = {https://complextrees.com/research/thesis/}\n}"
      }
    },
    {
      "id": "collinear-bandt-2024",
      "title": "Collinear Fractals and Bandt’s Conjecture",
      "authors": [
        "Bernat Espigulé",
        "David Juher",
        "Joan Saldaña"
      ],
      "status": "Published article",
      "publicationState": "published",
      "date": "2024-12-06",
      "description": "Connectedness and regular-closedness results for the specified collinear n-ary families. The conclusions depend on the family and the stated range of n.",
      "url": "https://doi.org/10.3390/fractalfract8120725",
      "links": [
        {
          "label": "Published article",
          "url": "https://doi.org/10.3390/fractalfract8120725"
        },
        {
          "label": "arXiv version",
          "url": "https://arxiv.org/abs/2411.00160"
        }
      ],
      "citation": {
        "text": "Bernat Espigulé, David Juher and Joan Saldaña. Collinear Fractals and Bandt’s Conjecture. Fractal and Fractional 8(12), 725 (2024). doi:10.3390/fractalfract8120725.",
        "bibtex": "@article{EspiguleJuherSaldana2024,\n  author = {Espigul{\\'e}, Bernat and Juher, David and Salda{\\~n}a, Joan},\n  title = {Collinear Fractals and {Bandt}'s Conjecture},\n  journal = {Fractal and Fractional},\n  year = {2024}, volume = {8}, number = {12}, pages = {725},\n  doi = {10.3390/fractalfract8120725},\n  eprint = {2411.00160}, archivePrefix = {arXiv}\n}"
      }
    },
    {
      "id": "finite-capture-2026",
      "title": "Finite capture and the closure of roots of restricted polynomials",
      "authors": [
        "Bernat Espigulé",
        "David Juher"
      ],
      "status": "arXiv preprint",
      "publicationState": "preprint",
      "date": "2026-03-08",
      "description": "Finite capture in a specified collinear lens links connectedness loci to closures of restricted polynomial root sets. It supplies methods for the broader programme without identifying those slices with the full 4D charts.",
      "url": "https://arxiv.org/abs/2603.07397",
      "links": [
        {
          "label": "Read preprint",
          "url": "https://arxiv.org/abs/2603.07397"
        },
        {
          "label": "Computational companion",
          "url": "https://github.com/espigule/collinear-fractals-gpu"
        }
      ],
      "citation": {
        "text": "Bernat Espigulé and David Juher. Finite capture and the closure of roots of restricted polynomials. arXiv:2603.07397 (2026).",
        "bibtex": "@misc{EspiguleJuher2026FiniteCapture,\n  author = {Espigul{\\'e}, Bernat and Juher, David},\n  title = {Finite capture and the closure of roots of restricted polynomials},\n  year = {2026}, eprint = {2603.07397}, archivePrefix = {arXiv},\n  url = {https://arxiv.org/abs/2603.07397}\n}"
      }
    },
    {
      "id": "collinear-holes-2026",
      "title": "Infinitely many holes in connectedness loci for collinear affine iterated function systems",
      "authors": [
        "Bernat Espigulé"
      ],
      "status": "arXiv preprint",
      "publicationState": "preprint",
      "date": "2026-06-02",
      "description": "Topology of one-complex-parameter collinear connectedness loci. Holes in these slices are distinct from questions about complements in an ambient four-dimensional chart.",
      "url": "https://arxiv.org/abs/2606.01467",
      "links": [
        {
          "label": "Read preprint",
          "url": "https://arxiv.org/abs/2606.01467"
        }
      ],
      "citation": {
        "text": "Bernat Espigulé. Infinitely many holes in connectedness loci for collinear affine iterated function systems. arXiv:2606.01467 (2026).",
        "bibtex": "@misc{Espigule2026CollinearHoles,\n  author = {Espigul{\\'e}, Bernat},\n  title = {Infinitely many holes in connectedness loci for collinear affine iterated function systems},\n  year = {2026}, eprint = {2606.01467}, archivePrefix = {arXiv},\n  url = {https://arxiv.org/abs/2606.01467}\n}"
      }
    },
    {
      "id": "complex-trees-2019",
      "title": "Families of connected self-similar sets generated by complex trees",
      "authors": [
        "Bernat Espigulé"
      ],
      "status": "arXiv preprint",
      "publicationState": "preprint",
      "date": "2019-02-28",
      "description": "Connected families organized by prescribed equivalences between symbolic tips, with additional contacts defining changes in the family.",
      "url": "https://arxiv.org/abs/1902.11282v4",
      "links": [
        {
          "label": "Read preprint",
          "url": "https://arxiv.org/abs/1902.11282v4"
        },
        {
          "label": "2018 master’s thesis",
          "url": "https://hdl.handle.net/2445/129385"
        }
      ],
      "citation": {
        "text": "Bernat Espigulé. Families of connected self-similar sets generated by complex trees. arXiv:1902.11282 (2019).",
        "bibtex": "@misc{Espigule2019ComplexTrees,\n  author = {Espigul{\\'e}, Bernat},\n  title = {Families of connected self-similar sets generated by complex trees},\n  year = {2019}, eprint = {1902.11282}, archivePrefix = {arXiv},\n  url = {https://arxiv.org/abs/1902.11282v4}\n}"
      }
    }
  ]
}