[
  {
    "id": "ARR-2025-2SZN7M8RMR9D18W8-v1",
    "type": "article",
    "title": "Heat Kernel Methods and the Sign of Induced Gravity: Resolving Conventions via the Laplacian—Lichnerowicz Identity",
    "author": [
      {
        "literal": "Lluis Eriksson"
      }
    ],
    "issued": {
      "date-parts": [
        [
          2025,
          12,
          31
        ]
      ]
    },
    "publisher": "AIRR.SCIENCE",
    "archive": "AIRR.SCIENCE",
    "archive_location": "ARR-2025-2SZN7M8RMR9D18W8",
    "version": "v1",
    "genre": "Archived manuscript",
    "URL": "https://airr.science/papers/ARR-2025-2SZN7M8RMR9D18W8/versions/v1/",
    "note": "Archived manuscript; ARR-2025-2SZN7M8RMR9D18W8 v1. Not peer reviewed by AIRR. Historical import; not assessed by AIRR.",
    "abstract": "We derive the local one-loop contribution proportional to the scalar curvature R in the Euclidean effective action obtained by integrating out matter fields on a curved background. Using a Schwinger proper-time cutoff epsilon = Lambda^(-2) and the Seeley—DeWitt coefficient a_1, we extract the quadratically divergent term multiplying int d^4x sqrt(g) R. We fix a single Euclidean convention for the Einstein—Hilbert action, state an explicit Laplacian convention, and write the Laplacian—Lichnerowicz identity in a sign-robust form so that the fermionic contribution is unambiguous. We provide a unified bookkeeping coefficient A_1^(eff), and hence an induced Newton coupling G_ind via comparison with the Euclidean Einstein—Hilbert action. We also include the minimal gauge+ghost package in background Feynman gauge, a species table, and a reproducible verification suite. v2 adds: the equivalence of the species table with the classic counting 1/G_ind = (Lambda^2/12pi)(N_0 + 2N_(1/2) - 4N_1), gauge- and scheme-dependence caveats for the vector sector, a Weyl/Majorana caveat, corrected Wick-rotation wording, and an exact-spectrum numerical verification of every a_1 entry against closed-form spectra on S^4."
  }
]