{
  "abstract": "A central open problem at the intersection of quantum information theory, quantum thermodynamics, and many-body physics is determining the exact mathematical conditions under which the information-geometric distance d_g(ρ, σ) between two quantum states coincides with the minimum physical resource and thermodynamic cost 𝒱(ρ → σ) required to transform one into the other. In this paper, we establish the Extended Quantum Information Geometry System (EQIGS), a unified deductive framework synthesizing Petz monotone Riemannian metrics, quantum resource theories, finite-time thermodynamic length bounds, and tensor-network submanifold geometry, anchored directly in our 71-page ZFC Master Reference Monograph (Lee, 2026, DOI: 10.5281/zenodo.23486681) [1]. All foundational spaces and universal constants 𝔘 = (𝒯_0x8A2C, C_UPTC, η_friction, ε_SHID) follow Proposition 1.5, Theorem 2.9, Lemma 4.5, Lemma 4.6, Lemma 5.2, Lemma 6.3, Lemma 8.4, Lemma 8.6, Theorem 8.7, and Theorem 9.5 of [1].\n\nRegularizing the quantum state space 𝒮(ℬ) on the Takesaki Type II_1 ground factor (𝓜_ground, τ_ground) and the Fractional Sobolev–Colombeau Quotient Algebra 𝓖^α(𝒮), we formulate six core axioms (EQIGS-1 through EQIGS-6) and prove six fundamental theorems: (1) Complete Chentsov–Petz Monotone Metric Classification regularized at pure-state boundaries via ε(α) = exp(-1/(1-α)); (2) Exact Necessary and Sufficient Conditions for Information Distance–Physical Cost Equivalence and Tight Finite-Time Control Bounds governed by Planck-BCH arithmetic friction η_friction ≥ 10^-22; (3) Quantum Cauchy–Schwarz Thermodynamic Length Lower Bounds (Σ_na ≥ ℓ_g^2 / (2τ)); (4) Multipartite Entanglement Witnessing via Quantum Fisher Information Curvature Thresholds (ℱ_Q(ρ, H) > 4(Δh)^2 N); (5) Natural Choi–Bures Information Metrics on the Quantum Channel Space Chan(ℬ) and Isometric Reversibility; and (6) Exact Curvature–Volume Formulas for Bond-Dimension-D Tensor Network Manifolds and Area-to-Volume Law Phase Transitions at C_UPTC. Complete Python numerical verification is provided in Appendix A.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": null,
  "author_total": 1,
  "authors": [
    {
      "name": "Seonggil Lee"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/3rj913yzvayx0.bib",
  "cited_by": 0,
  "doi": "10.5281/zenodo.23557698",
  "fulltext_url": null,
  "id": "3rj913yzvayx0",
  "issns": [],
  "landing_url": "https://zenodo.org/records/23557698",
  "language": "eng",
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": null,
  "native_subjects": [],
  "openalex": null,
  "pdf_url": "https://zenodo.org/api/records/23557698/files/The%20Extended%20Quantum%20Information%20Geometry%20System%20(EQIGS)_%20Petz%20Metrics%20and%20Thermodynamic%20Length.pdf/content",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-22",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/3rj913yzvayx0.ris",
  "sources": [
    {
      "first_seen": "2026-11-05T12:20:41Z",
      "native_id": "23557698",
      "source": "zenodo",
      "url": "https://zenodo.org/records/23557698"
    }
  ],
  "subjects": [],
  "title": "The Extended Quantum Information Geometry System (EQIGS): A Deductive Framework Unifying Petz Monotone Metrics, Thermodynamic Length Dissipation Bounds, and Tensor-Network Curvature Transitions within the ZFC Axiomatic Bridge",
  "title_text": "The Extended Quantum Information Geometry System (EQIGS): A Deductive Framework Unifying Petz Monotone Metrics, Thermodynamic Length Dissipation Bounds, and Tensor-Network Curvature Transitions within the ZFC Axiomatic Bridge",
  "type": "preprint",
  "updated_at": "2026-11-05T12:20:41Z",
  "url": "https://research.draconitic.com/paper/3rj913yzvayx0",
  "venue": "Zenodo",
  "versions": []
}