{
  "abstract": "We study two-step recurrences with positive step sizes and nonnegative momentum coefficients whose terminal residual is the Chebyshev minimax polynomial on a prescribed spectral interval $[μ,L]$. These recurrences have the same terminal error on a fixed quadratic, but their first-order responses to stepwise Hessian perturbations can differ. We prove that the sine-Jacobi recurrence of Part I is asymptotically optimal for this response norm within a factor of $1.000004$, uniformly over $0<μ<L$. Every terminal-exact recurrence satisfies $A_N\\ge(2\\sqrt{c_{cert}}-o(1))N^{3/2}ε_N^\\star/(L-μ)$ with $c_{cert}>1.14268353624$, whereas the sine-Jacobi recurrence attains the constant $2\\sqrt{c_{\\sin}}$ with $c_{\\sin}<1.14269218$. The proof reduces the gain to the diagonal energy of a Jacobi Green matrix. A centering lift represents this matrix by an exponential kernel; packing its diagonal into a density on the line preserves the energy and controls the change in the Birman-Schwinger spectrum. A calibrated identity gives a lower bound using the ground parameter and one Fredholm determinant. Two further determinants and a trace observation improve the bound through a pointwise inequality on an explicit compact state region. One rational certificate verifies this inequality by interval arithmetic. A second certificate constructs a density satisfying the selected observations and both normalizations with energy below the sine value. Finally, no $C^1$ function of finitely many observations of the specified kinds gives a locally sharp lower bound at the sine density.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.05164",
  "author_total": 2,
  "authors": [
    {
      "name": "Dmitry Pasechnyuk-Vilensky"
    },
    {
      "name": "Martin Takáč"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2ahbvjd8bns5h.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.05164",
  "fulltext_url": null,
  "id": "2ahbvjd8bns5h",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.05164",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.OC"
    ],
    [
      "arxiv",
      "math.SP"
    ],
    [
      "openalex",
      "2604|Mathematical functions and polynomials"
    ]
  ],
  "openalex": "W7220660338",
  "pdf_url": "https://arxiv.org/pdf/2610.05164",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-06",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2ahbvjd8bns5h.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:42Z",
      "native_id": "2610.05164",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.05164"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.SP",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "Chebyshev-Exact Acceleration under Hessian Variation, II: Computer-Assisted Variational Lower Bound",
  "title_text": "Chebyshev-Exact Acceleration under Hessian Variation, II: Computer-Assisted Variational Lower Bound",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:42Z",
  "url": "https://research.draconitic.com/paper/2ahbvjd8bns5h",
  "venue": "arXiv",
  "versions": []
}