{
  "id": "oai:papers.qnfo.org:renormalization-group-attractors-as-a-unifying-framework-for-physical-convergenc",
  "slug": "renormalization-group-attractors-as-a-unifying-framework-for-physical-convergenc",
  "title": "Renormalization‑Group Attractors as a Unifying Framework for Physical Convergence and Theory Polygenesis",
  "authors": [
    "Rowan Brad Quni-Gudzinas"
  ],
  "abstract": "Independent discovery of identical mathematical structures (polygenesis) and the parallel emergence of similar physical behavior in unrelated systems (convergence) suggest a common organizing principle. Existing work identifies fixed‑point structures in scalar‑curvature geometry, cosmological attractors, dual‑subgradient optimization, strong‑randomness renormalization, nonequilibrium functional RG, hierarchical glass models, and quark confinement, yet lacks a quantitative link between the geometry of theory space and the likelihood of independent discovery. We model theory space as a metric flow on the set of Lagrangians, define a Euclidean similarity metric, and derive two complementary quantitative results. First, using the inflationary attractor formulas n_s=1-2/N and r=12/N² we obtain a basin‑volume scaling V_rm basin(N)=1.0258 N^-2, which yields a polygenesis probability P_rm poly(N)=κ 1.0258 N^-2 for a uniform prior on efold numbers. Second, we adopt dual‑subgradient iteration‑count formulas T_rm simple= lceil1/εrceil and T_rm sliding= lceilln(1/ε)rceil, and under a concrete contraction assumption project $458.2$ iterations to reach ε=10^-2 precision. An alternative Herfindahl‑based model for a five‑basin landscape gives P₂=0.275 and P₃=0.08875. Both frameworks produce falsifiable predictions: the basin‑volume scaling predicts an N^-2 decline of polygenesis with efold number, while the Herfindahl model predicts specific coincidence probabilities for a given basin distribution. The results change practice by providing measurable criteria—basin volume and iteration‑count scaling—for assessing redundancy risk in theory development and for designing discovery processes.",
  "abstract_markdown": "Independent discovery of identical mathematical structures (polygenesis) and the parallel emergence of similar physical behavior in unrelated systems (convergence) suggest a common organizing principle. Existing work identifies fixed‑point structures in scalar‑curvature geometry, cosmological attractors, dual‑subgradient optimization, strong‑randomness renormalization, nonequilibrium functional RG, hierarchical glass models, and quark confinement, yet lacks a quantitative link between the geometry of theory space and the likelihood of independent discovery. We model theory space as a metric flow on the set of Lagrangians, define a Euclidean similarity metric, and derive two complementary quantitative results. First, using the inflationary attractor formulas $n_s=1-2/N$ and $r=12/N^{2}$ we obtain a basin‑volume scaling $V_{\\rm basin}(N)=1.0258\\,N^{-2}$, which yields a polygenesis probability $P_{\\rm poly}(N)=\\kappa\\,1.0258\\,N^{-2}$ for a uniform prior on efold numbers. Second, we adopt dual‑subgradient iteration‑count formulas $T_{\\rm simple}= \\lceil1/\\epsilon\\rceil$ and $T_{\\rm sliding}= \\lceil\\ln(1/\\epsilon)\\rceil$, and under a concrete contraction assumption project $458.2$ iterations to reach $\\epsilon=10^{-2}$ precision. An alternative Herfindahl‑based model for a five‑basin landscape gives $P_{2}=0.275$ and $P_{3}=0.08875$. Both frameworks produce falsifiable predictions: the basin‑volume scaling predicts an $N^{-2}$ decline of polygenesis with efold number, while the Herfindahl model predicts specific coincidence probabilities for a given basin distribution. The results change practice by providing measurable criteria—basin volume and iteration‑count scaling—for assessing redundancy risk in theory development and for designing discovery processes.",
  "date": "2026-10-20",
  "first_published": "2026-10-20",
  "last_revised": "2026-10-20T06:11:03Z",
  "modified": "2026-10-20T06:11:03Z",
  "version": "1.1.0",
  "version_count": 2,
  "language": "en",
  "keywords": [],
  "quality_tags": [
    "High-quality scholarly research",
    "open-access scholarly work",
    "versioned research publication"
  ],
  "quality_label": "High-quality scholarly research",
  "quality_basis": "QNFO publisher classification for open-access, versioned research with a public revision history and reader correction channel; this is not a claim of independent peer review.",
  "quality_evidence_url": "https://qnfo.org/about",
  "peer_review_status": "Not independently peer-reviewed",
  "resource_type": "ScholarlyArticle",
  "doi": null,
  "doi_url": null,
  "url": "https://papers.qnfo.org/papers/renormalization-group-attractors-as-a-unifying-framework-for-physical-convergenc",
  "license_url": "https://legal.qnfo.org/",
  "license_spdx": null,
  "sha256": "92ca3edd9da9b534a03d7a067bd5c17b3683f1bbd7775e15cfa7d86430598acd",
  "version_url": "https://papers.qnfo.org/papers/renormalization-group-attractors-as-a-unifying-framework-for-physical-convergenc/v/1.1.0",
  "datacite": {
    "schemaVersion": "http://datacite.org/schema/kernel-4",
    "identifiers": [
      {
        "identifier": "https://papers.qnfo.org/papers/renormalization-group-attractors-as-a-unifying-framework-for-physical-convergenc",
        "identifierType": "URL"
      }
    ],
    "creators": [
      {
        "name": "Rowan Brad Quni-Gudzinas",
        "nameType": "Personal",
        "nameIdentifiers": [
          {
            "nameIdentifier": "https://orcid.org/0009-0002-4317-5604",
            "nameIdentifierScheme": "ORCID",
            "schemeUri": "https://orcid.org"
          }
        ]
      }
    ],
    "titles": [
      {
        "title": "Renormalization‑Group Attractors as a Unifying Framework for Physical Convergence and Theory Polygenesis"
      }
    ],
    "publisher": "QNFO",
    "publicationYear": "2026",
    "resourceType": {
      "resourceTypeGeneral": "Text",
      "resourceType": "ScholarlyArticle"
    },
    "subjects": [
      {
        "subject": "High-quality scholarly research",
        "subjectScheme": "QNFO publisher classification",
        "schemeUri": "https://qnfo.org/about"
      },
      {
        "subject": "open-access scholarly work",
        "subjectScheme": "QNFO publisher classification",
        "schemeUri": "https://qnfo.org/about"
      },
      {
        "subject": "versioned research publication",
        "subjectScheme": "QNFO publisher classification",
        "schemeUri": "https://qnfo.org/about"
      }
    ],
    "dates": [
      {
        "date": "2026-10-20",
        "dateType": "Issued"
      },
      {
        "date": "2026-10-20",
        "dateType": "Updated"
      }
    ],
    "language": "en",
    "version": "1.1.0",
    "rightsList": [
      {
        "rightsUri": "https://legal.qnfo.org/"
      }
    ],
    "descriptions": [
      {
        "description": "Independent discovery of identical mathematical structures (polygenesis) and the parallel emergence of similar physical behavior in unrelated systems (convergence) suggest a common organizing principle. Existing work identifies fixed‑point structures in scalar‑curvature geometry, cosmological attractors, dual‑subgradient optimization, strong‑randomness renormalization, nonequilibrium functional RG, hierarchical glass models, and quark confinement, yet lacks a quantitative link between the geometry of theory space and the likelihood of independent discovery. We model theory space as a metric flow on the set of Lagrangians, define a Euclidean similarity metric, and derive two complementary quantitative results. First, using the inflationary attractor formulas n_s=1-2/N and r=12/N² we obtain a basin‑volume scaling V_rm basin(N)=1.0258 N^-2, which yields a polygenesis probability P_rm poly(N)=κ 1.0258 N^-2 for a uniform prior on efold numbers. Second, we adopt dual‑subgradient iteration‑count formulas T_rm simple= lceil1/εrceil and T_rm sliding= lceilln(1/ε)rceil, and under a concrete contraction assumption project $458.2$ iterations to reach ε=10^-2 precision. An alternative Herfindahl‑based model for a five‑basin landscape gives P₂=0.275 and P₃=0.08875. Both frameworks produce falsifiable predictions: the basin‑volume scaling predicts an N^-2 decline of polygenesis with efold number, while the Herfindahl model predicts specific coincidence probabilities for a given basin distribution. The results change practice by providing measurable criteria—basin volume and iteration‑count scaling—for assessing redundancy risk in theory development and for designing discovery processes.",
        "descriptionType": "Abstract"
      },
      {
        "description": "Publisher quality classification: High-quality scholarly research. QNFO publisher classification for open-access, versioned research with a public revision history and reader correction channel; this is not a claim of independent peer review.",
        "descriptionType": "Other"
      },
      {
        "description": "Peer review status: Not independently peer-reviewed",
        "descriptionType": "Other"
      }
    ],
    "formats": [
      "text/html"
    ]
  }
}