{
  "abstract": "In Einstein--Cartan--Kaluza--Klein compactification on $S^2\\times\\mathbb{C}P^2$, elimination of the non-propagating torsion generates a quartic spin-current contact interaction whose vacuum expectation value is nonzero even at zero fermion occupation. We reduce the ten-dimensional $Γ_{ABC}$ structure to the zero-mode sector and find that the reduction is channel-resolved: each of the three internal Cartan-plane bilinears contribute with the opposite sign to the external (axial) channel, so that the full trace is $R_{ch} = T_{\\rm vac}/T_{\\rm axial} = 1 + 3\\,(-1) = -2$. The vacuum term is therefore twice the axial estimate and opposite in sign, and, combined with the elimination constant $c_{10} = -κ_{10}/32$, verified by explicit Clifford computation, it is attractive and proportional to $N_{\\rm fam}^2$. We obtain the separated-point correlator, which in the continuum scales as $N_{\\rm fam}^2 d_R/(V_6\\,r^6)$, and, conditional on the physical quantum-boundary prescription, evaluate it at the minimum supported separation. The finite-density piece of the same correlator has the same sign and grows with chemical potential. Binding deepens after nucleation; the single-particle Hartree self-contraction vanishes for chiral zero modes. Using the derived $1/(a_1^2a_2^4)$ vacuum term with the Einstein-frame curvature and quantized-flux contributions, we analyze a coupled two-modulus toy potential. At fiducial couplings, the $(m,n)=(3,3)$ sector has a finite-radius stationary point with positive Hessian in both radion directions, while the four-family $(4,3)$ minimum lies beyond the adopted quantum-curvature boundary. The three-family sector $(1,5)$ is also locally stable but is less bound. 3-family dominance of the thermal nucleation weight further imposes the condition $κ_4 \\lesssim 7.5\\,(16/B)\\,\\ell_P^2$. These results serve as inputs to our higher-level synthesis.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.02909",
  "author_total": 1,
  "authors": [
    {
      "name": "Edward J. Shaya"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/09wjye55yabjf.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.02909",
  "fulltext_url": null,
  "id": "09wjye55yabjf",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.02909",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "physics.gen-ph"
    ],
    [
      "openalex",
      "3106|Black Holes and Theoretical Physics"
    ]
  ],
  "openalex": "W7208746155",
  "pdf_url": "https://arxiv.org/pdf/2609.02909",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/09wjye55yabjf.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:31Z",
      "native_id": "2609.02909",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.02909"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "openalex:3106|Black Holes and Theoretical Physics",
      "subfield": "high-energy"
    }
  ],
  "title": "Vacuum Spin-Torsion Energy Density and Two-Modulus Stability on $S^2\\times\\mathbb{C}P^2$",
  "title_text": "Vacuum Spin-Torsion Energy Density and Two-Modulus Stability on S^2×ℂP^2",
  "type": "preprint",
  "updated_at": "2026-10-30T12:18:31Z",
  "url": "https://research.draconitic.com/paper/09wjye55yabjf",
  "venue": "arXiv",
  "versions": []
}