[
  {
    "id": "ARR-2026-7EPM3V3DP796BBRR-v4",
    "type": "article",
    "title": "Coarse information and finite rank obstructions for flat lattice Hodge forms",
    "author": [
      {
        "literal": "Lluis Eriksson"
      }
    ],
    "issued": {
      "date-parts": [
        [
          2026,
          11,
          1
        ]
      ]
    },
    "publisher": "AIRR.SCIENCE",
    "archive": "AIRR.SCIENCE",
    "archive_location": "ARR-2026-7EPM3V3DP796BBRR",
    "version": "v4",
    "genre": "Research preprint",
    "URL": "https://airr.science/papers/ARR-2026-7EPM3V3DP796BBRR/versions/v4/",
    "note": "Research preprint; ARR-2026-7EPM3V3DP796BBRR v4. Not peer reviewed by AIRR. Working paper; not admitted to the AIRR accepted collection.",
    "abstract": "On a finite periodic lattice with unit spacing, we derive necessary coarse-information rank budgets for flat Hodge forms and constructed derivative repairs. For nonnegative componentwise repair weights, local coercivity on actual divergence-free fields with a fixed positive constant forces the output dimensions of differentiable observations to diverge when one directional spatial mean is subquadratic in lattice side length. The proof derives an exact transverse-character trace formula and composes it with the actual local derivative-kernel bound. A constructed quadratic-weight repair and arithmetic-mean observation show that fixed output dimension becomes possible at quadratic weight scale. Explicit polynomial/Lipschitz and C1 counterexamples retain the necessity of the stated quadratic penalty upper hypothesis in the merely differentiable observation class. Prior finite-rank, tangent and exact regular-sector results are consolidated with separately pinned Lean evidence and analytic arguments. Classical mechanisms are distinguished from original priority and physical relevance. No interacting or continuum Yang-Mills mass gap is established."
  }
]