{
  "command": "cd D:/Python/Quantum && ./.venv/Scripts/python.exe -c \"\nimport mpmath as mp\nimport numpy as np\nmp.dps = 200\nNMAX = 120\ngam = [mp.stieltjes(k) for k in range(NMAX+1)]\nN_ = [mp.mpf(0)]*(NMAX+2); D_ = [mp.mpf(0)]*(NMAX+2)\nN_[0] = 1; D_[0] = 1\nfor m in range(0, NMAX+1):\n    D_[m+1] = (-1)**m * gam[m] / mp.factorial(m)\nfor m in range(1, NMAX+1):\n    N_[m+1] = -(-1)**m * gam[m] / mp.factorial(m-1)\nE = [mp.mpf(0)]*(NMAX+2)\nfor k in range(0, NMAX+2):\n    s = N_[k]\n    for i in range(1, k+1):\n        s -= D_[i]*E[k-i]\n    E[k] = s\neta = [E[k+1] for k in range(NMAX+1)]\ndef lam(n, const_variant):\n    s = mp.mpf(0)\n    for j in range(1, n+1):\n        s -= (-1)**(j-1) * mp.binomial(n,j) * eta[j-1] / mp.factorial(j-1)\n    s += (1 if const_variant=='one' else n) - (mp.log(4*mp.pi)+mp.euler)*n/2\n    for j in range(2, n+1):\n        s -= (-1)**(j-1) * mp.binomial(n,j) * (1-mp.mpf(2)**(-j)) * mp.zeta(j)\n    return s\nd = np.loadtxt('research/numerics/data/E-008-li-coefficients.csv', delimiter=',', skiprows=1, usecols=(0,1,2), converters={3: lambda s: 0}, encoding='utf-8', ndmin=2)\n\" 2>&1 | head -3\n# simpler: read csv via csv module\n./.venv/Scripts/python.exe << 'EOF'\nimport mpmath as mp, csv\nmp.dps = 200\nNMAX = 120\ngam = [mp.stieltjes(k) for k in range(NMAX+1)]\nN_ = [mp.mpf(0)]*(NMAX+2); D_ = [mp.mpf(0)]*(NMAX+2)\nN_[0] = 1; D_[0] = 1\nfor m in range(0, NMAX+1):\n    D_[m+1] = (-1)**m * gam[m] / mp.factorial(m)\nfor m in range(1, NMAX+1):\n    N_[m+1] = -(-1)**m * gam[m] / mp.factorial(m-1)\nE = [mp.mpf(0)]*(NMAX+2)\nfor k in range(0, NMAX+2):\n    s = N_[k]\n    for i in range(1, k+1):\n        s -= D_[i]*E[k-i]\n    E[k] = s\neta = [E[k+1] for k in range(NMAX+1)]\ndef lam(n, cv):\n    s = mp.mpf(0)\n    for j in range(1, n+1):\n        s -= (-1)**(j-1) * mp.binomial(n,j) * eta[j-1] / mp.factorial(j-1)\n    s += (1 if cv=='one' else n) - (mp.log(4*mp.pi)+mp.euler)*n/2\n    for j in range(2, n+1):\n        s -= (-1)**(j-1) * mp.binomial(n,j) * (1-mp.mpf(2)**(-j)) * mp.zeta(j)\n    return s\nzero_side = {}\nwith open('research/numerics/data/E-008-li-coefficients.csv') as f:\n    for row in csv.DictReader(f):\n        zero_side[int(row['n'])] = float(row['lambda_n_trunc'])\nfor n in [1,2,3,10,50,100,116]:\n    print(n, 'one:', mp.nstr(lam(n,'one'), 12), '| n-var:', mp.nstr(lam(n,'n'), 12), '| zero-side:', zero_side[n])\nEOF",
  "description": "BL Theorem 2 prototype vs E-008 zero-side",
  "timeout": 300000
}

Bounding S(T).txt
De Bruijn–Newman — Detail.txt
Detailed_Derivations_ Riemann_Zeta_Compeddium_Step-by-Step.txt
Fractional-Part Integral.txt
Franel–Landau.txt
Hasse's Globally Convergent Series.txt
Hilbert–Pólya  Berry–Keating.txt
Keating–Snaith — the RMT Recipe.txt
Lagarias' Positivity.txt
Li's Criterion — Full Detail.txt
Lindelöf.txt
Mean Spacing — Direct Corollary.txt
Mertens Criterion.txt
Montgomery Pair Correlation — Derivation.txt
Negative Values — Step by Step.txt
Nyman–Beurling & Báez-Duarte.txt
Redheffer Determinant.txt
Riemann's π(x) Formula.txt
Riemann–Siegel Theta, Z(t), and the R–S Formula.txt
Riemann–von Mangoldt Counting Formula.txt
Riesz & Hardy–Littlewood.txt
Robin & Lagarias.txt
Salem's Criterion.txt
Second and Fourth Moments.txt
Selberg's CLT.txt
Speiser's Criterion (RH ⟺ ζ' ≠ 0 in 0  σ  ½).txt
Stieltjes Constants - Laurent Expansion at s equal 1.txt
The Dirichlet Series.txt
The Eta (Alternating) Representation.txt
The Euler Product.txt
The Functional Equation - Riemanns-Theta-Method-Full Derivation.txt
The Gamma-Integral Representation.txt
The Hadamard Product.txt
The ξ Function.txt
Trivial Zeros and the RH Statement.txt
Volchkov's Integral.txt
Von Koch  Schoenfeld.txt
Von Mangoldt's Explicit Formula — Full Derivation.txt
Weil's Explicit Formula.txt
index.md
Ξ(t) = ξ(½ + it) — Reality Proof.txt
ζ(2k) — Step-by-Step (Two Ways).txt
ζ(3) — Status.txt
−ζ'ζ = ΣΛ(n)n^{-s} — 3-Line Proof.txt