{
  "abstract": "A sheet modulated in space and in time is a space–time crystal. Among its symmetries is the glide time reversal: a reflection of time combined with a shift by half a lattice vector. It acts on the response by transposition. This article states what it enforces in 2+1 dimensions. Every space–time group falls into one of four reciprocity classes. Plain reciprocity comes with a time mirror, glide reciprocity with a glide time reversal. A primed point operation gives a mapped relation instead, in which the sign of the magnetic dipole is measurable. On a sheet a threefold or sixfold axis rules out glide reciprocity and every forced Kramers-type doublet, and a fourfold axis allows the glide only in fixed half-vector classes. In a bulk crystal a threefold axis still admits the class along the axis. In the band structure the glide forces diabolic doublets, with loss and gain. At a momentum-gap edge it doubles the exceptional point. A horizontal cone of second-order media is protected by a symplectic square root of the period map. The energy–momentum zone becomes a Klein bottle under a projective symmetry; the glide time reversal alone does not make it one. In scattering the glide forbids the Littrow orders with phase −1 and, without real loss, the partner channel of a time slab. It gives twin pair-creation channels, a frequency-weighted Kirchhoff law and an effective medium without drag. Around a pump vortex of odd charge the parametric response leaves the half-integer sector. A sector rule fixes which defects lock, and above threshold walls turn at a speed that falls as N^(−2) and grows with ℓ. Möbius closure forces a defect at the seam, a temporal one for a standing wave, and edges must run along the glide. The results hold for linear sheets with a real, causal kernel. They are measured on lattice and sheet models, not on a fabricated metasurface.",
  "abstract_shown": true,
  "affiliations": [
    "Independent Reseacer"
  ],
  "article_type": null,
  "arxiv": null,
  "author_total": 1,
  "authors": [
    {
      "affs": [
        0
      ],
      "name": "László Márk",
      "orcid": "0009-0006-5033-633X"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/05tfcw2srm9yp.bib",
  "cited_by": 5,
  "doi": "10.5281/zenodo.23136229",
  "fulltext_url": null,
  "id": "05tfcw2srm9yp",
  "issns": [],
  "landing_url": "https://doi.org/10.5281/zenodo.23136229",
  "language": "en",
  "licence": "CC-BY",
  "licence_label": "CC BY",
  "licence_source": "journal",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": null,
  "native_subjects": [
    [
      "openalex",
      "2505|Quasicrystal Structures and Properties"
    ]
  ],
  "openalex": "W7219835383",
  "pdf_url": null,
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-04",
  "publisher": "European Organization for Nuclear Research",
  "ris": "https://research.draconitic.com/paper/05tfcw2srm9yp.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T13:27:01Z",
      "native_id": "W7219835383",
      "source": "openalex",
      "url": "https://doi.org/10.5281/zenodo.23136229"
    }
  ],
  "subjects": [
    {
      "field": "chemistry",
      "origin": "openalex:2505|Quasicrystal Structures and Properties",
      "subfield": "materials-polymers"
    }
  ],
  "title": "Space–Time Crystals: Reciprocity Classes, Forced Doublets and Defects",
  "title_text": "Space–Time Crystals: Reciprocity Classes, Forced Doublets and Defects",
  "type": "preprint",
  "updated_at": "2026-11-06T13:20:45Z",
  "url": "https://research.draconitic.com/paper/05tfcw2srm9yp",
  "venue": "Zenodo (CERN European Organization for Nuclear Research)",
  "versions": []
}