{
  "annotation_id": "28551099-3c62-44d6-83ee-c25eded07c1b",
  "date_created": "2026-02-17T05:53:15.958000Z",
  "date_modified": "2026-02-17T05:53:15.958000Z",
  "file_hash": "efb50a1f1776822829ca469e8179cfcde08f01a9addb4b1948be7db81d721317",
  "private": false,
  "record": {
    "abstract": "We report a fundamental geometric constraint on the detection of kinetic energy release (KER) in three-dimensional quantum fragmentation. By investigating the sudden dissociation of Slater-type orbitals, physically motivated basis for localized states, we demonstrate that the ratio of the peak detected energy to the integrated mean, $R_E = E_{\\text{peak}}/\\langle E \\rangle$, is strictly bounded below $0.5$ for all physical parameter spaces. We systematically map the behavior of $R_E$ across the orbital localization ($\\zeta$) and effective repulsive charge ($Q$) landscape. Our results show that while $R_E$ exhibits sensitivity to the force-field geometry at atomic scales, it converges to a remarkably stable, scale-invariant constant of $\\approx 0.33$ in the high-localization limit ($M \\propto \\zeta$) characteristic of subatomic ground states ($n=1$,$Q=1$). This $1/3$ geometric constant provides a provocative first-principles interpretation of the historical ``missing energy\u0027\u0027 problem in nuclear physics. We suggest that the $1/3$ average energy ratio observed in Beta decay spectra may be a topological artifact of the $4\\pi r^2$ volume weighting inherent to 3D wavefunctions, rather than exclusively a signature of undetected mass. This work establishes $R_E \u003c 0.5$ as a universal geometric baseline for quantum simulations and offers a new framework for reconstructing the true energy budget in subatomic calorimetry by correcting for the intrinsic masking effects of 3D radial geometry.",
    "arxiv_id": "2601.08255",
    "authors": [
      "Jinzhen Zhu"
    ],
    "categories": [
      "physics.atom-ph"
    ],
    "license": "http://creativecommons.org/licenses/by-nc-sa/4.0/",
    "title": "The 1/3 Geometric Constant: Scale Invariance and the Origin of \"Missing Energy\" in 3D Quantum Fragmentation",
    "url": "https://arxiv.org/abs/2601.08255",
    "version": "v2"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "376932da-5279-4f7e-948f-734635667924",
    "id": "arXiv Dataset",
    "type": "Model",
    "variant": "snapshot-2026-01-17",
    "version": "0.1.0"
  },
  "user_id": 1000002
}