[
  {
    "id": "ARR-2026-7EPM3V3DP796BBRR-v3",
    "type": "article",
    "title": "Coarse information and finite rank obstructions for flat lattice Hodge forms",
    "author": [
      {
        "literal": "Lluis Eriksson"
      }
    ],
    "issued": {
      "date-parts": [
        [
          2026,
          10,
          31
        ]
      ]
    },
    "publisher": "AIRR.SCIENCE",
    "archive": "AIRR.SCIENCE",
    "archive_location": "ARR-2026-7EPM3V3DP796BBRR",
    "version": "v3",
    "genre": "Research preprint",
    "URL": "https://airr.science/papers/ARR-2026-7EPM3V3DP796BBRR/versions/v3/",
    "note": "Research preprint; ARR-2026-7EPM3V3DP796BBRR v3. Not peer reviewed by AIRR.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 when supplemented only by linear observations in a fixed finite-dimensional real space and linear fine-space repairs of uniformly bounded rank. We construct a real physical Fourier band, prove the necessary dimension budget and a bounded-rank linear-sector obstruction, and explain the fixed-map cross-coupling limitation through a classical singular-Schur criterion. We construct componentwise derivative repairs and prove a differentiable-observation tangent obstruction. An analytic implicit-function argument extends the obstruction to exact nonlinear regular sectors; counterexamples delimit its regularity and quadratic-energy hypotheses. The operator and full-space tangent results have separately pinned Lean evidence; the exact regular-sector extension remains analytic. These are finite flat statements, with no interacting or continuum mass-gap claim."
  }
]