NODE 734 — TERMINAL RELAY

{
  "type": "wave-superposition",
  "difficulty": 4,
  "sample_rate": 4000,
  "duration": 0.25,
  "num_frequencies": 4,
  "waveform": [
    -0.3435,
    -0.3946,
    1.002,
    0.8113,
    0.2562,
    -1.7175,
    -0.4076,
    0.9103,
    -0.8443,
    0.2658,
    0.9981,
    0.7489,
    -0.4169,
    -1.7967,
    0.5494,
    0.311,
    -0.8093,
    0.8296,
    0.8628,
    0.5759,
    -1.2221,
    -1.2174,
    1.0524,
    -0.446,
    -0.3099,
    1.0556,
    0.7898,
    0.1502,
    -1.7596,
    -0.2282,
    0.853,
    -0.8956,
    0.3688,
    1.0202,
    0.6887,
    -0.5725,
    -1.7203,
    0.6615,
    0.206,
    -0.7698,
    0.9026,
    0.8434,
    0.4973,
    -1.3175,
    -1.0834,
    1.0681,
    -0.5445,
    -0.1916,
    1.0978,
    0.7405,
    0.0313,
    -1.7727,
    -0.0681,
    0.789,
    -0.9344,
    0.4875,
    1.0238,
    0.6563,
    -0.6711,
    -1.66,
    0.7623,
    0.0618,
    -0.7064,
    0.9818,
    0.8519,
    0.415,
    -1.3898,
    -0.938,
    1.0592,
    -0.6301,
    -0.0978,
    1.156,
    0.7223,
    -0.1082,
    -1.7722,
    0.0599,
    0.7166,
    -0.9514,
    0.5757,
    1.0232,
    0.6042,
    -0.8081,
    -1.5427,
    0.8344,
    -0.0438,
    -0.6776,
    1.062,
    0.816,
    0.3139,
    -1.4661,
    -0.7962,
    1.0426,
    -0.7236,
    -0.022,
    1.1571,
    0.659,
    -0.206,
    -1.7821,
    0.2135,
    0.6018,
    -0.9638,
    0.6884,
    1.021,
    0.5194,
    -0.9178,
    -1.4504,
    0.9153,
    -0.1598,
    -0.5936,
    1.1218,
    0.7889,
    0.2354,
    -1.5426,
    -0.6181,
    1.0382,
    -0.804,
    0.0968,
    1.173,
    0.6059,
    -0.3284,
    -1.7398,
    0.3605,
    0.5071,
    -0.9631,
    0.8116,
    0.9807,
    0.4336,
    -1.0036,
    -1.3457,
    0.9929,
    -0.278,
    -0.5017,
    1.197,
    0.728,
    0.0774,
    -1.584,
    -0.4653,
    0.983,
    -0.8595,
    0.2233,
    1.1732,
    0.5643,
    -0.4596,
    -1.7026,
    0.4692,
    0.3978,
    -0.9257,
    0.9198,
    0.9809,
    0.3581,
    -1.1131,
    -1.2257,
    1.0228,
    -0.3942,
    -0.4223,
    1.2395,
    0.6926,
    0.0021,
    -1.6297,
    -0.3281,
    0.9483,
    -0.9288,
    0.3579,
    1.2225,
    0.505,
    -0.5497,
    -1.6499,
    0.6065,
    0.299,
    -0.9036,
    0.9968,
    0.9338,
    0.2794,
    -1.1961,
    -1.0748,
    1.0539,
    -0.5058,
    -0.3012,
    1.2938,
    0.6566,
    -0.0831,
    -1.6372,
    -0.1562,
    0.8664,
    -0.9618,
    0.463,
    1.1937,
    0.4175,
    -0.6591,
    -1.5715,
    0.7003,
    0.1736,
    -0.8491,
    1.0922,
    0.8919,
    0.192,
    -1.2744,
    -0.9434,
    1.0795,
    -0.6032,
    -0.2118,
    1.3255,
    0.5843,
    -0.1876,
    -1.6252,
    -0.0179,
    0.7837,
    -1.0047,
    0.5957,
    1.1743,
    0.3325,
    -0.767,
    -1.5084,
    0.7992,
    0.056,
    -0.7967,
    1.202,
    0.8376,
    0.1261,
    -1.3503,
    -0.8241,
    1.0705,
    -0.6982,
    -0.096,
    1.3667,
    0.5297,
    -0.2762,
    -1.6234,
    0.1314,
    0.6914,
    -1.0116,
    0.7176,
    1.1453,
    0.2748,
    -0.8402,
    -1.4084,
    0.8888,
    -0.0629,
    -0.7061,
    1.288,
    0.7902,
    0.0179,
    -1.384,
    -0.6494,
    1.0712,
    -0.7819,
    0.0313,
    1.3689,
    0.4659,
    -0.3924,
    -1.6081,
    0.2657,
    0.611,
    -1.0303,
    0.841,
    1.1245,
    0.2084,
    -0.9367,
    -1.3101,
    0.9563,
    -0.1848,
    -0.6348,
    1.3417,
    0.7206,
    -0.0837,
    -1.4405,
    -0.5165,
    1.0289,
    -0.8651,
    0.1722,
    1.3803,
    0.3612,
    -0.467,
    -1.5818,
    0.3955,
    0.4968,
    -1.0061,
    0.9665,
    1.0668,
    0.1248,
    -1.0329,
    -1.1963,
    0.9946,
    -0.3175,
    -0.5407,
    1.4121,
    0.6761,
    -0.1546,
    -1.4659,
    -0.3634,
    0.9714,
    -0.9394,
    0.3028,
    1.3783,
    0.3135,
    -0.5581,
    -1.5467,
    0.5074,
    0.3903,
    -0.9791,
    1.0667,
    1.0057,
    0.0469,
    -1.1126,
    -1.0684,
    1.0133,
    -0.4328,
    -0.402,
    1.4465,
    0.5738,
    -0.2252,
    -1.476,
    -0.2523,
    0.9385,
    -0.986,
    0.447,
    1.3641,
    0.2172,
    -0.6615,
    -1.4791,
    0.6235,
    0.2564,
    -0.9489,
    1.1668,
    0.9447,
    -0.0454,
    -1.1637,
    -0.9524,
    1.0661,
    -0.5465,
    -0.2846,
    1.4904,
    0.5004,
    -0.3353,
    -1.4656,
    -0.0818,
    0.8556,
    -1.0257,
    0.5644,
    1.3198,
    0.1436,
    -0.751,
    -1.3966,
    0.7025,
    0.1621,
    -0.8914,
    1.2828,
    0.8757,
    -0.1088,
    -1.2058,
    -0.8092,
    1.0656,
    -0.6389,
    -0.1815,
    1.5289,
    0.4181,
    -0.4221,
    -1.484,
    0.0531,
    0.7849,
    -1.0401,
    0.7011,
    1.3018,
    0.0533,
    -0.8172,
    -1.3323,
    0.8006,
    0.0115,
    -0.8181,
    1.3911,
    0.7956,
    -0.2147,
    -1.2626,
    -0.701,
    1.0518,
    -0.7432,
    -0.0523,
    1.5564,
    0.3075,
    -0.4989,
    -1.4577,
    0.1808,
    0.6857,
    -1.0549,
    0.8371,
    1.2585,
    -0.0328,
    -0.89,
    -1.2243,
    0.8757,
    -0.106,
    -0.7202,
    1.4618,
    0.6968,
    -0.2645,
    -1.2842,
    -0.5489,
    1.0147,
    -0.8121,
    0.0992,
    1.545,
    0.2351,
    -0.5652,
    -1.4158,
    0.2931,
    0.5837,
    -1.0454,
    0.9816,
    1.2089,
    -0.1301,
    -0.9671,
    -1.1244,
    0.9255,
    -0.2293,
    -0.6359,
    1.5244,
    0.6226,
    -0.3612,
    -1.3018,
    -0.4307,
    0.9861,
    -0.8894,
    0.2262,
    1.5432,
    0.1455,
    -0.6468,
    -1.3868,
    0.4118,
    0.4746,
    -1.0229,
    1.1214,
    1.1194,
    -0.1992,
    -0.9908,
    -1.0262,
    0.975,
    -0.342,
    -0.5255,
    1.5932,
    0.5241,
    -0.4175,
    -1.3028,
    -0.3076,
    0.9487,
    -0.9506,
    0.3748,
    1.5307,
    0.0507,
    -0.6985,
    -1.3324,
    0.5176,
    0.3658,
    -1.0,
    1.2279,
    1.0376,
    -0.2694,
    -1.0479,
    -0.9311,
    1.0045,
    -0.4526,
    -0.4002,
    1.6338,
    0.418,
    -0.4806,
    -1.3043,
    -0.1687,
    0.8768,
    -0.9832,
    0.5284,
    1.4869,
    -0.0509,
    -0.7662,
    -1.262,
    0.6114,
    0.2474,
    -0.9588,
    1.3363,
    0.9356,
    -0.3466,
    -1.0783,
    -0.8109,
    1.0101,
    -0.5531,
    -0.2727,
    1.672,
    0.3171,
    -0.5785,
    -1.295,
    -0.0356,
    0.8048,
    -1.0354,
    0.681,
    1.4321,
    -0.165,
    -0.8186,
    -1.2065,
    0.7014,
    0.1276,
    -0.8847,
    1.4657,
    0.866,
    -0.4243,
    -1.1062,
    -0.676,
    1.0097,
    -0.6477,
    -0.1357,
    1.6864,
    0.2059,
    -0.6286,
    -1.2915,
    0.0716,
    0.717,
    -1.0398,
    0.8365,
    1.3867,
    -0.2427,
    -0.8638,
    -1.1242,
    0.7691,
    0.0015,
    -0.8119,
    1.5396,
    0.7505,
    -0.4856,
    -1.1108,
    -0.5734,
    0.9818,
    -0.7262,
    0.0043,
    1.6949,
    0.0946,
    -0.682,
    -1.2391,
    0.2016,
    0.6506,
    -1.0627,
    0.9697,
    1.3021,
    -0.317,
    -0.9003,
    -1.0272,
    0.8217,
    -0.1323,
    -0.7052,
    1.6317,
    0.6334,
    -0.5557,
    -1.133,
    -0.4626,
    0.9796,
    -0.8183,
    0.1635,
    1.684,
    -0.0148,
    -0.736,
    -1.206,
    0.2928,
    0.5343,
    -1.0353,
    1.0948,
    1.2227,
    -0.4276,
    -0.9187,
    -0.9328,
    0.8605,
    -0.2413,
    -0.5957,
    1.691,
    0.5115,
    -0.6138,
    -1.1325,
    -0.3367,
    0.9329,
    -0.8751,
    0.3406,
    1.667,
    -0.1192,
    -0.7627,
    -1.1599,
    0.4214,
    0.4262,
    -0.9972,
    1.2663,
    1.1099,
    -0.5086,
    -0.936,
    -0.8445,
    0.8996,
    -0.3616,
    -0.4855,
    1.7424,
    0.3779,
    -0.6626,
    -1.1117,
    -0.2186,
    0.8416,
    -0.9564,
    0.4702,
    1.6307,
    -0.2282,
    -0.8049,
    -1.105,
    0.4894,
    0.3043,
    -0.9702,
    1.3609,
    1.0206,
    -0.5715,
    -0.9525,
    -0.7531,
    0.8887,
    -0.4621,
    -0.3687,
    1.7995,
    0.2542,
    -0.7035,
    -1.1109,
    -0.1083,
    0.7973,
    -1.0018,
    0.6354,
    1.6015,
    -0.3385,
    -0.8214,
    -1.0478,
    0.5696,
    0.2022,
    -0.8953,
    1.4755,
    0.9059,
    -0.6801,
    -0.96,
    -0.6634,
    0.9207,
    -0.5628,
    -0.2212,
    1.8061,
    0.131,
    -0.7625,
    -1.0666,
    -0.0156,
    0.7311,
    -1.026,
    0.7892,
    1.5151,
    -0.4488,
    -0.8426,
    -0.9812,
    0.634,
    0.09,
    -0.8373,
    1.5736,
    0.7937,
    -0.7127,
    -0.9709,
    -0.5574,
    0.9167,
    -0.6437,
    -0.0555,
    1.8167,
    0.0144,
    -0.7912,
    -1.0559,
    0.1178,
    0.6481,
    -1.0141,
    0.918,
    1.4284,
    -0.5651,
    -0.8617,
    -0.9015,
    0.6886,
    -0.0228,
    -0.7535,
    1.6609,
    0.6728,
    -0.7864,
    -0.9709,
    -0.4607,
    0.9027,
    -0.7229,
    0.0912,
    1.8242,
    -0.1155,
    -0.8242,
    -1.023,
    0.1834,
    0.5645,
    -1.0161,
    1.085,
    1.3489,
    -0.6386,
    -0.8629,
    -0.8323,
    0.746,
    -0.1246,
    -0.6521,
    1.7557,
    0.534,
    -0.8214,
    -0.9724,
    -0.3506,
    0.862,
    -0.8132,
    0.2331,
    1.7861,
    -0.267,
    -0.8537,
    -0.9487,
    0.2816,
    0.469,
    -0.9878,
    1.2101,
    1.2356,
    -0.7116,
    -0.8859,
    -0.7501,
    0.7827,
    -0.239,
    -0.5398,
    1.8295,
    0.396,
    -0.8911,
    -0.9232,
    -0.2444,
    0.839,
    -0.8513,
    0.4024,
    1.7469,
    -0.372,
    -0.8642,
    -0.9063,
    0.3677,
    0.3715,
    -0.9586,
    1.346,
    1.1068,
    -0.8117,
    -0.8643,
    -0.6738,
    0.7838,
    -0.3403,
    -0.414,
    1.8741,
    0.2468,
    -0.9153,
    -0.9004,
    -0.1596,
    0.7836,
    -0.8958,
    0.5715,
    1.6935,
    -0.4938,
    -0.8655,
    -0.8589,
    0.4471,
    0.2749,
    -0.8978,
    1.4785,
    1.0023,
    -0.8825,
    -0.8677,
    -0.5787,
    0.8057,
    -0.4362,
    -0.2726,
    1.8892,
    0.0756,
    -0.9383,
    -0.8776,
    -0.0679,
    0.7138,
    -0.9601,
    0.7245,
    1.6501,
    -0.6031,
    -0.8673,
    -0.8102,
    0.4899,
    0.1666,
    -0.8342,
    1.6126,
    0.8566,
    -0.9292,
    -0.8475,
    -0.5137,
    0.8172,
    -0.5258,
    -0.1446,
    1.9079,
    -0.0418,
    -0.9411,
    -0.8369,
    0.0097,
    0.6471,
    -0.9362,
    0.8545,
    1.5696,
    -0.7169,
    -0.8729,
    -0.7354,
    0.5477,
    0.0466,
    -0.7699,
    1.6883,
    0.7036,
    -0.9985,
    -0.8249,
    -0.4183,
    0.7914,
    -0.6196,
    0.0048,
    1.9127,
    -0.2289,
    -0.966,
    -0.7823,
    0.0903,
    0.5534,
    -0.9369,
    1.0356,
    1.4483,
    -0.8351,
    -0.8597,
    -0.6774,
    0.5697,
    -0.0475,
    -0.6678,
    1.7935,
    0.5581,
    -1.0179,
    -0.7888,
    -0.3428,
    0.7662,
    -0.6603,
    0.1605,
    1.8676,
    -0.3512,
    -0.9569,
    -0.7603,
    0.1693,
    0.4864,
    -0.9349,
    1.1603,
    1.3436,
    -0.9227,
    -0.8326,
    -0.6386,
    0.6353,
    -0.1431,
    -0.5564,
    1.8247,
    0.4032,
    -1.0956,
    -0.7596,
    -0.2617,
    0.7447,
    -0.7346,
    0.3229,
    1.8725,
    -0.4747,
    -0.9414,
    -0.7204,
    0.2333,
    0.4097,
    -0.9145,
    1.3141,
    1.1886,
    -1.0175,
    -0.8201,
    -0.5497,
    0.6542,
    -0.2508,
    -0.4493,
    1.9002,
    0.2564,
    -1.1076,
    -0.7136,
    -0.1829,
    0.6965,
    -0.7912,
    0.486,
    1.8121,
    -0.624,
    -0.952,
    -0.6429,
    0.3018,
    0.3256,
    -0.8692,
    1.4582,
    1.0871,
    -1.0775,
    -0.7796,
    -0.4738,
    0.6701,
    -0.3285,
    -0.3364,
    1.941,
    0.0728,
    -1.1212,
    -0.6855,
    -0.0934,
    0.6463,
    -0.8211,
    0.6521,
    1.7361,
    -0.7547,
    -0.9272,
    -0.6174,
    0.353,
    0.2335,
    -0.816,
    1.566,
    0.9339,
    -1.1551,
    -0.7401,
    -0.4182,
    0.6705,
    -0.4104,
    -0.1834,
    1.9578,
    -0.0755,
    -1.1124,
    -0.6243,
    -0.0397,
    0.5891,
    -0.849,
    0.8043,
    1.634,
    -0.8706,
    -0.9097,
    -0.5569,
    0.3968,
    0.1431,
    -0.7261,
    1.668,
    0.7847,
    -1.1998,
    -0.7103,
    -0.3671,
    0.6572,
    -0.4892,
    -0.0406,
    1.9597,
    -0.2503,
    -1.1104,
    -0.5771,
    0.0131,
    0.526,
    -0.8426,
    0.9583,
    1.5347,
    -0.9849,
    -0.8425,
    -0.5136,
    0.4433,
    0.048,
    -0.6645,
    1.7584,
    0.6112,
    -1.2586,
    -0.6529,
    -0.289,
    0.6505,
    -0.5505,
    0.1244,
    1.9567,
    -0.4204,
    -1.1152,
    -0.5413,
    0.0632,
    0.4809,
    -0.8307,
    1.1042,
    1.4286,
    -1.1018,
    -0.8059,
    -0.4681,
    0.4724,
    -0.0422,
    -0.5535,
    1.8428,
    0.4345,
    -1.2599,
    -0.5955,
    -0.2317,
    0.608,
    -0.6055,
    0.2718,
    1.9279,
    -0.5728,
    -1.1026,
    -0.5082,
    0.1357,
    0.3999,
    -0.8141,
    1.2356,
    1.3065,
    -1.1762,
    -0.7604
  ],
  "instructions": "This is a sampled audio waveform created by summing pure sine waves. Each sine wave has a rationally-related frequency (consonant musical interval). To decode:\n1. Compute FFT of the waveform to find frequency peaks\n2. Apply a Hann window before FFT to reduce spectral leakage\n3. Sort peaks by frequency (low to high)\n4. For each adjacent pair, compute: semitones = 12 * log2(f2/f1)\n5. Round semitones to the nearest integer\n6. Map each semitone count to a letter using the table\nConcatenate letters in order.\n\nWARNING: Noise floor is present (0.01). Filter frequencies with magnitude below the noise floor estimate.",
  "semitone_to_letter": {
    "0": "A",
    "2": "B",
    "3": "C",
    "4": "D",
    "5": "E",
    "7": "F",
    "8": "G",
    "9": "H",
    "10": "I",
    "11": "J",
    "12": "K",
    "14": "L",
    "15": "M",
    "16": "N",
    "17": "O",
    "19": "P",
    "21": "Q",
    "22": "R",
    "24": "S",
    "26": "T",
    "28": "U",
    "29": "V",
    "31": "W",
    "33": "X",
    "35": "Y",
    "36": "Z"
  },
  "hann_window_formula": "w[i] = 0.5 * (1 - cos(2*pi*i/(n-1)))",
  "fft_tip": "Sample rate = 4000 Hz (Nyquist = 2000 Hz). All signal frequencies are between 80 Hz and 1900 Hz.",
  "hint": "4 frequencies \u2192 3 semitone intervals \u2192 3 letters. Apply Hann window, FFT, find peaks, compute log2 ratios.",
  "answer_format": "single lowercase letter"
}