[
  {
    "id": "ARR-2026-7EPM3V3DP796BBRR-v2",
    "type": "article",
    "title": "Coarse information and finite rank obstructions for flat lattice Hodge forms",
    "author": [
      {
        "literal": "Lluis Eriksson"
      }
    ],
    "issued": {
      "date-parts": [
        [
          2026,
          10,
          30
        ]
      ]
    },
    "publisher": "AIRR.SCIENCE",
    "archive": "AIRR.SCIENCE",
    "archive_location": "ARR-2026-7EPM3V3DP796BBRR",
    "version": "v2",
    "genre": "Research preprint",
    "URL": "https://airr.science/papers/ARR-2026-7EPM3V3DP796BBRR/versions/v2/",
    "note": "Research preprint; ARR-2026-7EPM3V3DP796BBRR v2. Not peer reviewed by AIRR. Working paper; not admitted to the AIRR accepted collection.",
    "abstract": "On a finite periodic lattice with unit spacing, a flat Hodge form cannot have a positive coercivity constant uniform under refinement if it is supplemented only by linear observations in a fixed finite-dimensional real space and linear fine-space repairs of uniformly bounded rank. The linear observations may vary with refinement, and their scalar penalty need only vanish at zero. We prove a separate obstruction on kernels of bounded-rank linear constraints using a constructed real Fourier band, derive a necessary dimension budget and explain why it is not sufficient through a classical singular-Schur criterion and a cross-coupling example. Formal evidence is separately pinned; analytic statements and source specializations are identified. No interacting, continuum or Yang-Mills mass-gap claim is made."
  }
]