{
  "abstract": "We establish a structural rigidity principle for the nontrivial zeros of the Riemann zeta function by analyzing the asymptotic interaction between discrete Dirichlet oscillations and their continuous analytic envelope. The starting point is a renormalized discrepancy operator, the C-transformation, which isolates the finite structural difference between the Dirichlet series and its integral approximation. Applied to the kernel x^(-s), this operator yields a decomposition of the zeta function into three parts: an oscillatory Dirichlet component X_N(s), an explicit analytic growth envelope Y_N(s), and a polynomially decaying remainder R_N(s). We show that the vanishing condition zeta(s)=0 forces an asymptotic compatibility between the two dominant components. This relation is formalized in a Bridge Lemma, which proves that zeros require asymptotic equality of the squared magnitudes |X_N(s)|^2 and |Y_N(s)|^2. A detailed asymptotic analysis then reveals that the ratio of these magnitudes exhibits three distinct regimes depending on the real part sigma=Re(s): divergence for sigma>1/2, collapse for sigma<1/2, and exact balance for sigma=1/2. This incompatibility of growth regimes produces a rigidity mechanism: the asymptotic balance required by the zero condition can occur only on the critical line. Consequently, every nontrivial zero must satisfy Re(s)=1/2. The result provides a deterministic explanation for the location of the zeros, showing that the critical line emerges from an intrinsic structural constraint of the Dirichlet representation of the zeta function.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": "Journal reference: Journal of Theoretical Physics & Mathematics Research, May 2026",
  "arxiv": "2609.28529",
  "author_total": 1,
  "authors": [
    {
      "name": "Pedro Caceres"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/0cb7f6qeay2ym.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.28529",
  "fulltext_url": null,
  "id": "0cb7f6qeay2ym",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.28529",
  "language": null,
  "licence": "CC-BY-NC-ND-4.0",
  "licence_label": "CC BY-NC-ND 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.GM"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2609.28529",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/0cb7f6qeay2ym.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:35Z",
      "native_id": "2609.28529",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.28529"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.GM",
      "subfield": "general"
    }
  ],
  "title": "Asymptotic Balance and Structural Rigidity in the Riemann Zeta Function",
  "title_text": "Asymptotic Balance and Structural Rigidity in the Riemann Zeta Function",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:35Z",
  "url": "https://research.draconitic.com/paper/0cb7f6qeay2ym",
  "venue": "arXiv",
  "versions": [
    {
      "doi": "10.64030/3065-8802.04.03.02",
      "pid": null,
      "relation": "published-as",
      "title": null,
      "venue": null
    }
  ]
}