[
  {
    "id": "ARR-2026-7EPM3V3DP796BBRR-v5",
    "type": "article",
    "title": "Coarse information and finite rank obstructions for flat lattice Hodge forms",
    "author": [
      {
        "literal": "Lluis Eriksson"
      }
    ],
    "issued": {
      "date-parts": [
        [
          2026,
          11,
          4
        ]
      ]
    },
    "publisher": "AIRR.SCIENCE",
    "archive": "AIRR.SCIENCE",
    "archive_location": "ARR-2026-7EPM3V3DP796BBRR",
    "version": "v5",
    "genre": "Research preprint",
    "URL": "https://airr.science/papers/ARR-2026-7EPM3V3DP796BBRR/versions/v5/",
    "note": "Research preprint; ARR-2026-7EPM3V3DP796BBRR v5. Not peer reviewed by AIRR. Working paper; not admitted to the AIRR accepted collection.",
    "abstract": "On finite periodic unit-spacing lattices, necessary coarse-information budgets constrain flat Hodge forms and constructed derivative repairs. We consolidate physical Fourier-band, tangent, exact regular-sector, signed-weight and full-volume rank results with separately pinned formal evidence and analytic arguments. A critical inverse-conductance moment suffices for a global spectral observation of the mean-budget order. Actual rectangular means have a general D/4 upper rate and the target D/2 rate for an explicitly restricted scaled-cube class. Constructive counterexamples obstruct a retained-grid single-threshold algorithm and a universal exact supplied-cube decomposition, while the same profiles admit successful rectangular partitions. The unrestricted critical rectangular question remains open. No interacting or continuum Yang-Mills mass gap is established."
  }
]