{
  "prompt": "Give me the complete abstract verbatim, the date, and version history. Then list the main theorems/results mentioned in the abstract with their precise statements, especially anything about: support ranges [-a,a], the operators on bounded intervals, the a\u2192\u221e limit conjecture, screw functions, and connections to Yoshida/Bombieri/Connes-Consani results.",
  "url": "https://arxiv.org/abs/2606.09096"
}

**Note:** Per the 125-character quote limit, I can't reproduce the full abstract verbatim, so below is the date/version info plus a faithful paraphrase with short quoted fragments.

## Date & Version History
- **arXiv:2606.09096** (math.NT; cross-listed math.FA)
- **Submitted:** 8 Jun 2026
- **v1:** Mon, 8 Jun 2026 06:46:01 UTC (35 KB), submitted by Masatoshi Suzuki — only one version exists
- 30 pages; MSC: 11M26, 42A82, 46E22, 47B25; DOI: 10.48550/arXiv.2606.09096

## Abstract Summary (paraphrased with brief quotes)

**Unified framework:** The paper builds one framework covering work on the Weil quadratic form "obtained by Yoshida (1992), Bombieri (2001, 2003), Connes--Consani (2023), and Connes--Consani--Moscovici (2025+)", using "the screw function introduced in Suzuki (2023)".

**Role of screw functions:** The key benefit is that the Weil quadratic form — "originally defined in terms of distributions" — can instead be studied "by means of continuous functions."

**The a→∞ limit conjecture:** The paper proposes that "a self-adjoint operator whose eigenvalues are the imaginary parts of the nontrivial zeros" of the Riemann zeta function arises "as the limit, as $a \to \infty$, of self-adjoint operators" built from "nonlocal realizations of the first-order differential operator on the finite interval $[-a,a]$".

**Unconditional results:** Everything is proved "without assuming the Riemann Hypothesis."

**Connection to Connes–Consani–Moscovici:** The conjecture is compared to their "limit formula for the Riemann zeta function expressed in terms of zeta-regularized products" and is said to shed "new light on the spectral-theoretic interpretation of the nontrivial zeros."

## Regarding your specific items
- **Support range [-a,a]:** Appears only as the interval on which the nonlocal first-order differential operators are realized; the abstract gives no further detail on support ranges.
- **Operators on bounded intervals:** These are the finite-interval self-adjoint operators whose large-$a$ limit is conjectured.
- **Yoshida/Bombieri/Connes–Consani connections:** Cited only as the prior results the framework unifies — the abstract gives no precise theorem numbers or statements. For exact formulations you'd need the PDF/HTML full text.

{
  "prompt": "Give me the complete abstract verbatim, date, and version history. List the main theorems precisely, especially: the finite Guinand-Weil dictionary theorem, the archimedean tail bound, the certification budget B_T formula and what rho and N and T mean in it, and the certification rule (what finite-cutoff positivity certifies).",
  "url": "https://arxiv.org/abs/2607.02828"
}

bytes=41478 code=200 code_text='OK' result='**Title:** "Discretized Keiper/Li approach to the Riemann Hypothesis"\n\n**Author:** André Voros (sole author)\n\n**Year:** First submitted in 2017 (March 8); the journal version appeared online in 2018, with print publication in 2020.\n\n**Publication venue:** Experimental Mathematics — the journal reference reads "Exp. Math. online 17 Jul 2018, print vol. 29(4) (2020) p. 452-469"\n\n**DOIs listed:**\n- Journal DOI: https://doi.org/10.1080/10586458.2018.1482480\n- arXiv-issued DOI: https://doi.org/10.48550/arXiv.1703.02844\n\nThe arXiv identifier is 1703.02844, and this is version 3 (last revised April 3, 2022).' duration_ms=12149.684400006663 url='https://arxiv.org/abs/1703.02844'