Message #2331 · Riemann Hypothesis Research

← Session 36 — ii′-6-DL dog-leg + side bounds; Paper A review

#2331 assistant 2026-08-26 21:41:10.344 UTC · 4811→865 tok open ⤢

thinking (2307 chars)

Key facts: - Title date: "Started: 2026-08-17; revised 2026-08-20" → change to "revised 2026-08-26". - The bib entry: **Voros, André — "Discretized Keiper/Li approach to the Riemann hypothesis", Exp. Math. 29(4):452–469, 2020** — NOTE: the author is ANDRÉ VOROS (not Misguich–Voros!). The paper is BY VOROS (with Misguich presumably acknowledged?). The user's point stands: the paper is titled DISCRETIZED Keiper/Li approach — the citation key "voros2017li" and the paper text says "Misguich--Voros \cite{voros2017li}" — which is BOTH a miscitation (author is Voros) AND potentially a claim mismatch (discretized vs ordinary λ_n). Let me check the archive's record of what this source provides. NGUYEN.md says "finite verification ours to 3000 + Misguich–Voros to 5×10⁵ (10× overlap)". E-011/R-001/E-015 should describe it. Let me check R-001 and E-015's description, and then fetch the actual abstract of the Voros paper (arXiv:1702.05251? — let me check; the Exp. Math. paper by André Voros 2020, "Discretized Keiper/Li approach to the Riemann hypothesis"). What do I know about this paper from memory? André Voros, "Discretized Keiper/Li approach to the Riemann hypothesis" (2020): he studies a discretization of the Li coefficients where the infinite sum over zeros is replaced by a finite sum with rigorous truncation, and numerically verifies positivity. IIRC the paper verifies positivity of the Li coefficients for n up to ~5×10^5?? Hmm — actually I recall Voros (2006) "Sharpenings of Li's criterion for RH" and a later computational paper. The 2020 Exp. Math. paper: Misguich & Voros? or Voros alone? The bib says author = Voros, André. Hmm — actually, hold on. Let me recall more carefully: there IS a paper by Misguich and Voros?? — "Keiper-Li coefficients: numerical computations"?? — I genuinely am unsure. The bib entry we have says author is Voros alone, Exp. Math. 29(4):452-469, 2020. Let me fetch the arXiv abstract to describe its content accurately. The arXiv id for it: likely 1702.05251 ("Discretized Keiper/Li approach to the Riemann hypothesis" — Voros). Let me fetch. Also check the archive's own description (R-001/E-011/E-015/D-037) of what the 5×10⁵ figure comes from — the project used "Misguich–Voros to 5×10⁵" as an external input. Let me grep the archive for "Misguich".

Critical finding: the bib entry is **Voros alone** (Exp. Math. 29(4):452–469, 2020) — "Misguich–Voros" in the text is a miscitation, and the title says *discretized*. Checking how the archive described this source, then fetching the paper's actual abstract.

tool: Grep

input

{
  "pattern": "Misguich|Misguich\u2013Voros|discretized|Discretized",
  "path": "D:\\Python\\Quantum\\research",
  "output_mode": "content",
  "head_limit": 30
}

raw content_json (database row)

[{"type":"thinking","thinking":"Key facts:\n- Title date: \"Started: 2026-08-17; revised 2026-08-20\" → change to \"revised 2026-08-26\".\n- The bib entry: **Voros, André — \"Discretized Keiper/Li approach to the Riemann hypothesis\", Exp. Math. 29(4):452–469, 2020** — NOTE: the author is ANDRÉ VOROS (not Misguich–Voros!). The paper is BY VOROS (with Misguich presumably acknowledged?). The user's point stands: the paper is titled DISCRETIZED Keiper/Li approach — the citation key \"voros2017li\" and the paper text says \"Misguich--Voros \\cite{voros2017li}\" — which is BOTH a miscitation (author is Voros) AND potentially a claim mismatch (discretized vs ordinary λ_n).\n\nLet me check the archive's record of what this source provides. NGUYEN.md says \"finite verification ours to 3000 + Misguich–Voros to 5×10⁵ (10× overlap)\". E-011/R-001/E-015 should describe it. Let me check R-001 and E-015's description, and then fetch the actual abstract of the Voros paper (arXiv:1702.05251? — let me check; the Exp. Math. paper by André Voros 2020, \"Discretized Keiper/Li approach to the Riemann hypothesis\").\n\nWhat do I know about this paper from memory? André Voros, \"Discretized Keiper/Li approach to the Riemann hypothesis\" (2020): he studies a discretization of the Li coefficients where the infinite sum over zeros is replaced by a finite sum with rigorous truncation, and numerically verifies positivity. IIRC the paper verifies positivity of the Li coefficients for n up to ~5×10^5?? Hmm — actually I recall Voros (2006) \"Sharpenings of Li's criterion for RH\" and a later computational paper. The 2020 Exp. Math. paper: Misguich & Voros? or Voros alone? The bib says author = Voros, André.\n\nHmm — actually, hold on. Let me recall more carefully: there IS a paper by Misguich and Voros?? — \"Keiper-Li coefficients: numerical computations\"?? — I genuinely am unsure. The bib entry we have says author is Voros alone, Exp. Math. 29(4):452-469, 2020. Let me fetch the arXiv abstract to describe its content accurately. The arXiv id for it: likely 1702.05251 (\"Discretized Keiper/Li approach to the Riemann hypothesis\" — Voros). Let me fetch.\n\nAlso check the archive's own description (R-001/E-011/E-015/D-037) of what the 5×10⁵ figure comes from — the project used \"Misguich–Voros to 5×10⁵\" as an external input. Let me grep the archive for \"Misguich\".","signature":""},{"type":"text","text":"Critical finding: the bib entry is **Voros alone** (Exp. Math. 29(4):452–469, 2020) — \"Misguich–Voros\" in the text is a miscitation, and the title says *discretized*. Checking how the archive described this source, then fetching the paper's actual abstract."},{"type":"tool_use","id":"Grep_267","name":"Grep","input":{"pattern":"Misguich|Misguich–Voros|discretized|Discretized","path":"D:\\Python\\Quantum\\research","output_mode":"content","head_limit":30},"extra_content":null}]