{
  "abstract": "In Part I of this program, we unied the PT -symmetric spectral paradigm with the RuellePerronFrobenius ergodic theory of the Gauss continued-fraction map on the Hardy space H 2 (D). Through the WeinsteinAronszajn rank-one factorization det Fred (I -L s ) = det Fred (I -R s )W (s) and the block trigonalization of the parabolic core R s on C|1⟩ ⊕ H 2 0 (D), we showed that\n\nis the parabolic core response function enjoying O(n -5/2 ) branch super-convergence on Re(s) = 1/4. Crucially, we proved that any hypothetical o-critical zero\n\nIn the present treatise (Part II), we develop a variational and dierential-geometric framework to rule out this two-point collision. First, utilizing the O(n -2σ-2 ) super-convergence of R s on H 2 0 (D) alongside the Uniform Non-Integrability (UNI) of the continued-fraction roof function, we establish the spectral invertibility of I H 2 0 -R s and derive the convergent NeumannHurwitz hyperbolic correlation series for Φ core (s). Second, we introduce the radial LyapunovDirichlet energy functional E τ (σ) := |Φ core (σ + iτ )| 2 across horizontal segments σ ∈ [1/4 -δ, 1/4 + δ] and combine the subharmonic modulus Laplacian ∆E τ = 4|Φ ′ core (s)| 2 ≥ 0 with parametric operator calculus. Third, we explicitly compute the Lyapunov scale-dissipation operator D s := -∂ Rs ∂σ , proving the exact remainder-free right factorization\n\n. By intertwining D s with Mostafazadeh's pseudo-Hermitian metric η s = e -Qs , proving unconditional Koopman cylinder positivity and unconditional L 2 MontgomeryVaughan radial convexity, and formulating the BergmanPoisson subharmonic bridge, we establish that under pointwise bilinear chord coercivity, Rolle's Theorem forbids Φ core (σ +iτ ) from intersecting the Kato symmetrybreaking threshold 1 at two distinct symmetric points 1/4 ± δ + iτ , conning all non-trivial zeros to Re(z) = 1/2.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": null,
  "author_total": 1,
  "authors": [
    {
      "name": "Aziz Arbai"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/05vkt97j1b0fb.bib",
  "cited_by": 0,
  "doi": null,
  "fulltext_url": null,
  "id": "05vkt97j1b0fb",
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  "landing_url": "https://hal.science/hal-05852389v1",
  "language": "en",
  "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": [
    [
      "hal",
      "0.math"
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      "1.math.math-mp"
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      "1.math.math-nt"
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  "openalex": null,
  "pdf_url": "https://hal.science/hal-05852389/document",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-02",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/05vkt97j1b0fb.ris",
  "sources": [
    {
      "first_seen": "2026-11-06T12:20:44Z",
      "native_id": "hal-05852389",
      "source": "hal",
      "url": "https://hal.science/hal-05852389v1"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "hal:1.math.math-nt",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "hal:1.math.math-fa",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "hal:1.math.math-ds",
      "subfield": "dynamical-systems"
    },
    {
      "field": "mathematics",
      "origin": "hal:1.math.math-mp",
      "subfield": "mathematical-physics"
    }
  ],
  "title": "A Variational Principle for the Parabolic Response Function (Part II): Lyapunov Scale-Dissipation, Energy Curvature, and the Geometric Prohibition of O-Critical Zeros",
  "title_text": "A Variational Principle for the Parabolic Response Function (Part II): Lyapunov Scale-Dissipation, Energy Curvature, and the Geometric Prohibition of O-Critical Zeros",
  "type": "preprint",
  "updated_at": "2026-11-06T12:20:44Z",
  "url": "https://research.draconitic.com/paper/05vkt97j1b0fb",
  "venue": "HAL",
  "versions": []
}