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pi].\n","packages":[]},"physics-phase":{"url":"downloads/python-physics-phase.py","sha256":"f7144ebb5993a71c83fb5a4c740feb68390a2b2e887e61e4cba7676ddebc5981","expected_output":"Coordinate probabilities: 9/25, 16/25\nHadamard probabilities with phase i: 1/2, 1/2\nHadamard probabilities with phase 1: 49/50, 1/50\nPurity after coordinate dephasing: 337/625\n","packages":[]},"physics-centered":{"url":"downloads/python-physics-centered.py","sha256":"3a99ee8340e47cf8637c8184f0aca287867a1c3135c60c5221fab67907b8be18","expected_output":"Fixed momentum: (1, 2, -1)\nSpacings: 0.5, 0.25, 0.125, 0.0625\nExported 4 modal error comparisons.\nThese floating-point samples illustrate the bound; the Lean source supplies the general theorem.\n","packages":[]},"special-functions-coupled":{"url":"downloads/python-special-functions-coupled.py","sha256":"83cb0781b75b7f5e35539f3974aac03ffa82a5f65fe2fb72c70efd04ed5ed9e9","expected_output":"Scales (q, r, a, b): 1/3, 2/3, 1/2, 3/4\nCoefficients retained per component: 12 (through degree 23)\nu_1 = 2/27; v_1 = 1/8\nUniform omitted-tail envelope on |z| <= 1: 1/2048\nExported exact rational coefficients for both components.\n","packages":[]},"sequence-growth":{"url":"downloads/python-sequence-growth.py","sha256":"a561abfc7586e4767202832abaf97f77c46199fff524c49ecb6647eb3064e217","expected_output":"Reciprocal family: N=4, r=1\nComputed n=0 through 15 with exact integers.\nA(0..4): (1, 1, 69, 33661, 60376809)\nExported exact coefficients and rational normalizations.\n","packages":["numpy"]},"sequence-landscape":{"url":"downloads/python-sequence-landscape.py","sha256":"a36a5ab4441584a65eb54bb13599e90796ff6ec9162a8dd4506c891c6752eac5","expected_output":"Reciprocal landscape: N=2..8, r=1, n=0..15\nExact coefficient samples: 112\nSecant anchor A_2(0..5): (1, 1, 5, 61, 1385, 50521)\nExported exact coefficients. Plot heights are approximate logarithms.\n","packages":["numpy"]},"factorial-weights":{"url":"downloads/python-factorial-weights.py","sha256":"a41e9d430fd8d1206bfe1d82aa17b4abcf71576e884784cec4fa245930e8881c","expected_output":"Stirling row n=5: [0, 1, 15, 25, 10, 1]\nFactorial-weighted row: [0, 1, 30, 150, 240, 120]\nBell row sum: 52\nFubini row sum: 541\nAll 19 weighted row sums match Komorebi Math.\nExported exact contributions through n=18.\n","packages":["numpy"]},"packets":{"url":"downloads/python-packets.py","sha256":"4668b1e236f24245be052059b37b7daace9b480b0d0564d526ef3d20c4ba6ab1","expected_output":"Input: (2, 3)\nPacket parts: ((2, 0), (0, 3))\nBlock contributions: ((2, 0), (6, 0), (0, 6), (0, 12))\nDirect result: (8, 18)\nReconstructed result: (8, 18)\nWithout the final block: (8, 6)\nPASS: packets\n","packages":[]},"refinement":{"url":"downloads/python-refinement.py","sha256":"e93d00530427de51d6424d243808630323f8496afeb9e55a14ec8682f5da51d5","expected_output":"Input: (1, 2, 3, 4, 5, 6, 7, 8)\nTwo packets: ((1, 3, 5, 7), (2, 4, 6, 8))\nFour packets: ((1, 5), (2, 6), (3, 7), (4, 8))\nInterleaved: (1, 2, 3, 4, 5, 6, 7, 8)\nWithout remainder 2: (1, 2, 0, 4, 5, 6, 0, 8)\nResidual: (0, 0, 3, 0, 0, 0, 7, 0)\nSquared residual norm: 58\nPASS: refinement\n","packages":[]},"recovery":{"url":"downloads/python-recovery.py","sha256":"5b101113fd47a47dcb03fd5da041690ecd026a9530cff22c053cde66508d47dd","expected_output":"Inputs: (1, 0) and (0, 1)\nSame summary: 1\nRequested first coordinates: (1, 0)\nKernel witness: (1, -1)\nR(w): 0\nF(w): 1\nCompatible observation coefficients: (2, 2)\nPASS: recovery\n","packages":[]},"library":{"url":"downloads/python-library.py","sha256":"dbf8d80d2e0c20a406c9ff15c1f3d6b2c7cec5c57d3a5bab218b3612c6cfd4dd","expected_output":"Numerical reconstruction: [2.0, 3.0]\nExact coordinate change: (7/2, 3)\nExact inverse: (2, 3)\nPASS: first examples\n","packages":["numpy"]},"plot-2d":{"url":"downloads/python-plot-2d.py","sha256":"60b9fbfcdb63589003961fe14ebc6c6365c7559696e569ec29c20cdbb9843309","expected_output":"Plotted 201 samples of two waves and their sum.\n","packages":["numpy"]},"surface-3d":{"url":"downloads/python-surface-3d.py","sha256":"a782388406151960180b10e19f40c1ac8fdf4a1890c4b01ae0b3b6f0295f70c2","expected_output":"Surface grid: 41 x 41\nCenter height: 0.0\n","packages":["numpy"]},"curve-3d":{"url":"downloads/python-curve-3d.py","sha256":"215b157a66444c8d75187568e9b5ce8a53a03f0ea2843f1e97fc3c9662040654","expected_output":"Helix samples: 201\n","packages":["numpy"]},"matplotlib":{"url":"downloads/python-matplotlib.py","sha256":"719cc33485e719d81212832a07e1f57a743e4d58b3bf7bd58e94ce3e01c1bcd8","expected_output":"Created a Matplotlib figure and parabola.csv.\n","packages":["matplotlib"]},"symbolic":{"url":"downloads/python-symbolic.py","sha256":"a897406bd2d92452bdbd7d19d2481f9ec4f9a7a173997e40842f99ccbea21d75","expected_output":"Polynomial: x**3 - 3*x + 2\nDerivative: 3*x**2 - 3\nIntegral on [0, 1]: 3/4\nFactorization: (x - 1)**2*(x + 2)\n","packages":["sympy"]},"scientific":{"url":"downloads/python-scientific.py","sha256":"2b57cac8286659eba1e0dff4c90518aea7a5a87a72b098e90651d4428560d8c7","expected_output":"Integral of x squared on [0, 1]: 0.333333\nWithin 1e-12 of one third: True\n","packages":["scipy"]},"data":{"url":"downloads/python-data.py","sha256":"07954e8bcb3af6a0913495394a2c4ef70331ab58522eb3a647068bc02bde5399","expected_output":"Using sample data.\nPlotted 4 rows.\n","packages":[]}}}