[{"type":"thinking","thinking":"The mpmath quad over infinite interval with digamma of complex argument is slow. Restrict integration range: hhat decays like e^{−τ²/2}, integrate [−20, 20] — plenty. Also the sieve over 10^6 with inner while loop is slowish but OK (~seconds). The timeout likely from mp.quad with complex digamma over infinite range at dps 30. Reduce dps to 20 and range [−15,15].","signature":""},{"type":"text","text":"Retrying with bounded integration range and lower precision."},{"type":"tool_use","id":"Bash_44","name":"Bash","input":{"command":"cd D:/Python/Quantum && ./.venv/Scripts/python.exe -c \"\nimport numpy as np\nimport mpmath as mp\nmp.dps = 20\ngam = np.loadtxt('research/numerics/data/E-002-zeros-first-10000.csv', delimiter=',', skiprows=1, usecols=1)\nZ = float(mp.sqrt(2*mp.pi))*2*np.exp(-gam**2/2).sum()\nf1 = lambda x: mp.e**(-x**2/2)*2*mp.cosh(x/2)\nT1 = 2*mp.quad(f1, [0, 15])\nN = 200000\nlam_log = np.zeros(N+1); is_comp = np.zeros(N+1, bool)\nfor p in range(2, N+1):\n    if not is_comp[p]:\n        if p*p <= N: is_comp[p*p::p] = True\n        pk = p\n        while pk <= N:\n            lam_log[pk] = np.log(p); pk *= p\nns = np.arange(2, N+1)\nmask = lam_log[2:] > 0\nT2 = -2*float(np.sum(lam_log[2:][mask]/np.sqrt(ns[mask])*np.exp(-np.log(ns[mask])**2/2)))\nfA = lambda t: (mp.re(mp.digamma(mp.mpc(mp.mpf('0.25'), t/2))) - mp.log(mp.pi))*mp.sqrt(2*mp.pi)*mp.e**(-t**2/2)\nArch = mp.quad(fA, [-15, 0, 15])/(2*mp.pi)\nprint('zero side :', Z)\nprint('T1        :', mp.nstr(T1, 12))\nprint('prime T2  :', T2)\nprint('Arch      :', mp.nstr(Arch, 12))\nprint('RHS sum   :', mp.nstr(T1 + T2 + Arch, 12))\n\"","description":"Validate explicit formula conventions (bounded ranges)","timeout":300000},"extra_content":null}]