Certificate summary -- explicit counterexample of degree 29440 to Smale's mean value problem (K = 1) Specification: polynomial_N1840.json SHA-256 6a79964181564f7fa836117f6a46c7a2f90e97c4fa47063f47c5824df0b76d45 == Certificate 1: arb ball arithmetic, 1280 bits, Krawczyk boxes (verify_ball_N1840.py logic) == tranches 59/59, points 29439 = deg P' = 29439 echecs (Krawczyk ou |Q| <= 1 ou NaN) : 0 min |Q| certifie >= 1.00000093069254310174380708900 (point 543) rmax 7.35e-40 dmax 7.65e-12 nnmin 6.051e-05 disjonction globale : True CERTIFICAT N=1840 : PASS Per-range results. Indices refer to the order of critical_disks_N1840.csv (same order for both certificates); centres_N1840.csv lists the same points sorted by increasing |Q|: chunk 0 [0,500) min|Q|>= 1.000001277454725 echecs 0 rmax 1.8e-40 dmax 6.9e-16 nnmin 1.7e-04 chunk 1 [500,1000) min|Q|>= 1.000000930692543 echecs 0 rmax 1.8e-40 dmax 4.2e-16 nnmin 1.5e-04 chunk 2 [1000,1500) min|Q|>= 1.000001275863861 echecs 0 rmax 1.8e-40 dmax 2.2e-16 nnmin 1.2e-04 chunk 3 [1500,2000) min|Q|>= 1.000001275271761 echecs 0 rmax 1.8e-40 dmax 2.3e-16 nnmin 1.2e-04 chunk 4 [2000,2500) min|Q|>= 1.000001179218209 echecs 0 rmax 1.8e-40 dmax 2.5e-16 nnmin 2.5e-04 chunk 5 [2500,3000) min|Q|>= 1.000001271275517 echecs 0 rmax 1.8e-40 dmax 2.3e-16 nnmin 1.3e-04 chunk 6 [3000,3500) min|Q|>= 1.000001276499872 echecs 0 rmax 1.8e-40 dmax 2.3e-16 nnmin 1.3e-04 chunk 7 [3500,4000) min|Q|>= 1.000001276491866 echecs 0 rmax 1.8e-40 dmax 1.0e-15 nnmin 1.4e-04 chunk 8 [4000,4500) min|Q|>= 1.000001275992485 echecs 0 rmax 1.8e-40 dmax 1.4e-15 nnmin 2.0e-04 chunk 9 [4500,5000) min|Q|>= 1.000394869660399 echecs 0 rmax 1.8e-40 dmax 2.9e-15 nnmin 7.3e-05 chunk 10 [5000,5500) min|Q|>= 1.000078565393828 echecs 0 rmax 1.8e-40 dmax 5.6e-15 nnmin 1.2e-04 chunk 11 [5500,6000) min|Q|>= 1.000001273952591 echecs 0 rmax 1.8e-40 dmax 1.1e-14 nnmin 1.8e-04 chunk 12 [6000,6500) min|Q|>= 1.000001276313203 echecs 0 rmax 1.8e-40 dmax 3.6e-15 nnmin 1.5e-04 chunk 13 [6500,7000) min|Q|>= 1.000001277746838 echecs 0 rmax 1.8e-40 dmax 5.5e-14 nnmin 1.0e-04 chunk 14 [7000,7500) min|Q|>= 1.000001276353702 echecs 0 rmax 1.8e-40 dmax 2.2e-14 nnmin 1.3e-04 chunk 15 [7500,8000) min|Q|>= 1.000001276364981 echecs 0 rmax 1.8e-40 dmax 4.8e-14 nnmin 1.3e-04 chunk 16 [8000,8500) min|Q|>= 1.000001276417446 echecs 0 rmax 1.8e-40 dmax 2.6e-14 nnmin 1.3e-04 chunk 17 [8500,9000) min|Q|>= 1.000001276061398 echecs 0 rmax 1.8e-40 dmax 5.8e-14 nnmin 1.2e-04 chunk 18 [9000,9500) min|Q|>= 1.000001276374580 echecs 0 rmax 1.8e-40 dmax 5.6e-14 nnmin 1.5e-04 chunk 19 [9500,10000) min|Q|>= 1.000001276238840 echecs 0 rmax 1.8e-40 dmax 1.2e-13 nnmin 1.9e-04 chunk 20 [10000,10500) min|Q|>= 1.000067966476056 echecs 0 rmax 1.8e-40 dmax 5.9e-13 nnmin 7.1e-05 chunk 21 [10500,11000) min|Q|>= 1.000001275624697 echecs 0 rmax 1.8e-40 dmax 1.8e-13 nnmin 1.2e-04 chunk 22 [11000,11500) min|Q|>= 1.000001273085116 echecs 0 rmax 1.8e-40 dmax 2.3e-13 nnmin 1.8e-04 chunk 23 [11500,12000) min|Q|>= 1.000001276383777 echecs 0 rmax 1.8e-40 dmax 2.0e-13 nnmin 1.5e-04 chunk 24 [12000,12500) min|Q|>= 1.000001276279245 echecs 0 rmax 7.3e-40 dmax 1.9e-12 nnmin 8.9e-05 chunk 25 [12500,13000) min|Q|>= 1.000001239694650 echecs 0 rmax 1.8e-40 dmax 4.3e-13 nnmin 1.3e-04 chunk 26 [13000,13500) min|Q|>= 1.000001276377663 echecs 0 rmax 1.8e-40 dmax 2.6e-13 nnmin 2.7e-04 chunk 27 [13500,14000) min|Q|>= 1.000038196307385 echecs 0 rmax 1.8e-40 dmax 2.4e-12 nnmin 8.0e-05 chunk 28 [14000,14500) min|Q|>= 1.000201568117997 echecs 0 rmax 1.8e-40 dmax 3.4e-12 nnmin 9.8e-05 chunk 29 [14500,15000) min|Q|>= 1.000001278304928 echecs 0 rmax 1.8e-40 dmax 4.5e-13 nnmin 1.5e-04 chunk 30 [15000,15500) min|Q|>= 1.000001276188767 echecs 0 rmax 1.8e-40 dmax 8.1e-13 nnmin 1.9e-04 chunk 31 [15500,16000) min|Q|>= 1.000246382927753 echecs 0 rmax 1.8e-40 dmax 1.9e-12 nnmin 6.6e-05 chunk 32 [16000,16500) min|Q|>= 1.000123958261292 echecs 0 rmax 1.8e-40 dmax 4.7e-13 nnmin 1.3e-04 chunk 33 [16500,17000) min|Q|>= 1.000001276511743 echecs 0 rmax 1.8e-40 dmax 2.9e-13 nnmin 1.9e-04 chunk 34 [17000,17500) min|Q|>= 1.000001277349038 echecs 0 rmax 1.8e-40 dmax 3.7e-12 nnmin 1.1e-04 chunk 35 [17500,18000) min|Q|>= 1.001717534260888 echecs 0 rmax 1.8e-40 dmax 4.7e-12 nnmin 8.9e-05 chunk 36 [18000,18500) min|Q|>= 1.000001276875413 echecs 0 rmax 1.8e-40 dmax 1.8e-12 nnmin 1.1e-04 chunk 37 [18500,19000) min|Q|>= 1.000001276529061 echecs 0 rmax 1.8e-40 dmax 2.7e-13 nnmin 2.7e-04 chunk 38 [19000,19500) min|Q|>= 1.000001276243992 echecs 0 rmax 1.8e-40 dmax 2.7e-12 nnmin 6.1e-05 chunk 39 [19500,20000) min|Q|>= 1.000294168412315 echecs 0 rmax 1.8e-40 dmax 2.7e-12 nnmin 7.5e-05 chunk 40 [20000,20500) min|Q|>= 1.000001274199369 echecs 0 rmax 1.8e-40 dmax 4.8e-13 nnmin 1.5e-04 chunk 41 [20500,21000) min|Q|>= 1.000001276553102 echecs 0 rmax 1.8e-40 dmax 2.5e-13 nnmin 1.8e-04 chunk 42 [21000,21500) min|Q|>= 1.000001270906121 echecs 0 rmax 1.8e-40 dmax 1.1e-12 nnmin 8.0e-05 chunk 43 [21500,22000) min|Q|>= 1.000005331625337 echecs 0 rmax 1.8e-40 dmax 3.6e-13 nnmin 1.2e-04 chunk 44 [22000,22500) min|Q|>= 1.000001276566917 echecs 0 rmax 1.8e-40 dmax 8.9e-14 nnmin 2.0e-04 chunk 45 [22500,23000) min|Q|>= 1.000001280007534 echecs 0 rmax 1.8e-40 dmax 3.3e-13 nnmin 1.4e-04 chunk 46 [23000,23500) min|Q|>= 1.000933850433043 echecs 0 rmax 1.8e-40 dmax 3.2e-13 nnmin 1.2e-04 chunk 47 [23500,24000) min|Q|>= 1.000032887714127 echecs 0 rmax 1.8e-40 dmax 2.0e-13 nnmin 1.3e-04 chunk 48 [24000,24500) min|Q|>= 1.000001276591524 echecs 0 rmax 1.8e-40 dmax 2.7e-14 nnmin 2.5e-04 chunk 49 [24500,25000) min|Q|>= 1.000047189634770 echecs 0 rmax 1.8e-40 dmax 6.9e-13 nnmin 6.6e-05 chunk 50 [25000,25500) min|Q|>= 1.000671470841606 echecs 0 rmax 1.8e-40 dmax 4.5e-13 nnmin 7.8e-05 chunk 51 [25500,26000) min|Q|>= 1.000021274729362 echecs 0 rmax 1.8e-40 dmax 2.8e-14 nnmin 1.5e-04 chunk 52 [26000,26500) min|Q|>= 1.000001276709243 echecs 0 rmax 1.8e-40 dmax 1.5e-14 nnmin 1.6e-04 chunk 53 [26500,27000) min|Q|>= 1.002453713206005 echecs 0 rmax 1.8e-40 dmax 1.0e-13 nnmin 6.1e-05 chunk 54 [27000,27500) min|Q|>= 1.002726135183724 echecs 0 rmax 1.8e-40 dmax 4.6e-14 nnmin 9.6e-05 chunk 55 [27500,28000) min|Q|>= 1.005032764387429 echecs 0 rmax 1.8e-40 dmax 3.0e-16 nnmin 2.1e-04 chunk 56 [28000,28500) min|Q|>= 1.004076052808449 echecs 0 rmax 1.8e-40 dmax 6.1e-15 nnmin 1.4e-04 chunk 57 [28500,29000) min|Q|>= 1.011849814829495 echecs 0 rmax 1.8e-40 dmax 3.3e-15 nnmin 1.1e-04 chunk 58 [29000,29439) min|Q|>= 1.000002294657175 echecs 0 rmax 7.3e-40 dmax 7.6e-12 nnmin 6.1e-05 == Certificate 2: Adamczewski-Colbrook verify.cpp (Apache-2.0), N_PARAM=1840 BLOCKS_PARAM=64 TAIL_BLOCKS_PARAM=48 EXTRA_BLOCKS_PARAM=128, mode 'disk', disks of critical_disks_N1840.csv == traites 29439/29439 ; PASS avec borne > 1 : 29418 ; non concluants : 21 min borne inferieure (PASS) = 1.000000930692128537323 au disque 543 rayon max des disques acceptes = 1.455e-11 non concluants (debut) : [4295, 4296, 4297, 4298, 4299, 4300, 4301, 4848, 4849, 4850, 6126, 6127, 6128, 7960, 18937, 18938, 18939, 18940, 29298, 29307, 29323] full list of inconclusive disks: 4295 4296 4297 4298 4299 4300 4301 4848 4849 4850 6126 6127 6128 7960 18937 18938 18939 18940 29298 29307 29323 (inconclusive = 'Finite-centre Rouche failed' at the program's fixed working precision; all 21 are certified by Certificate 1)