From 76682349d09a1ed3cd10c8e38655d9dda8d1040f Mon Sep 17 00:00:00 2001 From: igneum-labs <337424239+igneum-labs@users.noreply.github.com> Date: Wed, 7 Oct 2026 18:56:05 +0000 Subject: [PATCH] adv-mixer: integral 32-day row, sibling 07 claim note, box-hours update Internal adversarial pass, not an independent review. Co-Authored-By: Claude Fable 5.1 --- .../logs/adv-mixer/integral-a1-32d.log | 609 ++++++++++++++++++ .../logs/adv-mixer/integral-a2-32d.log | 609 ++++++++++++++++++ .../queue-12-adv-mixer-integral-days.sh.log | 6 + docs/analysis/cryptanalysis/report-mixer.md | 31 +- 4 files changed, 1253 insertions(+), 2 deletions(-) create mode 100644 docs/analysis/cryptanalysis/logs/adv-mixer/integral-a1-32d.log create mode 100644 docs/analysis/cryptanalysis/logs/adv-mixer/integral-a2-32d.log create mode 100644 docs/analysis/cryptanalysis/logs/adv-mixer/queue-12-adv-mixer-integral-days.sh.log diff --git a/docs/analysis/cryptanalysis/logs/adv-mixer/integral-a1-32d.log b/docs/analysis/cryptanalysis/logs/adv-mixer/integral-a1-32d.log new file mode 100644 index 000000000..22c02df89 --- /dev/null +++ b/docs/analysis/cryptanalysis/logs/adv-mixer/integral-a1-32d.log @@ -0,0 +1,609 @@ +self-check: spec 1.8.1 and 1.8.4 genesis vectors OK; 72 application keys are 1..72 times 0x9E3779B9 +integral day=20729 apps=1 placements_per_d=2000 threads=44 + d = cube dimension; 'nonzero' = placements whose cube-sum is nonzero on >=1 output bit (degree >= d reached) + d= 1 nonzero 2000/2000 = 1.0000 mean out-bits set 236.0/512 [degree >= d reached] + d= 2 nonzero 2000/2000 = 1.0000 mean out-bits set 184.8/512 [degree >= d reached] + d= 3 nonzero 2000/2000 = 1.0000 mean out-bits set 175.0/512 [degree >= d reached] + d= 4 nonzero 2000/2000 = 1.0000 mean out-bits set 172.9/512 [degree >= d reached] + d= 5 nonzero 2000/2000 = 1.0000 mean out-bits set 172.0/512 [degree >= d reached] + d= 6 nonzero 2000/2000 = 1.0000 mean out-bits set 173.3/512 [degree >= d reached] + d= 7 nonzero 2000/2000 = 1.0000 mean out-bits set 175.1/512 [degree >= d reached] + d= 8 nonzero 2000/2000 = 1.0000 mean out-bits set 174.6/512 [degree >= d reached] + d= 9 nonzero 2000/2000 = 1.0000 mean out-bits set 175.7/512 [degree >= d reached] + d=10 nonzero 2000/2000 = 1.0000 mean out-bits set 177.6/512 [degree >= d reached] + d=11 nonzero 2000/2000 = 1.0000 mean out-bits set 182.1/512 [degree >= d reached] + d=12 nonzero 2000/2000 = 1.0000 mean out-bits set 184.2/512 [degree >= d reached] + d=13 nonzero 2000/2000 = 1.0000 mean out-bits set 187.2/512 [degree >= d reached] + d=14 nonzero 2000/2000 = 1.0000 mean out-bits set 191.5/512 [degree >= d reached] + d=15 nonzero 2000/2000 = 1.0000 mean out-bits set 196.1/512 [degree >= d reached] + d=16 nonzero 2000/2000 = 1.0000 mean out-bits set 203.3/512 [degree >= d reached] + READING: the smallest d at which nonzero is ~1.0 is the degree floor; high degree at small d means no low-degree algebraic shortcut across the applications +integral day=20730 apps=1 placements_per_d=2000 threads=44 + d = cube dimension; 'nonzero' = placements whose cube-sum is nonzero on >=1 output bit (degree >= d reached) + d= 1 nonzero 2000/2000 = 1.0000 mean out-bits set 229.8/512 [degree >= d reached] + d= 2 nonzero 2000/2000 = 1.0000 mean out-bits set 177.0/512 [degree >= d reached] + d= 3 nonzero 2000/2000 = 1.0000 mean out-bits set 165.9/512 [degree >= d reached] + d= 4 nonzero 1999/2000 = 0.9995 mean out-bits set 158.8/512 [degree >= d reached] + d= 5 nonzero 2000/2000 = 1.0000 mean out-bits set 157.5/512 [degree >= d reached] + d= 6 nonzero 2000/2000 = 1.0000 mean out-bits set 161.0/512 [degree >= d reached] + d= 7 nonzero 2000/2000 = 1.0000 mean out-bits set 162.2/512 [degree >= d reached] + d= 8 nonzero 2000/2000 = 1.0000 mean out-bits set 164.2/512 [degree >= d reached] + d= 9 nonzero 2000/2000 = 1.0000 mean out-bits set 169.2/512 [degree >= d reached] + d=10 nonzero 2000/2000 = 1.0000 mean out-bits set 174.1/512 [degree >= d reached] + d=11 nonzero 2000/2000 = 1.0000 mean out-bits set 183.0/512 [degree >= d reached] + d=12 nonzero 2000/2000 = 1.0000 mean out-bits set 188.1/512 [degree >= d reached] + d=13 nonzero 2000/2000 = 1.0000 mean out-bits set 192.3/512 [degree >= d reached] + d=14 nonzero 2000/2000 = 1.0000 mean out-bits set 198.6/512 [degree >= d reached] + d=15 nonzero 2000/2000 = 1.0000 mean out-bits set 205.7/512 [degree >= d reached] + d=16 nonzero 2000/2000 = 1.0000 mean out-bits set 213.0/512 [degree >= d reached] + READING: the smallest d at which nonzero is ~1.0 is the degree floor; high degree at small d means no low-degree algebraic shortcut across the applications +integral day=20731 apps=1 placements_per_d=2000 threads=44 + d = cube dimension; 'nonzero' = placements whose cube-sum is nonzero on >=1 output bit (degree >= d reached) + d= 1 nonzero 2000/2000 = 1.0000 mean out-bits set 242.2/512 [degree >= d reached] + d= 2 nonzero 2000/2000 = 1.0000 mean out-bits set 194.0/512 [degree >= d reached] + d= 3 nonzero 2000/2000 = 1.0000 mean out-bits set 184.9/512 [degree >= d reached] + d= 4 nonzero 2000/2000 = 1.0000 mean out-bits set 185.0/512 [degree >= d reached] + d= 5 nonzero 2000/2000 = 1.0000 mean out-bits set 186.4/512 [degree >= d reached] + d= 6 nonzero 2000/2000 = 1.0000 mean out-bits set 188.1/512 [degree >= d reached] + d= 7 nonzero 2000/2000 = 1.0000 mean out-bits set 190.1/512 [degree >= d reached] + d= 8 nonzero 2000/2000 = 1.0000 mean out-bits set 191.4/512 [degree >= d reached] + d= 9 nonzero 2000/2000 = 1.0000 mean out-bits set 195.0/512 [degree >= d reached] + d=10 nonzero 2000/2000 = 1.0000 mean out-bits set 199.2/512 [degree >= d reached] + d=11 nonzero 2000/2000 = 1.0000 mean out-bits set 202.4/512 [degree >= d reached] + d=12 nonzero 2000/2000 = 1.0000 mean out-bits set 206.7/512 [degree >= d reached] + d=13 nonzero 2000/2000 = 1.0000 mean out-bits set 210.7/512 [degree >= d reached] + d=14 nonzero 2000/2000 = 1.0000 mean out-bits set 216.2/512 [degree >= d reached] + d=15 nonzero 2000/2000 = 1.0000 mean out-bits set 219.5/512 [degree >= d reached] + d=16 nonzero 2000/2000 = 1.0000 mean out-bits set 223.8/512 [degree >= d reached] + READING: the smallest d at which nonzero is ~1.0 is the degree floor; high degree at small d means no low-degree algebraic shortcut across the applications +integral day=20732 apps=1 placements_per_d=2000 threads=44 + d = cube dimension; 'nonzero' = placements whose cube-sum is nonzero on >=1 output bit (degree >= d reached) + d= 1 nonzero 2000/2000 = 1.0000 mean out-bits set 233.5/512 [degree >= d reached] + d= 2 nonzero 2000/2000 = 1.0000 mean out-bits set 182.8/512 [degree >= d reached] + d= 3 nonzero 2000/2000 = 1.0000 mean out-bits set 170.5/512 [degree >= d reached] + d= 4 nonzero 2000/2000 = 1.0000 mean out-bits set 164.6/512 [degree >= d reached] + d= 5 nonzero 2000/2000 = 1.0000 mean out-bits set 160.9/512 [degree >= d reached] + d= 6 nonzero 2000/2000 = 1.0000 mean out-bits set 159.5/512 [degree >= d reached] + d= 7 nonzero 2000/2000 = 1.0000 mean out-bits set 159.3/512 [degree >= d reached] + d= 8 nonzero 2000/2000 = 1.0000 mean out-bits set 161.5/512 [degree >= d reached] + d= 9 nonzero 2000/2000 = 1.0000 mean out-bits set 165.1/512 [degree >= d reached] + d=10 nonzero 2000/2000 = 1.0000 mean out-bits set 168.1/512 [degree >= d reached] + d=11 nonzero 2000/2000 = 1.0000 mean out-bits set 173.1/512 [degree >= d reached] + d=12 nonzero 2000/2000 = 1.0000 mean out-bits set 176.8/512 [degree >= d reached] + d=13 nonzero 2000/2000 = 1.0000 mean out-bits set 181.2/512 [degree >= d reached] + d=14 nonzero 2000/2000 = 1.0000 mean out-bits set 185.1/512 [degree >= d reached] + d=15 nonzero 2000/2000 = 1.0000 mean out-bits set 187.1/512 [degree >= d reached] + d=16 nonzero 2000/2000 = 1.0000 mean out-bits set 190.2/512 [degree >= d reached] + READING: the smallest d at which nonzero is ~1.0 is the degree floor; high degree at small d means no low-degree algebraic shortcut across the applications +integral day=20733 apps=1 placements_per_d=2000 threads=44 + d = cube dimension; 'nonzero' = placements whose cube-sum is nonzero on >=1 output bit (degree >= d reached) + d= 1 nonzero 2000/2000 = 1.0000 mean out-bits set 234.2/512 [degree >= d reached] + d= 2 nonzero 2000/2000 = 1.0000 mean out-bits set 188.8/512 [degree >= d reached] + d= 3 nonzero 2000/2000 = 1.0000 mean out-bits set 175.5/512 [degree >= d reached] + d= 4 nonzero 2000/2000 = 1.0000 mean out-bits set 173.1/512 [degree >= d reached] + d= 5 nonzero 2000/2000 = 1.0000 mean out-bits set 171.5/512 [degree >= d reached] + d= 6 nonzero 2000/2000 = 1.0000 mean out-bits set 171.5/512 [degree >= d reached] + d= 7 nonzero 2000/2000 = 1.0000 mean out-bits set 175.0/512 [degree >= d reached] + d= 8 nonzero 2000/2000 = 1.0000 mean out-bits set 173.4/512 [degree >= d reached] + d= 9 nonzero 2000/2000 = 1.0000 mean out-bits set 176.7/512 [degree >= d reached] + d=10 nonzero 2000/2000 = 1.0000 mean out-bits set 178.9/512 [degree >= d reached] + d=11 nonzero 2000/2000 = 1.0000 mean out-bits set 181.2/512 [degree >= d reached] + d=12 nonzero 2000/2000 = 1.0000 mean out-bits set 185.7/512 [degree >= d reached] + d=13 nonzero 2000/2000 = 1.0000 mean out-bits set 187.8/512 [degree >= d reached] + d=14 nonzero 2000/2000 = 1.0000 mean out-bits set 190.6/512 [degree >= d reached] + d=15 nonzero 2000/2000 = 1.0000 mean out-bits set 192.4/512 [degree >= d reached] + d=16 nonzero 2000/2000 = 1.0000 mean out-bits set 194.9/512 [degree >= d reached] + READING: the smallest d at which nonzero is ~1.0 is the degree floor; high degree at small d means no low-degree algebraic shortcut across the applications +integral day=20734 apps=1 placements_per_d=2000 threads=44 + d = cube dimension; 'nonzero' = placements whose cube-sum is nonzero on >=1 output bit (degree >= d reached) + d= 1 nonzero 2000/2000 = 1.0000 mean out-bits set 232.8/512 [degree >= d reached] + d= 2 nonzero 2000/2000 = 1.0000 mean out-bits set 186.6/512 [degree >= d reached] + d= 3 nonzero 2000/2000 = 1.0000 mean out-bits set 177.3/512 [degree >= d reached] + d= 4 nonzero 2000/2000 = 1.0000 mean out-bits set 173.0/512 [degree >= d reached] + d= 5 nonzero 2000/2000 = 1.0000 mean out-bits set 170.4/512 [degree >= d reached] + d= 6 nonzero 2000/2000 = 1.0000 mean out-bits set 171.0/512 [degree >= d reached] + d= 7 nonzero 2000/2000 = 1.0000 mean out-bits set 174.0/512 [degree >= d reached] + d= 8 nonzero 2000/2000 = 1.0000 mean out-bits set 177.0/512 [degree >= d reached] + d= 9 nonzero 2000/2000 = 1.0000 mean out-bits set 178.8/512 [degree >= d reached] + d=10 nonzero 2000/2000 = 1.0000 mean out-bits set 181.6/512 [degree >= d reached] + d=11 nonzero 2000/2000 = 1.0000 mean out-bits set 188.1/512 [degree >= d reached] + d=12 nonzero 2000/2000 = 1.0000 mean out-bits set 193.1/512 [degree >= d reached] + d=13 nonzero 2000/2000 = 1.0000 mean out-bits set 200.6/512 [degree >= d reached] + d=14 nonzero 2000/2000 = 1.0000 mean out-bits set 208.8/512 [degree >= d reached] + d=15 nonzero 2000/2000 = 1.0000 mean out-bits set 213.6/512 [degree >= d reached] + d=16 nonzero 2000/2000 = 1.0000 mean out-bits set 220.9/512 [degree >= d reached] + READING: the smallest d at which nonzero is ~1.0 is the degree floor; high degree at small d means no low-degree algebraic shortcut across the applications +integral day=20735 apps=1 placements_per_d=2000 threads=44 + d = cube dimension; 'nonzero' = placements whose cube-sum is nonzero on >=1 output bit (degree >= d reached) + d= 1 nonzero 2000/2000 = 1.0000 mean out-bits set 230.6/512 [degree >= d reached] + d= 2 nonzero 2000/2000 = 1.0000 mean out-bits set 182.1/512 [degree >= d reached] + d= 3 nonzero 2000/2000 = 1.0000 mean out-bits set 168.7/512 [degree >= d reached] + d= 4 nonzero 2000/2000 = 1.0000 mean out-bits set 163.5/512 [degree >= d reached] + d= 5 nonzero 2000/2000 = 1.0000 mean out-bits set 161.0/512 [degree >= d reached] + d= 6 nonzero 2000/2000 = 1.0000 mean out-bits set 161.6/512 [degree >= d reached] + d= 7 nonzero 2000/2000 = 1.0000 mean out-bits set 164.2/512 [degree >= d reached] + d= 8 nonzero 2000/2000 = 1.0000 mean out-bits set 163.1/512 [degree >= d reached] + d= 9 nonzero 2000/2000 = 1.0000 mean out-bits set 167.6/512 [degree >= d reached] + d=10 nonzero 2000/2000 = 1.0000 mean out-bits set 168.8/512 [degree >= d reached] + d=11 nonzero 2000/2000 = 1.0000 mean out-bits set 176.4/512 [degree >= d reached] + d=12 nonzero 2000/2000 = 1.0000 mean out-bits set 182.4/512 [degree >= d reached] + d=13 nonzero 2000/2000 = 1.0000 mean out-bits set 188.2/512 [degree >= d reached] + d=14 nonzero 2000/2000 = 1.0000 mean out-bits set 191.6/512 [degree >= d reached] + d=15 nonzero 2000/2000 = 1.0000 mean out-bits set 199.1/512 [degree >= d reached] + d=16 nonzero 2000/2000 = 1.0000 mean out-bits set 205.2/512 [degree >= d reached] + READING: the smallest d at which nonzero is ~1.0 is the degree floor; high degree at small d means no low-degree algebraic shortcut across the applications +integral day=20736 apps=1 placements_per_d=2000 threads=44 + d = cube dimension; 'nonzero' = placements whose cube-sum is nonzero on >=1 output bit (degree >= d reached) + d= 1 nonzero 2000/2000 = 1.0000 mean out-bits set 238.6/512 [degree >= d reached] + d= 2 nonzero 2000/2000 = 1.0000 mean out-bits set 190.3/512 [degree >= d reached] + d= 3 nonzero 2000/2000 = 1.0000 mean out-bits set 178.8/512 [degree >= d reached] + d= 4 nonzero 2000/2000 = 1.0000 mean out-bits set 178.7/512 [degree >= d reached] + d= 5 nonzero 2000/2000 = 1.0000 mean out-bits set 178.3/512 [degree >= d reached] + d= 6 nonzero 2000/2000 = 1.0000 mean out-bits set 181.2/512 [degree >= d reached] + d= 7 nonzero 2000/2000 = 1.0000 mean out-bits set 181.2/512 [degree >= d reached] + d= 8 nonzero 2000/2000 = 1.0000 mean out-bits set 185.1/512 [degree >= d reached] + d= 9 nonzero 2000/2000 = 1.0000 mean out-bits set 190.6/512 [degree >= d reached] + d=10 nonzero 2000/2000 = 1.0000 mean out-bits set 194.8/512 [degree >= d reached] + d=11 nonzero 2000/2000 = 1.0000 mean out-bits set 198.4/512 [degree >= d reached] + d=12 nonzero 2000/2000 = 1.0000 mean out-bits set 204.0/512 [degree >= d reached] + d=13 nonzero 2000/2000 = 1.0000 mean out-bits set 209.6/512 [degree >= d reached] + d=14 nonzero 2000/2000 = 1.0000 mean out-bits set 214.7/512 [degree >= d reached] + d=15 nonzero 2000/2000 = 1.0000 mean out-bits set 220.5/512 [degree >= d reached] + d=16 nonzero 2000/2000 = 1.0000 mean out-bits set 225.9/512 [degree >= d reached] + READING: the smallest d at which nonzero is ~1.0 is the degree floor; high degree at small d means no low-degree algebraic shortcut across the applications +integral day=20737 apps=1 placements_per_d=2000 threads=44 + d = cube dimension; 'nonzero' = placements whose cube-sum is nonzero on >=1 output bit (degree >= d reached) + d= 1 nonzero 2000/2000 = 1.0000 mean out-bits set 237.4/512 [degree >= d reached] + d= 2 nonzero 2000/2000 = 1.0000 mean out-bits set 190.9/512 [degree >= d reached] + d= 3 nonzero 2000/2000 = 1.0000 mean out-bits set 180.5/512 [degree >= d reached] + d= 4 nonzero 2000/2000 = 1.0000 mean out-bits set 178.2/512 [degree >= d reached] + d= 5 nonzero 2000/2000 = 1.0000 mean out-bits set 177.1/512 [degree >= d reached] + d= 6 nonzero 2000/2000 = 1.0000 mean out-bits set 177.5/512 [degree >= d reached] + d= 7 nonzero 2000/2000 = 1.0000 mean out-bits set 180.7/512 [degree >= d reached] + d= 8 nonzero 2000/2000 = 1.0000 mean out-bits set 183.1/512 [degree >= d reached] + d= 9 nonzero 2000/2000 = 1.0000 mean out-bits set 186.9/512 [degree >= d reached] + d=10 nonzero 2000/2000 = 1.0000 mean out-bits set 190.6/512 [degree >= d reached] + d=11 nonzero 2000/2000 = 1.0000 mean out-bits set 193.0/512 [degree >= d reached] + d=12 nonzero 2000/2000 = 1.0000 mean out-bits set 195.9/512 [degree >= d reached] + d=13 nonzero 2000/2000 = 1.0000 mean out-bits set 199.4/512 [degree >= d reached] + d=14 nonzero 2000/2000 = 1.0000 mean out-bits set 202.7/512 [degree >= d reached] + d=15 nonzero 2000/2000 = 1.0000 mean out-bits set 204.6/512 [degree >= d reached] + d=16 nonzero 2000/2000 = 1.0000 mean out-bits set 206.1/512 [degree >= d reached] + READING: the smallest d at which nonzero is ~1.0 is the degree floor; high degree at small d means no low-degree algebraic shortcut across the applications +integral day=20738 apps=1 placements_per_d=2000 threads=44 + d = cube dimension; 'nonzero' = placements whose cube-sum is nonzero on >=1 output bit (degree >= d reached) + d= 1 nonzero 2000/2000 = 1.0000 mean out-bits set 240.9/512 [degree >= d reached] + d= 2 nonzero 2000/2000 = 1.0000 mean out-bits set 198.5/512 [degree >= d reached] + d= 3 nonzero 2000/2000 = 1.0000 mean out-bits set 189.9/512 [degree >= d reached] + d= 4 nonzero 2000/2000 = 1.0000 mean out-bits set 191.0/512 [degree >= d reached] + d= 5 nonzero 2000/2000 = 1.0000 mean out-bits set 194.3/512 [degree >= d reached] + d= 6 nonzero 2000/2000 = 1.0000 mean out-bits set 195.5/512 [degree >= d reached] + d= 7 nonzero 2000/2000 = 1.0000 mean out-bits set 199.4/512 [degree >= d reached] + d= 8 nonzero 2000/2000 = 1.0000 mean out-bits set 202.7/512 [degree >= d reached] + d= 9 nonzero 2000/2000 = 1.0000 mean out-bits set 204.9/512 [degree >= d reached] + d=10 nonzero 2000/2000 = 1.0000 mean out-bits set 208.8/512 [degree >= d reached] + d=11 nonzero 2000/2000 = 1.0000 mean out-bits set 210.7/512 [degree >= d reached] + d=12 nonzero 2000/2000 = 1.0000 mean out-bits set 216.6/512 [degree >= d reached] + d=13 nonzero 2000/2000 = 1.0000 mean out-bits set 219.9/512 [degree >= d reached] + d=14 nonzero 2000/2000 = 1.0000 mean out-bits set 223.9/512 [degree >= d reached] + d=15 nonzero 2000/2000 = 1.0000 mean out-bits set 228.7/512 [degree >= d reached] + d=16 nonzero 2000/2000 = 1.0000 mean out-bits set 232.4/512 [degree >= d reached] + READING: the smallest d at which nonzero is ~1.0 is the degree floor; high degree at small d means no low-degree algebraic shortcut across the applications +integral day=20739 apps=1 placements_per_d=2000 threads=44 + d = cube dimension; 'nonzero' = placements whose cube-sum is nonzero on >=1 output bit (degree >= d reached) + d= 1 nonzero 2000/2000 = 1.0000 mean out-bits set 240.0/512 [degree >= d reached] + d= 2 nonzero 2000/2000 = 1.0000 mean out-bits set 194.6/512 [degree >= d reached] + d= 3 nonzero 2000/2000 = 1.0000 mean out-bits set 189.0/512 [degree >= d reached] + d= 4 nonzero 2000/2000 = 1.0000 mean out-bits set 189.4/512 [degree >= d reached] + d= 5 nonzero 2000/2000 = 1.0000 mean out-bits set 191.3/512 [degree >= d reached] + d= 6 nonzero 2000/2000 = 1.0000 mean out-bits set 193.9/512 [degree >= d reached] + d= 7 nonzero 2000/2000 = 1.0000 mean out-bits set 196.4/512 [degree >= d reached] + d= 8 nonzero 2000/2000 = 1.0000 mean out-bits set 202.1/512 [degree >= d reached] + d= 9 nonzero 2000/2000 = 1.0000 mean out-bits set 204.1/512 [degree >= d reached] + d=10 nonzero 2000/2000 = 1.0000 mean out-bits set 206.4/512 [degree >= d reached] + d=11 nonzero 2000/2000 = 1.0000 mean out-bits set 209.8/512 [degree >= d reached] + d=12 nonzero 2000/2000 = 1.0000 mean out-bits set 212.6/512 [degree >= d reached] + d=13 nonzero 2000/2000 = 1.0000 mean out-bits set 216.0/512 [degree >= d reached] + d=14 nonzero 2000/2000 = 1.0000 mean out-bits set 218.9/512 [degree >= d reached] + d=15 nonzero 2000/2000 = 1.0000 mean out-bits set 218.8/512 [degree >= d reached] + d=16 nonzero 2000/2000 = 1.0000 mean out-bits set 221.1/512 [degree >= d reached] + READING: the smallest d at which nonzero is ~1.0 is the degree floor; high degree at small d means no low-degree algebraic shortcut across the applications +integral day=20740 apps=1 placements_per_d=2000 threads=44 + d = cube dimension; 'nonzero' = placements whose cube-sum is nonzero on >=1 output bit (degree >= d reached) + d= 1 nonzero 2000/2000 = 1.0000 mean out-bits set 241.9/512 [degree >= d reached] + d= 2 nonzero 2000/2000 = 1.0000 mean out-bits set 196.6/512 [degree >= d reached] + d= 3 nonzero 2000/2000 = 1.0000 mean out-bits set 186.9/512 [degree >= d reached] + d= 4 nonzero 2000/2000 = 1.0000 mean out-bits set 186.9/512 [degree >= d reached] + d= 5 nonzero 2000/2000 = 1.0000 mean out-bits set 189.6/512 [degree >= d reached] + d= 6 nonzero 2000/2000 = 1.0000 mean out-bits set 192.9/512 [degree >= d reached] + d= 7 nonzero 2000/2000 = 1.0000 mean out-bits set 196.5/512 [degree >= d reached] + d= 8 nonzero 2000/2000 = 1.0000 mean out-bits set 199.1/512 [degree >= d reached] + d= 9 nonzero 2000/2000 = 1.0000 mean out-bits set 202.4/512 [degree >= d reached] + d=10 nonzero 2000/2000 = 1.0000 mean out-bits set 208.1/512 [degree >= d reached] + d=11 nonzero 2000/2000 = 1.0000 mean out-bits set 210.7/512 [degree >= d reached] + d=12 nonzero 2000/2000 = 1.0000 mean out-bits set 214.9/512 [degree >= d reached] + d=13 nonzero 2000/2000 = 1.0000 mean out-bits set 218.8/512 [degree >= d reached] + d=14 nonzero 2000/2000 = 1.0000 mean out-bits set 223.5/512 [degree >= d reached] + d=15 nonzero 2000/2000 = 1.0000 mean out-bits set 227.4/512 [degree >= d reached] + d=16 nonzero 2000/2000 = 1.0000 mean out-bits set 231.6/512 [degree >= d reached] + READING: the smallest d at which nonzero is ~1.0 is the degree floor; high degree at small d means no low-degree algebraic shortcut across the applications +integral day=20741 apps=1 placements_per_d=2000 threads=44 + d = cube dimension; 'nonzero' = placements whose cube-sum is nonzero on >=1 output bit (degree >= d reached) + d= 1 nonzero 2000/2000 = 1.0000 mean out-bits set 231.6/512 [degree >= d reached] + d= 2 nonzero 2000/2000 = 1.0000 mean out-bits set 177.5/512 [degree >= d reached] + d= 3 nonzero 2000/2000 = 1.0000 mean out-bits set 163.4/512 [degree >= d reached] + d= 4 nonzero 2000/2000 = 1.0000 mean out-bits set 157.2/512 [degree >= d reached] + d= 5 nonzero 2000/2000 = 1.0000 mean out-bits set 153.5/512 [degree >= d reached] + d= 6 nonzero 2000/2000 = 1.0000 mean out-bits set 152.6/512 [degree >= d reached] + d= 7 nonzero 2000/2000 = 1.0000 mean out-bits set 152.0/512 [degree >= d reached] + d= 8 nonzero 2000/2000 = 1.0000 mean out-bits set 155.9/512 [degree >= d reached] + d= 9 nonzero 2000/2000 = 1.0000 mean out-bits set 159.1/512 [degree >= d reached] + d=10 nonzero 2000/2000 = 1.0000 mean out-bits set 164.0/512 [degree >= d reached] + d=11 nonzero 2000/2000 = 1.0000 mean out-bits set 169.0/512 [degree >= d reached] + d=12 nonzero 2000/2000 = 1.0000 mean out-bits set 173.6/512 [degree >= d reached] + d=13 nonzero 2000/2000 = 1.0000 mean out-bits set 178.8/512 [degree >= d reached] + d=14 nonzero 2000/2000 = 1.0000 mean out-bits set 183.2/512 [degree >= d reached] + d=15 nonzero 2000/2000 = 1.0000 mean out-bits set 187.3/512 [degree >= d reached] + d=16 nonzero 2000/2000 = 1.0000 mean out-bits set 191.8/512 [degree >= d reached] + READING: the smallest d at which nonzero is ~1.0 is the degree floor; high degree at small d means no low-degree algebraic shortcut across the applications +integral day=20742 apps=1 placements_per_d=2000 threads=44 + d = cube dimension; 'nonzero' = placements whose cube-sum is nonzero on >=1 output bit (degree >= d reached) + d= 1 nonzero 2000/2000 = 1.0000 mean out-bits set 244.5/512 [degree >= d reached] + d= 2 nonzero 2000/2000 = 1.0000 mean out-bits set 204.5/512 [degree >= d reached] + d= 3 nonzero 2000/2000 = 1.0000 mean out-bits set 197.1/512 [degree >= d reached] + d= 4 nonzero 2000/2000 = 1.0000 mean out-bits set 201.4/512 [degree >= d reached] + d= 5 nonzero 2000/2000 = 1.0000 mean out-bits set 204.6/512 [degree >= d reached] + d= 6 nonzero 2000/2000 = 1.0000 mean out-bits set 206.6/512 [degree >= d reached] + d= 7 nonzero 2000/2000 = 1.0000 mean out-bits set 211.5/512 [degree >= d reached] + d= 8 nonzero 2000/2000 = 1.0000 mean out-bits set 214.7/512 [degree >= d reached] + d= 9 nonzero 2000/2000 = 1.0000 mean out-bits set 216.8/512 [degree >= d reached] + d=10 nonzero 2000/2000 = 1.0000 mean out-bits set 219.7/512 [degree >= d reached] + d=11 nonzero 2000/2000 = 1.0000 mean out-bits set 222.1/512 [degree >= d reached] + d=12 nonzero 2000/2000 = 1.0000 mean out-bits set 224.0/512 [degree >= d reached] + d=13 nonzero 2000/2000 = 1.0000 mean out-bits set 225.1/512 [degree >= d reached] + d=14 nonzero 2000/2000 = 1.0000 mean out-bits set 226.0/512 [degree >= d reached] + d=15 nonzero 2000/2000 = 1.0000 mean out-bits set 226.7/512 [degree >= d reached] + d=16 nonzero 2000/2000 = 1.0000 mean out-bits set 228.1/512 [degree >= d reached] + READING: the smallest d at which nonzero is ~1.0 is the degree floor; high degree at small d means no low-degree algebraic shortcut across the applications +integral day=20743 apps=1 placements_per_d=2000 threads=44 + d = cube dimension; 'nonzero' = placements whose cube-sum is nonzero on >=1 output bit (degree >= d reached) + d= 1 nonzero 2000/2000 = 1.0000 mean out-bits set 238.8/512 [degree >= d reached] + d= 2 nonzero 2000/2000 = 1.0000 mean out-bits set 191.6/512 [degree >= d reached] + d= 3 nonzero 2000/2000 = 1.0000 mean out-bits set 183.7/512 [degree >= d reached] + d= 4 nonzero 2000/2000 = 1.0000 mean out-bits set 183.3/512 [degree >= d reached] + d= 5 nonzero 2000/2000 = 1.0000 mean out-bits set 184.0/512 [degree >= d reached] + d= 6 nonzero 2000/2000 = 1.0000 mean out-bits set 183.9/512 [degree >= d reached] + d= 7 nonzero 2000/2000 = 1.0000 mean out-bits set 186.7/512 [degree >= d reached] + d= 8 nonzero 2000/2000 = 1.0000 mean out-bits set 188.7/512 [degree >= d reached] + d= 9 nonzero 2000/2000 = 1.0000 mean out-bits set 190.7/512 [degree >= d reached] + d=10 nonzero 2000/2000 = 1.0000 mean out-bits set 193.2/512 [degree >= d reached] + d=11 nonzero 2000/2000 = 1.0000 mean out-bits set 196.6/512 [degree >= d reached] + d=12 nonzero 2000/2000 = 1.0000 mean out-bits set 201.4/512 [degree >= d reached] + d=13 nonzero 2000/2000 = 1.0000 mean out-bits set 206.7/512 [degree >= d reached] + d=14 nonzero 2000/2000 = 1.0000 mean out-bits set 211.4/512 [degree >= d reached] + d=15 nonzero 2000/2000 = 1.0000 mean out-bits set 214.6/512 [degree >= d reached] + d=16 nonzero 2000/2000 = 1.0000 mean out-bits set 219.4/512 [degree >= d reached] + READING: the smallest d at which nonzero is ~1.0 is the degree floor; high degree at small d means no low-degree algebraic shortcut across the applications +integral day=20744 apps=1 placements_per_d=2000 threads=44 + d = cube dimension; 'nonzero' = placements whose cube-sum is nonzero on >=1 output bit (degree >= d reached) + d= 1 nonzero 2000/2000 = 1.0000 mean out-bits set 233.3/512 [degree >= d reached] + d= 2 nonzero 2000/2000 = 1.0000 mean out-bits set 188.4/512 [degree >= d reached] + d= 3 nonzero 2000/2000 = 1.0000 mean out-bits set 175.6/512 [degree >= d reached] + d= 4 nonzero 2000/2000 = 1.0000 mean out-bits set 172.8/512 [degree >= d reached] + d= 5 nonzero 2000/2000 = 1.0000 mean out-bits set 173.7/512 [degree >= d reached] + d= 6 nonzero 2000/2000 = 1.0000 mean out-bits set 173.7/512 [degree >= d reached] + d= 7 nonzero 2000/2000 = 1.0000 mean out-bits set 177.9/512 [degree >= d reached] + d= 8 nonzero 2000/2000 = 1.0000 mean out-bits set 180.8/512 [degree >= d reached] + d= 9 nonzero 2000/2000 = 1.0000 mean out-bits set 184.2/512 [degree >= d reached] + d=10 nonzero 2000/2000 = 1.0000 mean out-bits set 189.6/512 [degree >= d reached] + d=11 nonzero 2000/2000 = 1.0000 mean out-bits set 191.8/512 [degree >= d reached] + d=12 nonzero 2000/2000 = 1.0000 mean out-bits set 196.3/512 [degree >= d reached] + d=13 nonzero 2000/2000 = 1.0000 mean out-bits set 200.2/512 [degree >= d reached] + d=14 nonzero 2000/2000 = 1.0000 mean out-bits set 203.7/512 [degree >= d reached] + d=15 nonzero 2000/2000 = 1.0000 mean out-bits set 206.2/512 [degree >= d reached] + d=16 nonzero 2000/2000 = 1.0000 mean out-bits set 207.4/512 [degree >= d reached] + READING: the smallest d at which nonzero is ~1.0 is the degree floor; high degree at small d means no low-degree algebraic shortcut across the applications +integral day=20745 apps=1 placements_per_d=2000 threads=44 + d = cube dimension; 'nonzero' = placements whose cube-sum is nonzero on >=1 output bit (degree >= d reached) + d= 1 nonzero 2000/2000 = 1.0000 mean out-bits set 240.6/512 [degree >= d reached] + d= 2 nonzero 2000/2000 = 1.0000 mean out-bits set 197.1/512 [degree >= d reached] + d= 3 nonzero 2000/2000 = 1.0000 mean out-bits set 189.3/512 [degree >= d reached] + d= 4 nonzero 2000/2000 = 1.0000 mean out-bits set 188.5/512 [degree >= d reached] + d= 5 nonzero 2000/2000 = 1.0000 mean out-bits set 188.9/512 [degree >= d reached] + d= 6 nonzero 2000/2000 = 1.0000 mean out-bits set 193.8/512 [degree >= d reached] + d= 7 nonzero 2000/2000 = 1.0000 mean out-bits set 194.7/512 [degree >= d reached] + d= 8 nonzero 2000/2000 = 1.0000 mean out-bits set 199.3/512 [degree >= d reached] + d= 9 nonzero 2000/2000 = 1.0000 mean out-bits set 201.8/512 [degree >= d reached] + d=10 nonzero 2000/2000 = 1.0000 mean out-bits set 206.0/512 [degree >= d reached] + d=11 nonzero 2000/2000 = 1.0000 mean out-bits set 209.8/512 [degree >= d reached] + d=12 nonzero 2000/2000 = 1.0000 mean out-bits set 213.5/512 [degree >= d reached] + d=13 nonzero 2000/2000 = 1.0000 mean out-bits set 218.6/512 [degree >= d reached] + d=14 nonzero 2000/2000 = 1.0000 mean out-bits set 221.3/512 [degree >= d reached] + d=15 nonzero 2000/2000 = 1.0000 mean out-bits set 224.3/512 [degree >= d reached] + d=16 nonzero 2000/2000 = 1.0000 mean out-bits set 228.3/512 [degree >= d reached] + READING: the smallest d at which nonzero is ~1.0 is the degree floor; high degree at small d means no low-degree algebraic shortcut across the applications +integral day=20746 apps=1 placements_per_d=2000 threads=44 + d = cube dimension; 'nonzero' = placements whose cube-sum is nonzero on >=1 output bit (degree >= d reached) + d= 1 nonzero 2000/2000 = 1.0000 mean out-bits set 236.4/512 [degree >= d reached] + d= 2 nonzero 2000/2000 = 1.0000 mean out-bits set 190.1/512 [degree >= d reached] + d= 3 nonzero 2000/2000 = 1.0000 mean out-bits set 180.2/512 [degree >= d reached] + d= 4 nonzero 2000/2000 = 1.0000 mean out-bits set 177.2/512 [degree >= d reached] + d= 5 nonzero 2000/2000 = 1.0000 mean out-bits set 179.0/512 [degree >= d reached] + d= 6 nonzero 2000/2000 = 1.0000 mean out-bits set 174.9/512 [degree >= d reached] + d= 7 nonzero 2000/2000 = 1.0000 mean out-bits set 178.1/512 [degree >= d reached] + d= 8 nonzero 2000/2000 = 1.0000 mean out-bits set 182.5/512 [degree >= d reached] + d= 9 nonzero 2000/2000 = 1.0000 mean out-bits set 183.4/512 [degree >= d reached] + d=10 nonzero 2000/2000 = 1.0000 mean out-bits set 185.7/512 [degree >= d reached] + d=11 nonzero 2000/2000 = 1.0000 mean out-bits set 189.9/512 [degree >= d reached] + d=12 nonzero 2000/2000 = 1.0000 mean out-bits set 194.4/512 [degree >= d reached] + d=13 nonzero 2000/2000 = 1.0000 mean out-bits set 196.9/512 [degree >= d reached] + d=14 nonzero 2000/2000 = 1.0000 mean out-bits set 199.9/512 [degree >= d reached] + d=15 nonzero 2000/2000 = 1.0000 mean out-bits set 201.8/512 [degree >= d reached] + d=16 nonzero 2000/2000 = 1.0000 mean out-bits set 204.4/512 [degree >= d reached] + READING: the smallest d at which nonzero is ~1.0 is the degree floor; high degree at small d means no low-degree algebraic shortcut across the applications +integral day=20747 apps=1 placements_per_d=2000 threads=44 + d = cube dimension; 'nonzero' = placements whose cube-sum is nonzero on >=1 output bit (degree >= d reached) + d= 1 nonzero 2000/2000 = 1.0000 mean out-bits set 234.9/512 [degree >= d reached] + d= 2 nonzero 2000/2000 = 1.0000 mean out-bits set 190.8/512 [degree >= d reached] + d= 3 nonzero 2000/2000 = 1.0000 mean out-bits set 181.3/512 [degree >= d reached] + d= 4 nonzero 2000/2000 = 1.0000 mean out-bits set 177.9/512 [degree >= d reached] + d= 5 nonzero 2000/2000 = 1.0000 mean out-bits set 178.9/512 [degree >= d reached] + d= 6 nonzero 2000/2000 = 1.0000 mean out-bits set 180.3/512 [degree >= d reached] + d= 7 nonzero 2000/2000 = 1.0000 mean out-bits set 177.7/512 [degree >= d reached] + d= 8 nonzero 2000/2000 = 1.0000 mean out-bits set 180.0/512 [degree >= d reached] + d= 9 nonzero 2000/2000 = 1.0000 mean out-bits set 183.7/512 [degree >= d reached] + d=10 nonzero 2000/2000 = 1.0000 mean out-bits set 186.3/512 [degree >= d reached] + d=11 nonzero 2000/2000 = 1.0000 mean out-bits set 189.3/512 [degree >= d reached] + d=12 nonzero 2000/2000 = 1.0000 mean out-bits set 190.5/512 [degree >= d reached] + d=13 nonzero 2000/2000 = 1.0000 mean out-bits set 195.0/512 [degree >= d reached] + d=14 nonzero 2000/2000 = 1.0000 mean out-bits set 198.4/512 [degree >= d reached] + d=15 nonzero 2000/2000 = 1.0000 mean out-bits set 203.1/512 [degree >= d reached] + d=16 nonzero 2000/2000 = 1.0000 mean out-bits set 206.1/512 [degree >= d reached] + READING: the smallest d at which nonzero is ~1.0 is the degree floor; high degree at small d means no low-degree algebraic shortcut across the applications +integral day=20748 apps=1 placements_per_d=2000 threads=44 + d = cube dimension; 'nonzero' = placements whose cube-sum is nonzero on >=1 output bit (degree >= d reached) + d= 1 nonzero 2000/2000 = 1.0000 mean out-bits set 242.2/512 [degree >= d reached] + d= 2 nonzero 2000/2000 = 1.0000 mean out-bits set 199.0/512 [degree >= d reached] + d= 3 nonzero 2000/2000 = 1.0000 mean out-bits set 190.9/512 [degree >= d reached] + d= 4 nonzero 2000/2000 = 1.0000 mean out-bits set 188.0/512 [degree >= d reached] + d= 5 nonzero 2000/2000 = 1.0000 mean out-bits set 189.2/512 [degree >= d reached] + d= 6 nonzero 2000/2000 = 1.0000 mean out-bits set 189.6/512 [degree >= d reached] + d= 7 nonzero 2000/2000 = 1.0000 mean out-bits set 190.4/512 [degree >= d reached] + d= 8 nonzero 2000/2000 = 1.0000 mean out-bits set 192.9/512 [degree >= d reached] + d= 9 nonzero 2000/2000 = 1.0000 mean out-bits set 193.7/512 [degree >= d reached] + d=10 nonzero 2000/2000 = 1.0000 mean out-bits set 196.7/512 [degree >= d reached] + d=11 nonzero 2000/2000 = 1.0000 mean out-bits set 198.6/512 [degree >= d reached] + d=12 nonzero 2000/2000 = 1.0000 mean out-bits set 202.2/512 [degree >= d reached] + d=13 nonzero 2000/2000 = 1.0000 mean out-bits set 205.4/512 [degree >= d reached] + d=14 nonzero 2000/2000 = 1.0000 mean out-bits set 210.5/512 [degree >= d reached] + d=15 nonzero 2000/2000 = 1.0000 mean out-bits set 215.2/512 [degree >= d reached] + d=16 nonzero 2000/2000 = 1.0000 mean out-bits set 218.9/512 [degree >= d reached] + READING: the smallest d at which nonzero is ~1.0 is the degree floor; high degree at small d means no low-degree algebraic shortcut across the applications +integral day=20749 apps=1 placements_per_d=2000 threads=44 + d = cube dimension; 'nonzero' = placements whose cube-sum is nonzero on >=1 output bit (degree >= d reached) + d= 1 nonzero 2000/2000 = 1.0000 mean out-bits set 240.5/512 [degree >= d reached] + d= 2 nonzero 2000/2000 = 1.0000 mean out-bits set 196.6/512 [degree >= d reached] + d= 3 nonzero 2000/2000 = 1.0000 mean out-bits set 187.3/512 [degree >= d reached] + d= 4 nonzero 2000/2000 = 1.0000 mean out-bits set 187.1/512 [degree >= d reached] + d= 5 nonzero 2000/2000 = 1.0000 mean out-bits set 188.7/512 [degree >= d reached] + d= 6 nonzero 2000/2000 = 1.0000 mean out-bits set 188.3/512 [degree >= d reached] + d= 7 nonzero 2000/2000 = 1.0000 mean out-bits set 191.5/512 [degree >= d reached] + d= 8 nonzero 2000/2000 = 1.0000 mean out-bits set 193.3/512 [degree >= d reached] + d= 9 nonzero 2000/2000 = 1.0000 mean out-bits set 197.8/512 [degree >= d reached] + d=10 nonzero 2000/2000 = 1.0000 mean out-bits set 200.1/512 [degree >= d reached] + d=11 nonzero 2000/2000 = 1.0000 mean out-bits set 204.8/512 [degree >= d reached] + d=12 nonzero 2000/2000 = 1.0000 mean out-bits set 207.3/512 [degree >= d reached] + d=13 nonzero 2000/2000 = 1.0000 mean out-bits set 212.4/512 [degree >= d reached] + d=14 nonzero 2000/2000 = 1.0000 mean out-bits set 215.8/512 [degree >= d reached] + d=15 nonzero 2000/2000 = 1.0000 mean out-bits set 219.6/512 [degree >= d reached] + d=16 nonzero 2000/2000 = 1.0000 mean out-bits set 223.5/512 [degree >= d reached] + READING: the smallest d at which nonzero is ~1.0 is the degree floor; high degree at small d means no low-degree algebraic shortcut across the applications +integral day=20750 apps=1 placements_per_d=2000 threads=44 + d = cube dimension; 'nonzero' = placements whose cube-sum is nonzero on >=1 output bit (degree >= d reached) + d= 1 nonzero 2000/2000 = 1.0000 mean out-bits set 236.7/512 [degree >= d reached] + d= 2 nonzero 2000/2000 = 1.0000 mean out-bits set 186.8/512 [degree >= d reached] + d= 3 nonzero 2000/2000 = 1.0000 mean out-bits set 179.7/512 [degree >= d reached] + d= 4 nonzero 2000/2000 = 1.0000 mean out-bits set 177.9/512 [degree >= d reached] + d= 5 nonzero 2000/2000 = 1.0000 mean out-bits set 178.7/512 [degree >= d reached] + d= 6 nonzero 2000/2000 = 1.0000 mean out-bits set 182.6/512 [degree >= d reached] + d= 7 nonzero 2000/2000 = 1.0000 mean out-bits set 185.7/512 [degree >= d reached] + d= 8 nonzero 2000/2000 = 1.0000 mean out-bits set 191.8/512 [degree >= d reached] + d= 9 nonzero 2000/2000 = 1.0000 mean out-bits set 194.9/512 [degree >= d reached] + d=10 nonzero 2000/2000 = 1.0000 mean out-bits set 198.7/512 [degree >= d reached] + d=11 nonzero 2000/2000 = 1.0000 mean out-bits set 202.1/512 [degree >= d reached] + d=12 nonzero 2000/2000 = 1.0000 mean out-bits set 208.2/512 [degree >= d reached] + d=13 nonzero 2000/2000 = 1.0000 mean out-bits set 212.6/512 [degree >= d reached] + d=14 nonzero 2000/2000 = 1.0000 mean out-bits set 216.9/512 [degree >= d reached] + d=15 nonzero 2000/2000 = 1.0000 mean out-bits set 221.8/512 [degree >= d reached] + d=16 nonzero 2000/2000 = 1.0000 mean out-bits set 225.3/512 [degree >= d reached] + READING: the smallest d at which nonzero is ~1.0 is the degree floor; high degree at small d means no low-degree algebraic shortcut across the applications +integral day=20751 apps=1 placements_per_d=2000 threads=44 + d = cube dimension; 'nonzero' = placements whose cube-sum is nonzero on >=1 output bit (degree >= d reached) + d= 1 nonzero 2000/2000 = 1.0000 mean out-bits set 242.5/512 [degree >= d reached] + d= 2 nonzero 2000/2000 = 1.0000 mean out-bits set 196.4/512 [degree >= d reached] + d= 3 nonzero 2000/2000 = 1.0000 mean out-bits set 187.0/512 [degree >= d reached] + d= 4 nonzero 2000/2000 = 1.0000 mean out-bits set 186.5/512 [degree >= d reached] + d= 5 nonzero 2000/2000 = 1.0000 mean out-bits set 187.6/512 [degree >= d reached] + d= 6 nonzero 2000/2000 = 1.0000 mean out-bits set 189.0/512 [degree >= d reached] + d= 7 nonzero 2000/2000 = 1.0000 mean out-bits set 190.6/512 [degree >= d reached] + d= 8 nonzero 2000/2000 = 1.0000 mean out-bits set 194.0/512 [degree >= d reached] + d= 9 nonzero 2000/2000 = 1.0000 mean out-bits set 196.8/512 [degree >= d reached] + d=10 nonzero 2000/2000 = 1.0000 mean out-bits set 200.0/512 [degree >= d reached] + d=11 nonzero 2000/2000 = 1.0000 mean out-bits set 203.9/512 [degree >= d reached] + d=12 nonzero 2000/2000 = 1.0000 mean out-bits set 207.5/512 [degree >= d reached] + d=13 nonzero 2000/2000 = 1.0000 mean out-bits set 210.7/512 [degree >= d reached] + d=14 nonzero 2000/2000 = 1.0000 mean out-bits set 215.6/512 [degree >= d reached] + d=15 nonzero 2000/2000 = 1.0000 mean out-bits set 219.1/512 [degree >= d reached] + d=16 nonzero 2000/2000 = 1.0000 mean out-bits set 223.0/512 [degree >= d reached] + READING: the smallest d at which nonzero is ~1.0 is the degree floor; high degree at small d means no low-degree algebraic shortcut across the applications +integral day=20752 apps=1 placements_per_d=2000 threads=44 + d = cube dimension; 'nonzero' = placements whose cube-sum is nonzero on >=1 output bit (degree >= d reached) + d= 1 nonzero 2000/2000 = 1.0000 mean out-bits set 234.1/512 [degree >= d reached] + d= 2 nonzero 2000/2000 = 1.0000 mean out-bits set 182.8/512 [degree >= d reached] + d= 3 nonzero 2000/2000 = 1.0000 mean out-bits set 172.2/512 [degree >= d reached] + d= 4 nonzero 2000/2000 = 1.0000 mean out-bits set 168.5/512 [degree >= d reached] + d= 5 nonzero 2000/2000 = 1.0000 mean out-bits set 166.3/512 [degree >= d reached] + d= 6 nonzero 2000/2000 = 1.0000 mean out-bits set 166.7/512 [degree >= d reached] + d= 7 nonzero 2000/2000 = 1.0000 mean out-bits set 167.7/512 [degree >= d reached] + d= 8 nonzero 2000/2000 = 1.0000 mean out-bits set 167.8/512 [degree >= d reached] + d= 9 nonzero 2000/2000 = 1.0000 mean out-bits set 169.3/512 [degree >= d reached] + d=10 nonzero 2000/2000 = 1.0000 mean out-bits set 170.7/512 [degree >= d reached] + d=11 nonzero 2000/2000 = 1.0000 mean out-bits set 172.9/512 [degree >= d reached] + d=12 nonzero 2000/2000 = 1.0000 mean out-bits set 175.0/512 [degree >= d reached] + d=13 nonzero 2000/2000 = 1.0000 mean out-bits set 177.4/512 [degree >= d reached] + d=14 nonzero 2000/2000 = 1.0000 mean out-bits set 179.3/512 [degree >= d reached] + d=15 nonzero 2000/2000 = 1.0000 mean out-bits set 183.7/512 [degree >= d reached] + d=16 nonzero 2000/2000 = 1.0000 mean out-bits set 188.9/512 [degree >= d reached] + READING: the smallest d at which nonzero is ~1.0 is the degree floor; high degree at small d means no low-degree algebraic shortcut across the applications +integral day=20753 apps=1 placements_per_d=2000 threads=44 + d = cube dimension; 'nonzero' = placements whose cube-sum is nonzero on >=1 output bit (degree >= d reached) + d= 1 nonzero 2000/2000 = 1.0000 mean out-bits set 240.7/512 [degree >= d reached] + d= 2 nonzero 2000/2000 = 1.0000 mean out-bits set 198.2/512 [degree >= d reached] + d= 3 nonzero 2000/2000 = 1.0000 mean out-bits set 190.9/512 [degree >= d reached] + d= 4 nonzero 2000/2000 = 1.0000 mean out-bits set 190.0/512 [degree >= d reached] + d= 5 nonzero 2000/2000 = 1.0000 mean out-bits set 190.4/512 [degree >= d reached] + d= 6 nonzero 2000/2000 = 1.0000 mean out-bits set 192.4/512 [degree >= d reached] + d= 7 nonzero 2000/2000 = 1.0000 mean out-bits set 193.5/512 [degree >= d reached] + d= 8 nonzero 2000/2000 = 1.0000 mean out-bits set 195.7/512 [degree >= d reached] + d= 9 nonzero 2000/2000 = 1.0000 mean out-bits set 196.2/512 [degree >= d reached] + d=10 nonzero 2000/2000 = 1.0000 mean out-bits set 198.5/512 [degree >= d reached] + d=11 nonzero 2000/2000 = 1.0000 mean out-bits set 199.1/512 [degree >= d reached] + d=12 nonzero 2000/2000 = 1.0000 mean out-bits set 201.3/512 [degree >= d reached] + d=13 nonzero 2000/2000 = 1.0000 mean out-bits set 200.4/512 [degree >= d reached] + d=14 nonzero 2000/2000 = 1.0000 mean out-bits set 204.1/512 [degree >= d reached] + d=15 nonzero 2000/2000 = 1.0000 mean out-bits set 203.8/512 [degree >= d reached] + d=16 nonzero 2000/2000 = 1.0000 mean out-bits set 205.9/512 [degree >= d reached] + READING: the smallest d at which nonzero is ~1.0 is the degree floor; high degree at small d means no low-degree algebraic shortcut across the applications +integral day=20754 apps=1 placements_per_d=2000 threads=44 + d = cube dimension; 'nonzero' = placements whose cube-sum is nonzero on >=1 output bit (degree >= d reached) + d= 1 nonzero 2000/2000 = 1.0000 mean out-bits set 238.7/512 [degree >= d reached] + d= 2 nonzero 2000/2000 = 1.0000 mean out-bits set 190.9/512 [degree >= d reached] + d= 3 nonzero 2000/2000 = 1.0000 mean out-bits set 181.6/512 [degree >= d reached] + d= 4 nonzero 2000/2000 = 1.0000 mean out-bits set 178.5/512 [degree >= d reached] + d= 5 nonzero 2000/2000 = 1.0000 mean out-bits set 180.2/512 [degree >= d reached] + d= 6 nonzero 2000/2000 = 1.0000 mean out-bits set 177.9/512 [degree >= d reached] + d= 7 nonzero 2000/2000 = 1.0000 mean out-bits set 178.5/512 [degree >= d reached] + d= 8 nonzero 2000/2000 = 1.0000 mean out-bits set 179.4/512 [degree >= d reached] + d= 9 nonzero 2000/2000 = 1.0000 mean out-bits set 183.4/512 [degree >= d reached] + d=10 nonzero 2000/2000 = 1.0000 mean out-bits set 186.4/512 [degree >= d reached] + d=11 nonzero 2000/2000 = 1.0000 mean out-bits set 192.0/512 [degree >= d reached] + d=12 nonzero 2000/2000 = 1.0000 mean out-bits set 196.3/512 [degree >= d reached] + d=13 nonzero 2000/2000 = 1.0000 mean out-bits set 202.2/512 [degree >= d reached] + d=14 nonzero 2000/2000 = 1.0000 mean out-bits set 208.0/512 [degree >= d reached] + d=15 nonzero 2000/2000 = 1.0000 mean out-bits set 211.0/512 [degree >= d reached] + d=16 nonzero 2000/2000 = 1.0000 mean out-bits set 217.1/512 [degree >= d reached] + READING: the smallest d at which nonzero is ~1.0 is the degree floor; high degree at small d means no low-degree algebraic shortcut across the applications +integral day=20755 apps=1 placements_per_d=2000 threads=44 + d = cube dimension; 'nonzero' = placements whose cube-sum is nonzero on >=1 output bit (degree >= d reached) + d= 1 nonzero 2000/2000 = 1.0000 mean out-bits set 239.9/512 [degree >= d reached] + d= 2 nonzero 2000/2000 = 1.0000 mean out-bits set 196.0/512 [degree >= d reached] + d= 3 nonzero 2000/2000 = 1.0000 mean out-bits set 187.4/512 [degree >= d reached] + d= 4 nonzero 2000/2000 = 1.0000 mean out-bits set 185.7/512 [degree >= d reached] + d= 5 nonzero 2000/2000 = 1.0000 mean out-bits set 186.5/512 [degree >= d reached] + d= 6 nonzero 2000/2000 = 1.0000 mean out-bits set 184.7/512 [degree >= d reached] + d= 7 nonzero 2000/2000 = 1.0000 mean out-bits set 185.6/512 [degree >= d reached] + d= 8 nonzero 2000/2000 = 1.0000 mean out-bits set 186.3/512 [degree >= d reached] + d= 9 nonzero 2000/2000 = 1.0000 mean out-bits set 189.4/512 [degree >= d reached] + d=10 nonzero 2000/2000 = 1.0000 mean out-bits set 190.4/512 [degree >= d reached] + d=11 nonzero 2000/2000 = 1.0000 mean out-bits set 191.9/512 [degree >= d reached] + d=12 nonzero 2000/2000 = 1.0000 mean out-bits set 195.9/512 [degree >= d reached] + d=13 nonzero 2000/2000 = 1.0000 mean out-bits set 198.3/512 [degree >= d reached] + d=14 nonzero 2000/2000 = 1.0000 mean out-bits set 202.0/512 [degree >= d reached] + d=15 nonzero 2000/2000 = 1.0000 mean out-bits set 205.2/512 [degree >= d reached] + d=16 nonzero 2000/2000 = 1.0000 mean out-bits set 208.4/512 [degree >= d reached] + READING: the smallest d at which nonzero is ~1.0 is the degree floor; high degree at small d means no low-degree algebraic shortcut across the applications +integral day=20756 apps=1 placements_per_d=2000 threads=44 + d = cube dimension; 'nonzero' = placements whose cube-sum is nonzero on >=1 output bit (degree >= d reached) + d= 1 nonzero 2000/2000 = 1.0000 mean out-bits set 230.8/512 [degree >= d reached] + d= 2 nonzero 2000/2000 = 1.0000 mean out-bits set 181.2/512 [degree >= d reached] + d= 3 nonzero 2000/2000 = 1.0000 mean out-bits set 166.6/512 [degree >= d reached] + d= 4 nonzero 2000/2000 = 1.0000 mean out-bits set 163.0/512 [degree >= d reached] + d= 5 nonzero 2000/2000 = 1.0000 mean out-bits set 162.1/512 [degree >= d reached] + d= 6 nonzero 2000/2000 = 1.0000 mean out-bits set 164.6/512 [degree >= d reached] + d= 7 nonzero 2000/2000 = 1.0000 mean out-bits set 169.2/512 [degree >= d reached] + d= 8 nonzero 2000/2000 = 1.0000 mean out-bits set 172.5/512 [degree >= d reached] + d= 9 nonzero 2000/2000 = 1.0000 mean out-bits set 177.4/512 [degree >= d reached] + d=10 nonzero 2000/2000 = 1.0000 mean out-bits set 182.2/512 [degree >= d reached] + d=11 nonzero 2000/2000 = 1.0000 mean out-bits set 187.7/512 [degree >= d reached] + d=12 nonzero 2000/2000 = 1.0000 mean out-bits set 193.8/512 [degree >= d reached] + d=13 nonzero 2000/2000 = 1.0000 mean out-bits set 200.8/512 [degree >= d reached] + d=14 nonzero 2000/2000 = 1.0000 mean out-bits set 205.7/512 [degree >= d reached] + d=15 nonzero 2000/2000 = 1.0000 mean out-bits set 210.6/512 [degree >= d reached] + d=16 nonzero 2000/2000 = 1.0000 mean out-bits set 215.4/512 [degree >= d reached] + READING: the smallest d at which nonzero is ~1.0 is the degree floor; high degree at small d means no low-degree algebraic shortcut across the applications +integral day=20757 apps=1 placements_per_d=2000 threads=44 + d = cube dimension; 'nonzero' = placements whose cube-sum is nonzero on >=1 output bit (degree >= d reached) + d= 1 nonzero 2000/2000 = 1.0000 mean out-bits set 241.2/512 [degree >= d reached] + d= 2 nonzero 2000/2000 = 1.0000 mean out-bits set 197.6/512 [degree >= d reached] + d= 3 nonzero 2000/2000 = 1.0000 mean out-bits set 192.8/512 [degree >= d reached] + d= 4 nonzero 2000/2000 = 1.0000 mean out-bits set 193.5/512 [degree >= d reached] + d= 5 nonzero 2000/2000 = 1.0000 mean out-bits set 193.0/512 [degree >= d reached] + d= 6 nonzero 2000/2000 = 1.0000 mean out-bits set 199.4/512 [degree >= d reached] + d= 7 nonzero 2000/2000 = 1.0000 mean out-bits set 203.0/512 [degree >= d reached] + d= 8 nonzero 2000/2000 = 1.0000 mean out-bits set 207.5/512 [degree >= d reached] + d= 9 nonzero 2000/2000 = 1.0000 mean out-bits set 210.9/512 [degree >= d reached] + d=10 nonzero 2000/2000 = 1.0000 mean out-bits set 215.2/512 [degree >= d reached] + d=11 nonzero 2000/2000 = 1.0000 mean out-bits set 219.8/512 [degree >= d reached] + d=12 nonzero 2000/2000 = 1.0000 mean out-bits set 223.2/512 [degree >= d reached] + d=13 nonzero 2000/2000 = 1.0000 mean out-bits set 226.3/512 [degree >= d reached] + d=14 nonzero 2000/2000 = 1.0000 mean out-bits set 229.0/512 [degree >= d reached] + d=15 nonzero 2000/2000 = 1.0000 mean out-bits set 231.9/512 [degree >= d reached] + d=16 nonzero 2000/2000 = 1.0000 mean out-bits set 232.5/512 [degree >= d reached] + READING: the smallest d at which nonzero is ~1.0 is the degree floor; high degree at small d means no low-degree algebraic shortcut across the applications +integral day=20758 apps=1 placements_per_d=2000 threads=44 + d = cube dimension; 'nonzero' = placements whose cube-sum is nonzero on >=1 output bit (degree >= d reached) + d= 1 nonzero 2000/2000 = 1.0000 mean out-bits set 235.0/512 [degree >= d reached] + d= 2 nonzero 2000/2000 = 1.0000 mean out-bits set 189.4/512 [degree >= d reached] + d= 3 nonzero 2000/2000 = 1.0000 mean out-bits set 174.4/512 [degree >= d reached] + d= 4 nonzero 2000/2000 = 1.0000 mean out-bits set 172.2/512 [degree >= d reached] + d= 5 nonzero 2000/2000 = 1.0000 mean out-bits set 169.6/512 [degree >= d reached] + d= 6 nonzero 2000/2000 = 1.0000 mean out-bits set 170.8/512 [degree >= d reached] + d= 7 nonzero 2000/2000 = 1.0000 mean out-bits set 169.6/512 [degree >= d reached] + d= 8 nonzero 2000/2000 = 1.0000 mean out-bits set 174.8/512 [degree >= d reached] + d= 9 nonzero 2000/2000 = 1.0000 mean out-bits set 177.7/512 [degree >= d reached] + d=10 nonzero 2000/2000 = 1.0000 mean out-bits set 181.6/512 [degree >= d reached] + d=11 nonzero 2000/2000 = 1.0000 mean out-bits set 184.5/512 [degree >= d reached] + d=12 nonzero 2000/2000 = 1.0000 mean out-bits set 188.2/512 [degree >= d reached] + d=13 nonzero 2000/2000 = 1.0000 mean out-bits set 193.9/512 [degree >= d reached] + d=14 nonzero 2000/2000 = 1.0000 mean out-bits set 197.2/512 [degree >= d reached] + d=15 nonzero 2000/2000 = 1.0000 mean out-bits set 204.0/512 [degree >= d reached] + d=16 nonzero 2000/2000 = 1.0000 mean out-bits set 208.4/512 [degree >= d reached] + READING: the smallest d at which nonzero is ~1.0 is the degree floor; high degree at small d means no low-degree algebraic shortcut across the applications +integral day=20759 apps=1 placements_per_d=2000 threads=44 + d = cube dimension; 'nonzero' = placements whose cube-sum is nonzero on >=1 output bit (degree >= d reached) + d= 1 nonzero 2000/2000 = 1.0000 mean out-bits set 240.8/512 [degree >= d reached] + d= 2 nonzero 2000/2000 = 1.0000 mean out-bits set 200.3/512 [degree >= d reached] + d= 3 nonzero 2000/2000 = 1.0000 mean out-bits set 190.6/512 [degree >= d reached] + d= 4 nonzero 2000/2000 = 1.0000 mean out-bits set 189.9/512 [degree >= d reached] + d= 5 nonzero 2000/2000 = 1.0000 mean out-bits set 192.9/512 [degree >= d reached] + d= 6 nonzero 2000/2000 = 1.0000 mean out-bits set 193.2/512 [degree >= d reached] + d= 7 nonzero 2000/2000 = 1.0000 mean out-bits set 197.9/512 [degree >= d reached] + d= 8 nonzero 2000/2000 = 1.0000 mean out-bits set 197.8/512 [degree >= d reached] + d= 9 nonzero 2000/2000 = 1.0000 mean out-bits set 200.8/512 [degree >= d reached] + d=10 nonzero 2000/2000 = 1.0000 mean out-bits set 202.6/512 [degree >= d reached] + d=11 nonzero 2000/2000 = 1.0000 mean out-bits set 207.1/512 [degree >= d reached] + d=12 nonzero 2000/2000 = 1.0000 mean out-bits set 208.8/512 [degree >= d reached] + d=13 nonzero 2000/2000 = 1.0000 mean out-bits set 215.1/512 [degree >= d reached] + d=14 nonzero 2000/2000 = 1.0000 mean out-bits set 219.3/512 [degree >= d reached] + d=15 nonzero 2000/2000 = 1.0000 mean out-bits set 223.1/512 [degree >= d reached] + d=16 nonzero 2000/2000 = 1.0000 mean out-bits set 227.9/512 [degree >= d reached] + READING: the smallest d at which nonzero is ~1.0 is the degree floor; high degree at small d means no low-degree algebraic shortcut across the applications +integral day=20760 apps=1 placements_per_d=2000 threads=44 + d = cube dimension; 'nonzero' = placements whose cube-sum is nonzero on >=1 output bit (degree >= d reached) + d= 1 nonzero 2000/2000 = 1.0000 mean out-bits set 234.7/512 [degree >= d reached] + d= 2 nonzero 2000/2000 = 1.0000 mean out-bits set 184.1/512 [degree >= d reached] + d= 3 nonzero 2000/2000 = 1.0000 mean out-bits set 176.2/512 [degree >= d reached] + d= 4 nonzero 2000/2000 = 1.0000 mean out-bits set 177.9/512 [degree >= d reached] + d= 5 nonzero 2000/2000 = 1.0000 mean out-bits set 177.8/512 [degree >= d reached] + d= 6 nonzero 2000/2000 = 1.0000 mean out-bits set 178.8/512 [degree >= d reached] + d= 7 nonzero 2000/2000 = 1.0000 mean out-bits set 182.2/512 [degree >= d reached] + d= 8 nonzero 2000/2000 = 1.0000 mean out-bits set 184.4/512 [degree >= d reached] + d= 9 nonzero 2000/2000 = 1.0000 mean out-bits set 188.3/512 [degree >= d reached] + d=10 nonzero 2000/2000 = 1.0000 mean out-bits set 190.4/512 [degree >= d reached] + d=11 nonzero 2000/2000 = 1.0000 mean out-bits set 191.2/512 [degree >= d reached] + d=12 nonzero 2000/2000 = 1.0000 mean out-bits set 195.6/512 [degree >= d reached] + d=13 nonzero 2000/2000 = 1.0000 mean out-bits set 199.4/512 [degree >= d reached] + d=14 nonzero 2000/2000 = 1.0000 mean out-bits set 201.2/512 [degree >= d reached] + d=15 nonzero 2000/2000 = 1.0000 mean out-bits set 205.8/512 [degree >= d reached] + d=16 nonzero 2000/2000 = 1.0000 mean out-bits set 211.2/512 [degree >= d reached] + READING: the smallest d at which nonzero is ~1.0 is the degree floor; high degree at small d means no low-degree algebraic shortcut across the applications diff --git a/docs/analysis/cryptanalysis/logs/adv-mixer/integral-a2-32d.log b/docs/analysis/cryptanalysis/logs/adv-mixer/integral-a2-32d.log new file mode 100644 index 000000000..2e3843483 --- /dev/null +++ b/docs/analysis/cryptanalysis/logs/adv-mixer/integral-a2-32d.log @@ -0,0 +1,609 @@ +self-check: spec 1.8.1 and 1.8.4 genesis vectors OK; 72 application keys are 1..72 times 0x9E3779B9 +integral day=20729 apps=2 placements_per_d=2000 threads=44 + d = cube dimension; 'nonzero' = placements whose cube-sum is nonzero on >=1 output bit (degree >= d reached) + d= 1 nonzero 2000/2000 = 1.0000 mean out-bits set 256.0/512 [degree >= d reached] + d= 2 nonzero 2000/2000 = 1.0000 mean out-bits set 256.1/512 [degree >= d reached] + d= 3 nonzero 2000/2000 = 1.0000 mean out-bits set 255.5/512 [degree >= d reached] + d= 4 nonzero 2000/2000 = 1.0000 mean out-bits set 255.9/512 [degree >= d reached] + d= 5 nonzero 2000/2000 = 1.0000 mean out-bits set 256.2/512 [degree >= d reached] + d= 6 nonzero 2000/2000 = 1.0000 mean out-bits set 255.7/512 [degree >= d reached] + d= 7 nonzero 2000/2000 = 1.0000 mean out-bits set 255.6/512 [degree >= d reached] + d= 8 nonzero 2000/2000 = 1.0000 mean out-bits set 255.9/512 [degree >= d reached] + d= 9 nonzero 2000/2000 = 1.0000 mean out-bits set 255.8/512 [degree >= d reached] + d=10 nonzero 2000/2000 = 1.0000 mean out-bits set 256.2/512 [degree >= d reached] + d=11 nonzero 2000/2000 = 1.0000 mean out-bits set 256.5/512 [degree >= d reached] + d=12 nonzero 2000/2000 = 1.0000 mean out-bits set 255.9/512 [degree >= d reached] + d=13 nonzero 2000/2000 = 1.0000 mean out-bits set 255.9/512 [degree >= d reached] + d=14 nonzero 2000/2000 = 1.0000 mean out-bits set 255.7/512 [degree >= d reached] + d=15 nonzero 2000/2000 = 1.0000 mean out-bits set 255.6/512 [degree >= d reached] + d=16 nonzero 2000/2000 = 1.0000 mean out-bits set 255.9/512 [degree >= d reached] + READING: the smallest d at which nonzero is ~1.0 is the degree floor; high degree at small d means no low-degree algebraic shortcut across the applications +integral day=20730 apps=2 placements_per_d=2000 threads=44 + d = cube dimension; 'nonzero' = placements whose cube-sum is nonzero on >=1 output bit (degree >= d reached) + d= 1 nonzero 2000/2000 = 1.0000 mean out-bits set 256.0/512 [degree >= d reached] + d= 2 nonzero 2000/2000 = 1.0000 mean out-bits set 255.7/512 [degree >= d reached] + d= 3 nonzero 2000/2000 = 1.0000 mean out-bits set 255.8/512 [degree >= d reached] + d= 4 nonzero 2000/2000 = 1.0000 mean out-bits set 256.0/512 [degree >= d reached] + d= 5 nonzero 2000/2000 = 1.0000 mean out-bits set 255.7/512 [degree >= d reached] + d= 6 nonzero 2000/2000 = 1.0000 mean out-bits set 256.5/512 [degree >= d reached] + d= 7 nonzero 2000/2000 = 1.0000 mean out-bits set 255.9/512 [degree >= d reached] + d= 8 nonzero 2000/2000 = 1.0000 mean out-bits set 256.4/512 [degree >= d reached] + d= 9 nonzero 2000/2000 = 1.0000 mean out-bits set 256.5/512 [degree >= d reached] + d=10 nonzero 2000/2000 = 1.0000 mean out-bits set 256.0/512 [degree >= d reached] + d=11 nonzero 2000/2000 = 1.0000 mean out-bits set 256.2/512 [degree >= d reached] + d=12 nonzero 2000/2000 = 1.0000 mean out-bits set 255.8/512 [degree >= d reached] + d=13 nonzero 2000/2000 = 1.0000 mean out-bits set 256.4/512 [degree >= d reached] + d=14 nonzero 2000/2000 = 1.0000 mean out-bits set 256.6/512 [degree >= d reached] + d=15 nonzero 2000/2000 = 1.0000 mean out-bits set 255.9/512 [degree >= d reached] + d=16 nonzero 2000/2000 = 1.0000 mean out-bits set 256.2/512 [degree >= d reached] + READING: the smallest d at which nonzero is ~1.0 is the degree floor; high degree at small d means no low-degree algebraic shortcut across the applications +integral day=20731 apps=2 placements_per_d=2000 threads=44 + d = cube dimension; 'nonzero' = placements whose cube-sum is nonzero on >=1 output bit (degree >= d reached) + d= 1 nonzero 2000/2000 = 1.0000 mean out-bits set 256.0/512 [degree >= d reached] + d= 2 nonzero 2000/2000 = 1.0000 mean out-bits set 255.9/512 [degree >= d reached] + d= 3 nonzero 2000/2000 = 1.0000 mean out-bits set 256.3/512 [degree >= d reached] + d= 4 nonzero 2000/2000 = 1.0000 mean out-bits set 256.5/512 [degree >= d reached] + d= 5 nonzero 2000/2000 = 1.0000 mean out-bits set 256.2/512 [degree >= d reached] + d= 6 nonzero 2000/2000 = 1.0000 mean out-bits set 256.3/512 [degree >= d reached] + d= 7 nonzero 2000/2000 = 1.0000 mean out-bits set 256.1/512 [degree >= d reached] + d= 8 nonzero 2000/2000 = 1.0000 mean out-bits set 256.3/512 [degree >= d reached] + d= 9 nonzero 2000/2000 = 1.0000 mean out-bits set 255.9/512 [degree >= d reached] + d=10 nonzero 2000/2000 = 1.0000 mean out-bits set 255.5/512 [degree >= d reached] + d=11 nonzero 2000/2000 = 1.0000 mean out-bits set 256.1/512 [degree >= d reached] + d=12 nonzero 2000/2000 = 1.0000 mean out-bits set 256.0/512 [degree >= d reached] + d=13 nonzero 2000/2000 = 1.0000 mean out-bits set 256.2/512 [degree >= d reached] + d=14 nonzero 2000/2000 = 1.0000 mean out-bits set 256.1/512 [degree >= d reached] + d=15 nonzero 2000/2000 = 1.0000 mean out-bits set 256.2/512 [degree >= d reached] + d=16 nonzero 2000/2000 = 1.0000 mean out-bits set 256.0/512 [degree >= d reached] + READING: the smallest d at which nonzero is ~1.0 is the degree floor; high degree at small d means no low-degree algebraic shortcut across the applications +integral day=20732 apps=2 placements_per_d=2000 threads=44 + d = cube dimension; 'nonzero' = placements whose cube-sum is nonzero on >=1 output bit (degree >= d reached) + d= 1 nonzero 2000/2000 = 1.0000 mean out-bits set 255.9/512 [degree >= d reached] + d= 2 nonzero 2000/2000 = 1.0000 mean out-bits set 256.5/512 [degree >= d reached] + d= 3 nonzero 2000/2000 = 1.0000 mean out-bits set 256.1/512 [degree >= d reached] + d= 4 nonzero 2000/2000 = 1.0000 mean out-bits set 256.4/512 [degree >= d reached] + d= 5 nonzero 2000/2000 = 1.0000 mean out-bits set 255.9/512 [degree >= d reached] + d= 6 nonzero 2000/2000 = 1.0000 mean out-bits set 256.1/512 [degree >= d reached] + d= 7 nonzero 2000/2000 = 1.0000 mean out-bits set 256.4/512 [degree >= d reached] + d= 8 nonzero 2000/2000 = 1.0000 mean out-bits set 255.9/512 [degree >= d reached] + d= 9 nonzero 2000/2000 = 1.0000 mean out-bits set 256.1/512 [degree >= d reached] + d=10 nonzero 2000/2000 = 1.0000 mean out-bits set 256.1/512 [degree >= d reached] + d=11 nonzero 2000/2000 = 1.0000 mean out-bits set 255.5/512 [degree >= d reached] + d=12 nonzero 2000/2000 = 1.0000 mean out-bits set 255.7/512 [degree >= d reached] + d=13 nonzero 2000/2000 = 1.0000 mean out-bits set 255.7/512 [degree >= d reached] + d=14 nonzero 2000/2000 = 1.0000 mean out-bits set 256.1/512 [degree >= d reached] + d=15 nonzero 2000/2000 = 1.0000 mean out-bits set 256.2/512 [degree >= d reached] + d=16 nonzero 2000/2000 = 1.0000 mean out-bits set 255.5/512 [degree >= d reached] + READING: the smallest d at which nonzero is ~1.0 is the degree floor; high degree at small d means no low-degree algebraic shortcut across the applications +integral day=20733 apps=2 placements_per_d=2000 threads=44 + d = cube dimension; 'nonzero' = placements whose cube-sum is nonzero on >=1 output bit (degree >= d reached) + d= 1 nonzero 2000/2000 = 1.0000 mean out-bits set 255.7/512 [degree >= d reached] + d= 2 nonzero 2000/2000 = 1.0000 mean out-bits set 256.4/512 [degree >= d reached] + d= 3 nonzero 2000/2000 = 1.0000 mean out-bits set 256.7/512 [degree >= d reached] + d= 4 nonzero 2000/2000 = 1.0000 mean out-bits set 255.8/512 [degree >= d reached] + d= 5 nonzero 2000/2000 = 1.0000 mean out-bits set 255.6/512 [degree >= d reached] + d= 6 nonzero 2000/2000 = 1.0000 mean out-bits set 255.8/512 [degree >= d reached] + d= 7 nonzero 2000/2000 = 1.0000 mean out-bits set 256.3/512 [degree >= d reached] + d= 8 nonzero 2000/2000 = 1.0000 mean out-bits set 256.0/512 [degree >= d reached] + d= 9 nonzero 2000/2000 = 1.0000 mean out-bits set 255.6/512 [degree >= d reached] + d=10 nonzero 2000/2000 = 1.0000 mean out-bits set 255.9/512 [degree >= d reached] + d=11 nonzero 2000/2000 = 1.0000 mean out-bits set 256.3/512 [degree >= d reached] + d=12 nonzero 2000/2000 = 1.0000 mean out-bits set 255.6/512 [degree >= d reached] + d=13 nonzero 2000/2000 = 1.0000 mean out-bits set 256.1/512 [degree >= d reached] + d=14 nonzero 2000/2000 = 1.0000 mean out-bits set 255.6/512 [degree >= d reached] + d=15 nonzero 2000/2000 = 1.0000 mean out-bits set 256.4/512 [degree >= d reached] + d=16 nonzero 2000/2000 = 1.0000 mean out-bits set 256.1/512 [degree >= d reached] + READING: the smallest d at which nonzero is ~1.0 is the degree floor; high degree at small d means no low-degree algebraic shortcut across the applications +integral day=20734 apps=2 placements_per_d=2000 threads=44 + d = cube dimension; 'nonzero' = placements whose cube-sum is nonzero on >=1 output bit (degree >= d reached) + d= 1 nonzero 2000/2000 = 1.0000 mean out-bits set 256.3/512 [degree >= d reached] + d= 2 nonzero 2000/2000 = 1.0000 mean out-bits set 255.9/512 [degree >= d reached] + d= 3 nonzero 2000/2000 = 1.0000 mean out-bits set 255.9/512 [degree >= d reached] + d= 4 nonzero 2000/2000 = 1.0000 mean out-bits set 255.8/512 [degree >= d reached] + d= 5 nonzero 2000/2000 = 1.0000 mean out-bits set 255.7/512 [degree >= d reached] + d= 6 nonzero 2000/2000 = 1.0000 mean out-bits set 256.2/512 [degree >= d reached] + d= 7 nonzero 2000/2000 = 1.0000 mean out-bits set 255.8/512 [degree >= d reached] + d= 8 nonzero 2000/2000 = 1.0000 mean out-bits set 255.8/512 [degree >= d reached] + d= 9 nonzero 2000/2000 = 1.0000 mean out-bits set 256.2/512 [degree >= d reached] + d=10 nonzero 2000/2000 = 1.0000 mean out-bits set 255.7/512 [degree >= d reached] + d=11 nonzero 2000/2000 = 1.0000 mean out-bits set 256.1/512 [degree >= d reached] + d=12 nonzero 2000/2000 = 1.0000 mean out-bits set 255.7/512 [degree >= d reached] + d=13 nonzero 2000/2000 = 1.0000 mean out-bits set 255.8/512 [degree >= d reached] + d=14 nonzero 2000/2000 = 1.0000 mean out-bits set 255.7/512 [degree >= d reached] + d=15 nonzero 2000/2000 = 1.0000 mean out-bits set 256.1/512 [degree >= d reached] + d=16 nonzero 2000/2000 = 1.0000 mean out-bits set 255.9/512 [degree >= d reached] + READING: the smallest d at which nonzero is ~1.0 is the degree floor; high degree at small d means no low-degree algebraic shortcut across the applications +integral day=20735 apps=2 placements_per_d=2000 threads=44 + d = cube dimension; 'nonzero' = placements whose cube-sum is nonzero on >=1 output bit (degree >= d reached) + d= 1 nonzero 2000/2000 = 1.0000 mean out-bits set 256.2/512 [degree >= d reached] + d= 2 nonzero 2000/2000 = 1.0000 mean out-bits set 255.5/512 [degree >= d reached] + d= 3 nonzero 2000/2000 = 1.0000 mean out-bits set 256.1/512 [degree >= d reached] + d= 4 nonzero 2000/2000 = 1.0000 mean out-bits set 256.0/512 [degree >= d reached] + d= 5 nonzero 2000/2000 = 1.0000 mean out-bits set 256.7/512 [degree >= d reached] + d= 6 nonzero 2000/2000 = 1.0000 mean out-bits set 256.0/512 [degree >= d reached] + d= 7 nonzero 2000/2000 = 1.0000 mean out-bits set 256.0/512 [degree >= d reached] + d= 8 nonzero 2000/2000 = 1.0000 mean out-bits set 255.9/512 [degree >= d reached] + d= 9 nonzero 2000/2000 = 1.0000 mean out-bits set 256.1/512 [degree >= d reached] + d=10 nonzero 2000/2000 = 1.0000 mean out-bits set 256.0/512 [degree >= d reached] + d=11 nonzero 2000/2000 = 1.0000 mean out-bits set 256.2/512 [degree >= d reached] + d=12 nonzero 2000/2000 = 1.0000 mean out-bits set 256.4/512 [degree >= d reached] + d=13 nonzero 2000/2000 = 1.0000 mean out-bits set 255.8/512 [degree >= d reached] + d=14 nonzero 2000/2000 = 1.0000 mean out-bits set 255.7/512 [degree >= d reached] + d=15 nonzero 2000/2000 = 1.0000 mean out-bits set 255.9/512 [degree >= d reached] + d=16 nonzero 2000/2000 = 1.0000 mean out-bits set 255.8/512 [degree >= d reached] + READING: the smallest d at which nonzero is ~1.0 is the degree floor; high degree at small d means no low-degree algebraic shortcut across the applications +integral day=20736 apps=2 placements_per_d=2000 threads=44 + d = cube dimension; 'nonzero' = placements whose cube-sum is nonzero on >=1 output bit (degree >= d reached) + d= 1 nonzero 2000/2000 = 1.0000 mean out-bits set 256.7/512 [degree >= d reached] + d= 2 nonzero 2000/2000 = 1.0000 mean out-bits set 256.5/512 [degree >= d reached] + d= 3 nonzero 2000/2000 = 1.0000 mean out-bits set 256.2/512 [degree >= d reached] + d= 4 nonzero 2000/2000 = 1.0000 mean out-bits set 256.2/512 [degree >= d reached] + d= 5 nonzero 2000/2000 = 1.0000 mean out-bits set 256.2/512 [degree >= d reached] + d= 6 nonzero 2000/2000 = 1.0000 mean out-bits set 256.2/512 [degree >= d reached] + d= 7 nonzero 2000/2000 = 1.0000 mean out-bits set 255.9/512 [degree >= d reached] + d= 8 nonzero 2000/2000 = 1.0000 mean out-bits set 255.8/512 [degree >= d reached] + d= 9 nonzero 2000/2000 = 1.0000 mean out-bits set 255.9/512 [degree >= d reached] + d=10 nonzero 2000/2000 = 1.0000 mean out-bits set 255.8/512 [degree >= d reached] + d=11 nonzero 2000/2000 = 1.0000 mean out-bits set 255.9/512 [degree >= d reached] + d=12 nonzero 2000/2000 = 1.0000 mean out-bits set 256.3/512 [degree >= d reached] + d=13 nonzero 2000/2000 = 1.0000 mean out-bits set 255.8/512 [degree >= d reached] + d=14 nonzero 2000/2000 = 1.0000 mean out-bits set 256.5/512 [degree >= d reached] + d=15 nonzero 2000/2000 = 1.0000 mean out-bits set 256.2/512 [degree >= d reached] + d=16 nonzero 2000/2000 = 1.0000 mean out-bits set 255.5/512 [degree >= d reached] + READING: the smallest d at which nonzero is ~1.0 is the degree floor; high degree at small d means no low-degree algebraic shortcut across the applications +integral day=20737 apps=2 placements_per_d=2000 threads=44 + d = cube dimension; 'nonzero' = placements whose cube-sum is nonzero on >=1 output bit (degree >= d reached) + d= 1 nonzero 2000/2000 = 1.0000 mean out-bits set 255.5/512 [degree >= d reached] + d= 2 nonzero 2000/2000 = 1.0000 mean out-bits set 256.6/512 [degree >= d reached] + d= 3 nonzero 2000/2000 = 1.0000 mean out-bits set 256.5/512 [degree >= d reached] + d= 4 nonzero 2000/2000 = 1.0000 mean out-bits set 255.8/512 [degree >= d reached] + d= 5 nonzero 2000/2000 = 1.0000 mean out-bits set 256.0/512 [degree >= d reached] + d= 6 nonzero 2000/2000 = 1.0000 mean out-bits set 256.1/512 [degree >= d reached] + d= 7 nonzero 2000/2000 = 1.0000 mean out-bits set 255.8/512 [degree >= d reached] + d= 8 nonzero 2000/2000 = 1.0000 mean out-bits set 256.0/512 [degree >= d reached] + d= 9 nonzero 2000/2000 = 1.0000 mean out-bits set 255.8/512 [degree >= d reached] + d=10 nonzero 2000/2000 = 1.0000 mean out-bits set 255.9/512 [degree >= d reached] + d=11 nonzero 2000/2000 = 1.0000 mean out-bits set 256.3/512 [degree >= d reached] + d=12 nonzero 2000/2000 = 1.0000 mean out-bits set 256.0/512 [degree >= d reached] + d=13 nonzero 2000/2000 = 1.0000 mean out-bits set 256.0/512 [degree >= d reached] + d=14 nonzero 2000/2000 = 1.0000 mean out-bits set 256.1/512 [degree >= d reached] + d=15 nonzero 2000/2000 = 1.0000 mean out-bits set 255.7/512 [degree >= d reached] + d=16 nonzero 2000/2000 = 1.0000 mean out-bits set 256.0/512 [degree >= d reached] + READING: the smallest d at which nonzero is ~1.0 is the degree floor; high degree at small d means no low-degree algebraic shortcut across the applications +integral day=20738 apps=2 placements_per_d=2000 threads=44 + d = cube dimension; 'nonzero' = placements whose cube-sum is nonzero on >=1 output bit (degree >= d reached) + d= 1 nonzero 2000/2000 = 1.0000 mean out-bits set 255.9/512 [degree >= d reached] + d= 2 nonzero 2000/2000 = 1.0000 mean out-bits set 256.1/512 [degree >= d reached] + d= 3 nonzero 2000/2000 = 1.0000 mean out-bits set 256.0/512 [degree >= d reached] + d= 4 nonzero 2000/2000 = 1.0000 mean out-bits set 256.2/512 [degree >= d reached] + d= 5 nonzero 2000/2000 = 1.0000 mean out-bits set 256.2/512 [degree >= d reached] + d= 6 nonzero 2000/2000 = 1.0000 mean out-bits set 255.8/512 [degree >= d reached] + d= 7 nonzero 2000/2000 = 1.0000 mean out-bits set 255.8/512 [degree >= d reached] + d= 8 nonzero 2000/2000 = 1.0000 mean out-bits set 256.1/512 [degree >= d reached] + d= 9 nonzero 2000/2000 = 1.0000 mean out-bits set 256.3/512 [degree >= d reached] + d=10 nonzero 2000/2000 = 1.0000 mean out-bits set 255.8/512 [degree >= d reached] + d=11 nonzero 2000/2000 = 1.0000 mean out-bits set 256.2/512 [degree >= d reached] + d=12 nonzero 2000/2000 = 1.0000 mean out-bits set 255.7/512 [degree >= d reached] + d=13 nonzero 2000/2000 = 1.0000 mean out-bits set 255.7/512 [degree >= d reached] + d=14 nonzero 2000/2000 = 1.0000 mean out-bits set 256.1/512 [degree >= d reached] + d=15 nonzero 2000/2000 = 1.0000 mean out-bits set 256.2/512 [degree >= d reached] + d=16 nonzero 2000/2000 = 1.0000 mean out-bits set 256.4/512 [degree >= d reached] + READING: the smallest d at which nonzero is ~1.0 is the degree floor; high degree at small d means no low-degree algebraic shortcut across the applications +integral day=20739 apps=2 placements_per_d=2000 threads=44 + d = cube dimension; 'nonzero' = placements whose cube-sum is nonzero on >=1 output bit (degree >= d reached) + d= 1 nonzero 2000/2000 = 1.0000 mean out-bits set 256.2/512 [degree >= d reached] + d= 2 nonzero 2000/2000 = 1.0000 mean out-bits set 256.2/512 [degree >= d reached] + d= 3 nonzero 2000/2000 = 1.0000 mean out-bits set 255.5/512 [degree >= d reached] + d= 4 nonzero 2000/2000 = 1.0000 mean out-bits set 256.3/512 [degree >= d reached] + d= 5 nonzero 2000/2000 = 1.0000 mean out-bits set 255.8/512 [degree >= d reached] + d= 6 nonzero 2000/2000 = 1.0000 mean out-bits set 256.3/512 [degree >= d reached] + d= 7 nonzero 2000/2000 = 1.0000 mean out-bits set 256.5/512 [degree >= d reached] + d= 8 nonzero 2000/2000 = 1.0000 mean out-bits set 256.1/512 [degree >= d reached] + d= 9 nonzero 2000/2000 = 1.0000 mean out-bits set 255.7/512 [degree >= d reached] + d=10 nonzero 2000/2000 = 1.0000 mean out-bits set 256.3/512 [degree >= d reached] + d=11 nonzero 2000/2000 = 1.0000 mean out-bits set 256.1/512 [degree >= d reached] + d=12 nonzero 2000/2000 = 1.0000 mean out-bits set 256.1/512 [degree >= d reached] + d=13 nonzero 2000/2000 = 1.0000 mean out-bits set 256.3/512 [degree >= d reached] + d=14 nonzero 2000/2000 = 1.0000 mean out-bits set 255.9/512 [degree >= d reached] + d=15 nonzero 2000/2000 = 1.0000 mean out-bits set 255.6/512 [degree >= d reached] + d=16 nonzero 2000/2000 = 1.0000 mean out-bits set 256.3/512 [degree >= d reached] + READING: the smallest d at which nonzero is ~1.0 is the degree floor; high degree at small d means no low-degree algebraic shortcut across the applications +integral day=20740 apps=2 placements_per_d=2000 threads=44 + d = cube dimension; 'nonzero' = placements whose cube-sum is nonzero on >=1 output bit (degree >= d reached) + d= 1 nonzero 2000/2000 = 1.0000 mean out-bits set 256.2/512 [degree >= d reached] + d= 2 nonzero 2000/2000 = 1.0000 mean out-bits set 256.1/512 [degree >= d reached] + d= 3 nonzero 2000/2000 = 1.0000 mean out-bits set 255.9/512 [degree >= d reached] + d= 4 nonzero 2000/2000 = 1.0000 mean out-bits set 255.9/512 [degree >= d reached] + d= 5 nonzero 2000/2000 = 1.0000 mean out-bits set 255.9/512 [degree >= d reached] + d= 6 nonzero 2000/2000 = 1.0000 mean out-bits set 256.3/512 [degree >= d reached] + d= 7 nonzero 2000/2000 = 1.0000 mean out-bits set 256.2/512 [degree >= d reached] + d= 8 nonzero 2000/2000 = 1.0000 mean out-bits set 255.6/512 [degree >= d reached] + d= 9 nonzero 2000/2000 = 1.0000 mean out-bits set 255.8/512 [degree >= d reached] + d=10 nonzero 2000/2000 = 1.0000 mean out-bits set 256.0/512 [degree >= d reached] + d=11 nonzero 2000/2000 = 1.0000 mean out-bits set 256.3/512 [degree >= d reached] + d=12 nonzero 2000/2000 = 1.0000 mean out-bits set 256.5/512 [degree >= d reached] + d=13 nonzero 2000/2000 = 1.0000 mean out-bits set 256.4/512 [degree >= d reached] + d=14 nonzero 2000/2000 = 1.0000 mean out-bits set 256.1/512 [degree >= d reached] + d=15 nonzero 2000/2000 = 1.0000 mean out-bits set 255.8/512 [degree >= d reached] + d=16 nonzero 2000/2000 = 1.0000 mean out-bits set 255.6/512 [degree >= d reached] + READING: the smallest d at which nonzero is ~1.0 is the degree floor; high degree at small d means no low-degree algebraic shortcut across the applications +integral day=20741 apps=2 placements_per_d=2000 threads=44 + d = cube dimension; 'nonzero' = placements whose cube-sum is nonzero on >=1 output bit (degree >= d reached) + d= 1 nonzero 2000/2000 = 1.0000 mean out-bits set 256.4/512 [degree >= d reached] + d= 2 nonzero 2000/2000 = 1.0000 mean out-bits set 256.3/512 [degree >= d reached] + d= 3 nonzero 2000/2000 = 1.0000 mean out-bits set 256.2/512 [degree >= d reached] + d= 4 nonzero 2000/2000 = 1.0000 mean out-bits set 256.5/512 [degree >= d reached] + d= 5 nonzero 2000/2000 = 1.0000 mean out-bits set 255.8/512 [degree >= d reached] + d= 6 nonzero 2000/2000 = 1.0000 mean out-bits set 255.7/512 [degree >= d reached] + d= 7 nonzero 2000/2000 = 1.0000 mean out-bits set 255.9/512 [degree >= d reached] + d= 8 nonzero 2000/2000 = 1.0000 mean out-bits set 256.1/512 [degree >= d reached] + d= 9 nonzero 2000/2000 = 1.0000 mean out-bits set 256.2/512 [degree >= d reached] + d=10 nonzero 2000/2000 = 1.0000 mean out-bits set 256.3/512 [degree >= d reached] + d=11 nonzero 2000/2000 = 1.0000 mean out-bits set 255.7/512 [degree >= d reached] + d=12 nonzero 2000/2000 = 1.0000 mean out-bits set 256.0/512 [degree >= d reached] + d=13 nonzero 2000/2000 = 1.0000 mean out-bits set 255.8/512 [degree >= d reached] + d=14 nonzero 2000/2000 = 1.0000 mean out-bits set 256.3/512 [degree >= d reached] + d=15 nonzero 2000/2000 = 1.0000 mean out-bits set 255.9/512 [degree >= d reached] + d=16 nonzero 2000/2000 = 1.0000 mean out-bits set 256.2/512 [degree >= d reached] + READING: the smallest d at which nonzero is ~1.0 is the degree floor; high degree at small d means no low-degree algebraic shortcut across the applications +integral day=20742 apps=2 placements_per_d=2000 threads=44 + d = cube dimension; 'nonzero' = placements whose cube-sum is nonzero on >=1 output bit (degree >= d reached) + d= 1 nonzero 2000/2000 = 1.0000 mean out-bits set 255.9/512 [degree >= d reached] + d= 2 nonzero 2000/2000 = 1.0000 mean out-bits set 255.7/512 [degree >= d reached] + d= 3 nonzero 2000/2000 = 1.0000 mean out-bits set 256.4/512 [degree >= d reached] + d= 4 nonzero 2000/2000 = 1.0000 mean out-bits set 255.8/512 [degree >= d reached] + d= 5 nonzero 2000/2000 = 1.0000 mean out-bits set 256.2/512 [degree >= d reached] + d= 6 nonzero 2000/2000 = 1.0000 mean out-bits set 256.5/512 [degree >= d reached] + d= 7 nonzero 2000/2000 = 1.0000 mean out-bits set 255.9/512 [degree >= d reached] + d= 8 nonzero 2000/2000 = 1.0000 mean out-bits set 255.5/512 [degree >= d reached] + d= 9 nonzero 2000/2000 = 1.0000 mean out-bits set 256.5/512 [degree >= d reached] + d=10 nonzero 2000/2000 = 1.0000 mean out-bits set 255.7/512 [degree >= d reached] + d=11 nonzero 2000/2000 = 1.0000 mean out-bits set 255.8/512 [degree >= d reached] + d=12 nonzero 2000/2000 = 1.0000 mean out-bits set 256.1/512 [degree >= d reached] + d=13 nonzero 2000/2000 = 1.0000 mean out-bits set 256.4/512 [degree >= d reached] + d=14 nonzero 2000/2000 = 1.0000 mean out-bits set 256.1/512 [degree >= d reached] + d=15 nonzero 2000/2000 = 1.0000 mean out-bits set 256.1/512 [degree >= d reached] + d=16 nonzero 2000/2000 = 1.0000 mean out-bits set 255.7/512 [degree >= d reached] + READING: the smallest d at which nonzero is ~1.0 is the degree floor; high degree at small d means no low-degree algebraic shortcut across the applications +integral day=20743 apps=2 placements_per_d=2000 threads=44 + d = cube dimension; 'nonzero' = placements whose cube-sum is nonzero on >=1 output bit (degree >= d reached) + d= 1 nonzero 2000/2000 = 1.0000 mean out-bits set 256.0/512 [degree >= d reached] + d= 2 nonzero 2000/2000 = 1.0000 mean out-bits set 256.2/512 [degree >= d reached] + d= 3 nonzero 2000/2000 = 1.0000 mean out-bits set 255.9/512 [degree >= d reached] + d= 4 nonzero 2000/2000 = 1.0000 mean out-bits set 255.9/512 [degree >= d reached] + d= 5 nonzero 2000/2000 = 1.0000 mean out-bits set 256.0/512 [degree >= d reached] + d= 6 nonzero 2000/2000 = 1.0000 mean out-bits set 255.9/512 [degree >= d reached] + d= 7 nonzero 2000/2000 = 1.0000 mean out-bits set 255.8/512 [degree >= d reached] + d= 8 nonzero 2000/2000 = 1.0000 mean out-bits set 255.9/512 [degree >= d reached] + d= 9 nonzero 2000/2000 = 1.0000 mean out-bits set 256.4/512 [degree >= d reached] + d=10 nonzero 2000/2000 = 1.0000 mean out-bits set 256.4/512 [degree >= d reached] + d=11 nonzero 2000/2000 = 1.0000 mean out-bits set 255.9/512 [degree >= d reached] + d=12 nonzero 2000/2000 = 1.0000 mean out-bits set 256.1/512 [degree >= d reached] + d=13 nonzero 2000/2000 = 1.0000 mean out-bits set 256.1/512 [degree >= d reached] + d=14 nonzero 2000/2000 = 1.0000 mean out-bits set 255.8/512 [degree >= d reached] + d=15 nonzero 2000/2000 = 1.0000 mean out-bits set 256.1/512 [degree >= d reached] + d=16 nonzero 2000/2000 = 1.0000 mean out-bits set 256.0/512 [degree >= d reached] + READING: the smallest d at which nonzero is ~1.0 is the degree floor; high degree at small d means no low-degree algebraic shortcut across the applications +integral day=20744 apps=2 placements_per_d=2000 threads=44 + d = cube dimension; 'nonzero' = placements whose cube-sum is nonzero on >=1 output bit (degree >= d reached) + d= 1 nonzero 2000/2000 = 1.0000 mean out-bits set 256.6/512 [degree >= d reached] + d= 2 nonzero 2000/2000 = 1.0000 mean out-bits set 256.0/512 [degree >= d reached] + d= 3 nonzero 2000/2000 = 1.0000 mean out-bits set 256.3/512 [degree >= d reached] + d= 4 nonzero 2000/2000 = 1.0000 mean out-bits set 256.0/512 [degree >= d reached] + d= 5 nonzero 2000/2000 = 1.0000 mean out-bits set 256.1/512 [degree >= d reached] + d= 6 nonzero 2000/2000 = 1.0000 mean out-bits set 256.6/512 [degree >= d reached] + d= 7 nonzero 2000/2000 = 1.0000 mean out-bits set 256.1/512 [degree >= d reached] + d= 8 nonzero 2000/2000 = 1.0000 mean out-bits set 256.3/512 [degree >= d reached] + d= 9 nonzero 2000/2000 = 1.0000 mean out-bits set 256.0/512 [degree >= d reached] + d=10 nonzero 2000/2000 = 1.0000 mean out-bits set 256.2/512 [degree >= d reached] + d=11 nonzero 2000/2000 = 1.0000 mean out-bits set 256.2/512 [degree >= d reached] + d=12 nonzero 2000/2000 = 1.0000 mean out-bits set 255.9/512 [degree >= d reached] + d=13 nonzero 2000/2000 = 1.0000 mean out-bits set 255.9/512 [degree >= d reached] + d=14 nonzero 2000/2000 = 1.0000 mean out-bits set 255.9/512 [degree >= d reached] + d=15 nonzero 2000/2000 = 1.0000 mean out-bits set 255.9/512 [degree >= d reached] + d=16 nonzero 2000/2000 = 1.0000 mean out-bits set 256.3/512 [degree >= d reached] + READING: the smallest d at which nonzero is ~1.0 is the degree floor; high degree at small d means no low-degree algebraic shortcut across the applications +integral day=20745 apps=2 placements_per_d=2000 threads=44 + d = cube dimension; 'nonzero' = placements whose cube-sum is nonzero on >=1 output bit (degree >= d reached) + d= 1 nonzero 2000/2000 = 1.0000 mean out-bits set 256.1/512 [degree >= d reached] + d= 2 nonzero 2000/2000 = 1.0000 mean out-bits set 255.9/512 [degree >= d reached] + d= 3 nonzero 2000/2000 = 1.0000 mean out-bits set 255.9/512 [degree >= d reached] + d= 4 nonzero 2000/2000 = 1.0000 mean out-bits set 255.8/512 [degree >= d reached] + d= 5 nonzero 2000/2000 = 1.0000 mean out-bits set 256.1/512 [degree >= d reached] + d= 6 nonzero 2000/2000 = 1.0000 mean out-bits set 256.0/512 [degree >= d reached] + d= 7 nonzero 2000/2000 = 1.0000 mean out-bits set 256.1/512 [degree >= d reached] + d= 8 nonzero 2000/2000 = 1.0000 mean out-bits set 255.6/512 [degree >= d reached] + d= 9 nonzero 2000/2000 = 1.0000 mean out-bits set 256.0/512 [degree >= d reached] + d=10 nonzero 2000/2000 = 1.0000 mean out-bits set 256.6/512 [degree >= d reached] + d=11 nonzero 2000/2000 = 1.0000 mean out-bits set 255.8/512 [degree >= d reached] + d=12 nonzero 2000/2000 = 1.0000 mean out-bits set 256.0/512 [degree >= d reached] + d=13 nonzero 2000/2000 = 1.0000 mean out-bits set 256.0/512 [degree >= d reached] + d=14 nonzero 2000/2000 = 1.0000 mean out-bits set 256.0/512 [degree >= d reached] + d=15 nonzero 2000/2000 = 1.0000 mean out-bits set 255.8/512 [degree >= d reached] + d=16 nonzero 2000/2000 = 1.0000 mean out-bits set 256.2/512 [degree >= d reached] + READING: the smallest d at which nonzero is ~1.0 is the degree floor; high degree at small d means no low-degree algebraic shortcut across the applications +integral day=20746 apps=2 placements_per_d=2000 threads=44 + d = cube dimension; 'nonzero' = placements whose cube-sum is nonzero on >=1 output bit (degree >= d reached) + d= 1 nonzero 2000/2000 = 1.0000 mean out-bits set 255.7/512 [degree >= d reached] + d= 2 nonzero 2000/2000 = 1.0000 mean out-bits set 255.8/512 [degree >= d reached] + d= 3 nonzero 2000/2000 = 1.0000 mean out-bits set 255.8/512 [degree >= d reached] + d= 4 nonzero 2000/2000 = 1.0000 mean out-bits set 255.7/512 [degree >= d reached] + d= 5 nonzero 2000/2000 = 1.0000 mean out-bits set 256.2/512 [degree >= d reached] + d= 6 nonzero 2000/2000 = 1.0000 mean out-bits set 256.0/512 [degree >= d reached] + d= 7 nonzero 2000/2000 = 1.0000 mean out-bits set 256.3/512 [degree >= d reached] + d= 8 nonzero 2000/2000 = 1.0000 mean out-bits set 256.0/512 [degree >= d reached] + d= 9 nonzero 2000/2000 = 1.0000 mean out-bits set 255.7/512 [degree >= d reached] + d=10 nonzero 2000/2000 = 1.0000 mean out-bits set 256.3/512 [degree >= d reached] + d=11 nonzero 2000/2000 = 1.0000 mean out-bits set 255.8/512 [degree >= d reached] + d=12 nonzero 2000/2000 = 1.0000 mean out-bits set 256.1/512 [degree >= d reached] + d=13 nonzero 2000/2000 = 1.0000 mean out-bits set 255.9/512 [degree >= d reached] + d=14 nonzero 2000/2000 = 1.0000 mean out-bits set 256.3/512 [degree >= d reached] + d=15 nonzero 2000/2000 = 1.0000 mean out-bits set 255.6/512 [degree >= d reached] + d=16 nonzero 2000/2000 = 1.0000 mean out-bits set 256.0/512 [degree >= d reached] + READING: the smallest d at which nonzero is ~1.0 is the degree floor; high degree at small d means no low-degree algebraic shortcut across the applications +integral day=20747 apps=2 placements_per_d=2000 threads=44 + d = cube dimension; 'nonzero' = placements whose cube-sum is nonzero on >=1 output bit (degree >= d reached) + d= 1 nonzero 2000/2000 = 1.0000 mean out-bits set 256.2/512 [degree >= d reached] + d= 2 nonzero 2000/2000 = 1.0000 mean out-bits set 255.7/512 [degree >= d reached] + d= 3 nonzero 2000/2000 = 1.0000 mean out-bits set 256.2/512 [degree >= d reached] + d= 4 nonzero 2000/2000 = 1.0000 mean out-bits set 256.1/512 [degree >= d reached] + d= 5 nonzero 2000/2000 = 1.0000 mean out-bits set 255.5/512 [degree >= d reached] + d= 6 nonzero 2000/2000 = 1.0000 mean out-bits set 255.9/512 [degree >= d reached] + d= 7 nonzero 2000/2000 = 1.0000 mean out-bits set 256.0/512 [degree >= d reached] + d= 8 nonzero 2000/2000 = 1.0000 mean out-bits set 255.5/512 [degree >= d reached] + d= 9 nonzero 2000/2000 = 1.0000 mean out-bits set 255.9/512 [degree >= d reached] + d=10 nonzero 2000/2000 = 1.0000 mean out-bits set 256.0/512 [degree >= d reached] + d=11 nonzero 2000/2000 = 1.0000 mean out-bits set 255.8/512 [degree >= d reached] + d=12 nonzero 2000/2000 = 1.0000 mean out-bits set 256.2/512 [degree >= d reached] + d=13 nonzero 2000/2000 = 1.0000 mean out-bits set 255.9/512 [degree >= d reached] + d=14 nonzero 2000/2000 = 1.0000 mean out-bits set 256.2/512 [degree >= d reached] + d=15 nonzero 2000/2000 = 1.0000 mean out-bits set 256.1/512 [degree >= d reached] + d=16 nonzero 2000/2000 = 1.0000 mean out-bits set 256.1/512 [degree >= d reached] + READING: the smallest d at which nonzero is ~1.0 is the degree floor; high degree at small d means no low-degree algebraic shortcut across the applications +integral day=20748 apps=2 placements_per_d=2000 threads=44 + d = cube dimension; 'nonzero' = placements whose cube-sum is nonzero on >=1 output bit (degree >= d reached) + d= 1 nonzero 2000/2000 = 1.0000 mean out-bits set 256.0/512 [degree >= d reached] + d= 2 nonzero 2000/2000 = 1.0000 mean out-bits set 256.0/512 [degree >= d reached] + d= 3 nonzero 2000/2000 = 1.0000 mean out-bits set 255.8/512 [degree >= d reached] + d= 4 nonzero 2000/2000 = 1.0000 mean out-bits set 255.6/512 [degree >= d reached] + d= 5 nonzero 2000/2000 = 1.0000 mean out-bits set 256.1/512 [degree >= d reached] + d= 6 nonzero 2000/2000 = 1.0000 mean out-bits set 256.2/512 [degree >= d reached] + d= 7 nonzero 2000/2000 = 1.0000 mean out-bits set 255.9/512 [degree >= d reached] + d= 8 nonzero 2000/2000 = 1.0000 mean out-bits set 255.7/512 [degree >= d reached] + d= 9 nonzero 2000/2000 = 1.0000 mean out-bits set 256.0/512 [degree >= d reached] + d=10 nonzero 2000/2000 = 1.0000 mean out-bits set 256.1/512 [degree >= d reached] + d=11 nonzero 2000/2000 = 1.0000 mean out-bits set 256.0/512 [degree >= d reached] + d=12 nonzero 2000/2000 = 1.0000 mean out-bits set 256.0/512 [degree >= d reached] + d=13 nonzero 2000/2000 = 1.0000 mean out-bits set 255.8/512 [degree >= d reached] + d=14 nonzero 2000/2000 = 1.0000 mean out-bits set 256.0/512 [degree >= d reached] + d=15 nonzero 2000/2000 = 1.0000 mean out-bits set 256.4/512 [degree >= d reached] + d=16 nonzero 2000/2000 = 1.0000 mean out-bits set 256.0/512 [degree >= d reached] + READING: the smallest d at which nonzero is ~1.0 is the degree floor; high degree at small d means no low-degree algebraic shortcut across the applications +integral day=20749 apps=2 placements_per_d=2000 threads=44 + d = cube dimension; 'nonzero' = placements whose cube-sum is nonzero on >=1 output bit (degree >= d reached) + d= 1 nonzero 2000/2000 = 1.0000 mean out-bits set 255.9/512 [degree >= d reached] + d= 2 nonzero 2000/2000 = 1.0000 mean out-bits set 256.1/512 [degree >= d reached] + d= 3 nonzero 2000/2000 = 1.0000 mean out-bits set 255.7/512 [degree >= d reached] + d= 4 nonzero 2000/2000 = 1.0000 mean out-bits set 255.9/512 [degree >= d reached] + d= 5 nonzero 2000/2000 = 1.0000 mean out-bits set 255.6/512 [degree >= d reached] + d= 6 nonzero 2000/2000 = 1.0000 mean out-bits set 255.9/512 [degree >= d reached] + d= 7 nonzero 2000/2000 = 1.0000 mean out-bits set 255.6/512 [degree >= d reached] + d= 8 nonzero 2000/2000 = 1.0000 mean out-bits set 255.6/512 [degree >= d reached] + d= 9 nonzero 2000/2000 = 1.0000 mean out-bits set 256.4/512 [degree >= d reached] + d=10 nonzero 2000/2000 = 1.0000 mean out-bits set 256.4/512 [degree >= d reached] + d=11 nonzero 2000/2000 = 1.0000 mean out-bits set 255.9/512 [degree >= d reached] + d=12 nonzero 2000/2000 = 1.0000 mean out-bits set 256.3/512 [degree >= d reached] + d=13 nonzero 2000/2000 = 1.0000 mean out-bits set 255.9/512 [degree >= d reached] + d=14 nonzero 2000/2000 = 1.0000 mean out-bits set 256.1/512 [degree >= d reached] + d=15 nonzero 2000/2000 = 1.0000 mean out-bits set 256.3/512 [degree >= d reached] + d=16 nonzero 2000/2000 = 1.0000 mean out-bits set 256.0/512 [degree >= d reached] + READING: the smallest d at which nonzero is ~1.0 is the degree floor; high degree at small d means no low-degree algebraic shortcut across the applications +integral day=20750 apps=2 placements_per_d=2000 threads=44 + d = cube dimension; 'nonzero' = placements whose cube-sum is nonzero on >=1 output bit (degree >= d reached) + d= 1 nonzero 2000/2000 = 1.0000 mean out-bits set 256.1/512 [degree >= d reached] + d= 2 nonzero 2000/2000 = 1.0000 mean out-bits set 255.8/512 [degree >= d reached] + d= 3 nonzero 2000/2000 = 1.0000 mean out-bits set 256.2/512 [degree >= d reached] + d= 4 nonzero 2000/2000 = 1.0000 mean out-bits set 256.2/512 [degree >= d reached] + d= 5 nonzero 2000/2000 = 1.0000 mean out-bits set 256.1/512 [degree >= d reached] + d= 6 nonzero 2000/2000 = 1.0000 mean out-bits set 256.2/512 [degree >= d reached] + d= 7 nonzero 2000/2000 = 1.0000 mean out-bits set 255.9/512 [degree >= d reached] + d= 8 nonzero 2000/2000 = 1.0000 mean out-bits set 256.0/512 [degree >= d reached] + d= 9 nonzero 2000/2000 = 1.0000 mean out-bits set 256.1/512 [degree >= d reached] + d=10 nonzero 2000/2000 = 1.0000 mean out-bits set 255.9/512 [degree >= d reached] + d=11 nonzero 2000/2000 = 1.0000 mean out-bits set 256.0/512 [degree >= d reached] + d=12 nonzero 2000/2000 = 1.0000 mean out-bits set 256.2/512 [degree >= d reached] + d=13 nonzero 2000/2000 = 1.0000 mean out-bits set 255.8/512 [degree >= d reached] + d=14 nonzero 2000/2000 = 1.0000 mean out-bits set 255.8/512 [degree >= d reached] + d=15 nonzero 2000/2000 = 1.0000 mean out-bits set 255.6/512 [degree >= d reached] + d=16 nonzero 2000/2000 = 1.0000 mean out-bits set 255.9/512 [degree >= d reached] + READING: the smallest d at which nonzero is ~1.0 is the degree floor; high degree at small d means no low-degree algebraic shortcut across the applications +integral day=20751 apps=2 placements_per_d=2000 threads=44 + d = cube dimension; 'nonzero' = placements whose cube-sum is nonzero on >=1 output bit (degree >= d reached) + d= 1 nonzero 2000/2000 = 1.0000 mean out-bits set 256.4/512 [degree >= d reached] + d= 2 nonzero 2000/2000 = 1.0000 mean out-bits set 256.0/512 [degree >= d reached] + d= 3 nonzero 2000/2000 = 1.0000 mean out-bits set 256.3/512 [degree >= d reached] + d= 4 nonzero 2000/2000 = 1.0000 mean out-bits set 256.0/512 [degree >= d reached] + d= 5 nonzero 2000/2000 = 1.0000 mean out-bits set 256.2/512 [degree >= d reached] + d= 6 nonzero 2000/2000 = 1.0000 mean out-bits set 255.7/512 [degree >= d reached] + d= 7 nonzero 2000/2000 = 1.0000 mean out-bits set 256.2/512 [degree >= d reached] + d= 8 nonzero 2000/2000 = 1.0000 mean out-bits set 256.1/512 [degree >= d reached] + d= 9 nonzero 2000/2000 = 1.0000 mean out-bits set 256.1/512 [degree >= d reached] + d=10 nonzero 2000/2000 = 1.0000 mean out-bits set 256.4/512 [degree >= d reached] + d=11 nonzero 2000/2000 = 1.0000 mean out-bits set 256.3/512 [degree >= d reached] + d=12 nonzero 2000/2000 = 1.0000 mean out-bits set 256.2/512 [degree >= d reached] + d=13 nonzero 2000/2000 = 1.0000 mean out-bits set 256.5/512 [degree >= d reached] + d=14 nonzero 2000/2000 = 1.0000 mean out-bits set 255.6/512 [degree >= d reached] + d=15 nonzero 2000/2000 = 1.0000 mean out-bits set 256.5/512 [degree >= d reached] + d=16 nonzero 2000/2000 = 1.0000 mean out-bits set 256.0/512 [degree >= d reached] + READING: the smallest d at which nonzero is ~1.0 is the degree floor; high degree at small d means no low-degree algebraic shortcut across the applications +integral day=20752 apps=2 placements_per_d=2000 threads=44 + d = cube dimension; 'nonzero' = placements whose cube-sum is nonzero on >=1 output bit (degree >= d reached) + d= 1 nonzero 2000/2000 = 1.0000 mean out-bits set 256.0/512 [degree >= d reached] + d= 2 nonzero 2000/2000 = 1.0000 mean out-bits set 256.0/512 [degree >= d reached] + d= 3 nonzero 2000/2000 = 1.0000 mean out-bits set 255.9/512 [degree >= d reached] + d= 4 nonzero 2000/2000 = 1.0000 mean out-bits set 255.5/512 [degree >= d reached] + d= 5 nonzero 2000/2000 = 1.0000 mean out-bits set 256.0/512 [degree >= d reached] + d= 6 nonzero 2000/2000 = 1.0000 mean out-bits set 255.8/512 [degree >= d reached] + d= 7 nonzero 2000/2000 = 1.0000 mean out-bits set 255.6/512 [degree >= d reached] + d= 8 nonzero 2000/2000 = 1.0000 mean out-bits set 256.5/512 [degree >= d reached] + d= 9 nonzero 2000/2000 = 1.0000 mean out-bits set 256.2/512 [degree >= d reached] + d=10 nonzero 2000/2000 = 1.0000 mean out-bits set 256.0/512 [degree >= d reached] + d=11 nonzero 2000/2000 = 1.0000 mean out-bits set 256.5/512 [degree >= d reached] + d=12 nonzero 2000/2000 = 1.0000 mean out-bits set 256.1/512 [degree >= d reached] + d=13 nonzero 2000/2000 = 1.0000 mean out-bits set 255.9/512 [degree >= d reached] + d=14 nonzero 2000/2000 = 1.0000 mean out-bits set 255.7/512 [degree >= d reached] + d=15 nonzero 2000/2000 = 1.0000 mean out-bits set 255.7/512 [degree >= d reached] + d=16 nonzero 2000/2000 = 1.0000 mean out-bits set 255.7/512 [degree >= d reached] + READING: the smallest d at which nonzero is ~1.0 is the degree floor; high degree at small d means no low-degree algebraic shortcut across the applications +integral day=20753 apps=2 placements_per_d=2000 threads=44 + d = cube dimension; 'nonzero' = placements whose cube-sum is nonzero on >=1 output bit (degree >= d reached) + d= 1 nonzero 2000/2000 = 1.0000 mean out-bits set 255.9/512 [degree >= d reached] + d= 2 nonzero 2000/2000 = 1.0000 mean out-bits set 255.7/512 [degree >= d reached] + d= 3 nonzero 2000/2000 = 1.0000 mean out-bits set 256.2/512 [degree >= d reached] + d= 4 nonzero 2000/2000 = 1.0000 mean out-bits set 255.6/512 [degree >= d reached] + d= 5 nonzero 2000/2000 = 1.0000 mean out-bits set 256.1/512 [degree >= d reached] + d= 6 nonzero 2000/2000 = 1.0000 mean out-bits set 255.9/512 [degree >= d reached] + d= 7 nonzero 2000/2000 = 1.0000 mean out-bits set 255.7/512 [degree >= d reached] + d= 8 nonzero 2000/2000 = 1.0000 mean out-bits set 256.0/512 [degree >= d reached] + d= 9 nonzero 2000/2000 = 1.0000 mean out-bits set 256.2/512 [degree >= d reached] + d=10 nonzero 2000/2000 = 1.0000 mean out-bits set 256.4/512 [degree >= d reached] + d=11 nonzero 2000/2000 = 1.0000 mean out-bits set 255.9/512 [degree >= d reached] + d=12 nonzero 2000/2000 = 1.0000 mean out-bits set 256.1/512 [degree >= d reached] + d=13 nonzero 2000/2000 = 1.0000 mean out-bits set 255.6/512 [degree >= d reached] + d=14 nonzero 2000/2000 = 1.0000 mean out-bits set 255.8/512 [degree >= d reached] + d=15 nonzero 2000/2000 = 1.0000 mean out-bits set 256.2/512 [degree >= d reached] + d=16 nonzero 2000/2000 = 1.0000 mean out-bits set 255.9/512 [degree >= d reached] + READING: the smallest d at which nonzero is ~1.0 is the degree floor; high degree at small d means no low-degree algebraic shortcut across the applications +integral day=20754 apps=2 placements_per_d=2000 threads=44 + d = cube dimension; 'nonzero' = placements whose cube-sum is nonzero on >=1 output bit (degree >= d reached) + d= 1 nonzero 2000/2000 = 1.0000 mean out-bits set 255.9/512 [degree >= d reached] + d= 2 nonzero 2000/2000 = 1.0000 mean out-bits set 256.0/512 [degree >= d reached] + d= 3 nonzero 2000/2000 = 1.0000 mean out-bits set 255.9/512 [degree >= d reached] + d= 4 nonzero 2000/2000 = 1.0000 mean out-bits set 255.8/512 [degree >= d reached] + d= 5 nonzero 2000/2000 = 1.0000 mean out-bits set 255.9/512 [degree >= d reached] + d= 6 nonzero 2000/2000 = 1.0000 mean out-bits set 255.7/512 [degree >= d reached] + d= 7 nonzero 2000/2000 = 1.0000 mean out-bits set 256.1/512 [degree >= d reached] + d= 8 nonzero 2000/2000 = 1.0000 mean out-bits set 256.1/512 [degree >= d reached] + d= 9 nonzero 2000/2000 = 1.0000 mean out-bits set 255.3/512 [degree >= d reached] + d=10 nonzero 2000/2000 = 1.0000 mean out-bits set 255.9/512 [degree >= d reached] + d=11 nonzero 2000/2000 = 1.0000 mean out-bits set 256.0/512 [degree >= d reached] + d=12 nonzero 2000/2000 = 1.0000 mean out-bits set 255.6/512 [degree >= d reached] + d=13 nonzero 2000/2000 = 1.0000 mean out-bits set 256.2/512 [degree >= d reached] + d=14 nonzero 2000/2000 = 1.0000 mean out-bits set 256.5/512 [degree >= d reached] + d=15 nonzero 2000/2000 = 1.0000 mean out-bits set 256.3/512 [degree >= d reached] + d=16 nonzero 2000/2000 = 1.0000 mean out-bits set 256.0/512 [degree >= d reached] + READING: the smallest d at which nonzero is ~1.0 is the degree floor; high degree at small d means no low-degree algebraic shortcut across the applications +integral day=20755 apps=2 placements_per_d=2000 threads=44 + d = cube dimension; 'nonzero' = placements whose cube-sum is nonzero on >=1 output bit (degree >= d reached) + d= 1 nonzero 2000/2000 = 1.0000 mean out-bits set 256.2/512 [degree >= d reached] + d= 2 nonzero 2000/2000 = 1.0000 mean out-bits set 255.8/512 [degree >= d reached] + d= 3 nonzero 2000/2000 = 1.0000 mean out-bits set 256.1/512 [degree >= d reached] + d= 4 nonzero 2000/2000 = 1.0000 mean out-bits set 256.0/512 [degree >= d reached] + d= 5 nonzero 2000/2000 = 1.0000 mean out-bits set 256.3/512 [degree >= d reached] + d= 6 nonzero 2000/2000 = 1.0000 mean out-bits set 256.1/512 [degree >= d reached] + d= 7 nonzero 2000/2000 = 1.0000 mean out-bits set 256.1/512 [degree >= d reached] + d= 8 nonzero 2000/2000 = 1.0000 mean out-bits set 255.9/512 [degree >= d reached] + d= 9 nonzero 2000/2000 = 1.0000 mean out-bits set 256.3/512 [degree >= d reached] + d=10 nonzero 2000/2000 = 1.0000 mean out-bits set 255.8/512 [degree >= d reached] + d=11 nonzero 2000/2000 = 1.0000 mean out-bits set 255.8/512 [degree >= d reached] + d=12 nonzero 2000/2000 = 1.0000 mean out-bits set 255.7/512 [degree >= d reached] + d=13 nonzero 2000/2000 = 1.0000 mean out-bits set 256.1/512 [degree >= d reached] + d=14 nonzero 2000/2000 = 1.0000 mean out-bits set 256.1/512 [degree >= d reached] + d=15 nonzero 2000/2000 = 1.0000 mean out-bits set 256.5/512 [degree >= d reached] + d=16 nonzero 2000/2000 = 1.0000 mean out-bits set 255.8/512 [degree >= d reached] + READING: the smallest d at which nonzero is ~1.0 is the degree floor; high degree at small d means no low-degree algebraic shortcut across the applications +integral day=20756 apps=2 placements_per_d=2000 threads=44 + d = cube dimension; 'nonzero' = placements whose cube-sum is nonzero on >=1 output bit (degree >= d reached) + d= 1 nonzero 2000/2000 = 1.0000 mean out-bits set 256.2/512 [degree >= d reached] + d= 2 nonzero 2000/2000 = 1.0000 mean out-bits set 256.3/512 [degree >= d reached] + d= 3 nonzero 2000/2000 = 1.0000 mean out-bits set 256.3/512 [degree >= d reached] + d= 4 nonzero 2000/2000 = 1.0000 mean out-bits set 255.9/512 [degree >= d reached] + d= 5 nonzero 2000/2000 = 1.0000 mean out-bits set 256.0/512 [degree >= d reached] + d= 6 nonzero 2000/2000 = 1.0000 mean out-bits set 255.9/512 [degree >= d reached] + d= 7 nonzero 2000/2000 = 1.0000 mean out-bits set 256.1/512 [degree >= d reached] + d= 8 nonzero 2000/2000 = 1.0000 mean out-bits set 256.3/512 [degree >= d reached] + d= 9 nonzero 2000/2000 = 1.0000 mean out-bits set 256.3/512 [degree >= d reached] + d=10 nonzero 2000/2000 = 1.0000 mean out-bits set 256.3/512 [degree >= d reached] + d=11 nonzero 2000/2000 = 1.0000 mean out-bits set 256.0/512 [degree >= d reached] + d=12 nonzero 2000/2000 = 1.0000 mean out-bits set 255.6/512 [degree >= d reached] + d=13 nonzero 2000/2000 = 1.0000 mean out-bits set 255.9/512 [degree >= d reached] + d=14 nonzero 2000/2000 = 1.0000 mean out-bits set 255.9/512 [degree >= d reached] + d=15 nonzero 2000/2000 = 1.0000 mean out-bits set 256.0/512 [degree >= d reached] + d=16 nonzero 2000/2000 = 1.0000 mean out-bits set 255.7/512 [degree >= d reached] + READING: the smallest d at which nonzero is ~1.0 is the degree floor; high degree at small d means no low-degree algebraic shortcut across the applications +integral day=20757 apps=2 placements_per_d=2000 threads=44 + d = cube dimension; 'nonzero' = placements whose cube-sum is nonzero on >=1 output bit (degree >= d reached) + d= 1 nonzero 2000/2000 = 1.0000 mean out-bits set 256.0/512 [degree >= d reached] + d= 2 nonzero 2000/2000 = 1.0000 mean out-bits set 255.9/512 [degree >= d reached] + d= 3 nonzero 2000/2000 = 1.0000 mean out-bits set 255.9/512 [degree >= d reached] + d= 4 nonzero 2000/2000 = 1.0000 mean out-bits set 256.5/512 [degree >= d reached] + d= 5 nonzero 2000/2000 = 1.0000 mean out-bits set 256.0/512 [degree >= d reached] + d= 6 nonzero 2000/2000 = 1.0000 mean out-bits set 256.0/512 [degree >= d reached] + d= 7 nonzero 2000/2000 = 1.0000 mean out-bits set 255.9/512 [degree >= d reached] + d= 8 nonzero 2000/2000 = 1.0000 mean out-bits set 255.9/512 [degree >= d reached] + d= 9 nonzero 2000/2000 = 1.0000 mean out-bits set 256.3/512 [degree >= d reached] + d=10 nonzero 2000/2000 = 1.0000 mean out-bits set 256.0/512 [degree >= d reached] + d=11 nonzero 2000/2000 = 1.0000 mean out-bits set 256.4/512 [degree >= d reached] + d=12 nonzero 2000/2000 = 1.0000 mean out-bits set 256.0/512 [degree >= d reached] + d=13 nonzero 2000/2000 = 1.0000 mean out-bits set 255.5/512 [degree >= d reached] + d=14 nonzero 2000/2000 = 1.0000 mean out-bits set 256.2/512 [degree >= d reached] + d=15 nonzero 2000/2000 = 1.0000 mean out-bits set 256.0/512 [degree >= d reached] + d=16 nonzero 2000/2000 = 1.0000 mean out-bits set 256.2/512 [degree >= d reached] + READING: the smallest d at which nonzero is ~1.0 is the degree floor; high degree at small d means no low-degree algebraic shortcut across the applications +integral day=20758 apps=2 placements_per_d=2000 threads=44 + d = cube dimension; 'nonzero' = placements whose cube-sum is nonzero on >=1 output bit (degree >= d reached) + d= 1 nonzero 2000/2000 = 1.0000 mean out-bits set 256.3/512 [degree >= d reached] + d= 2 nonzero 2000/2000 = 1.0000 mean out-bits set 255.9/512 [degree >= d reached] + d= 3 nonzero 2000/2000 = 1.0000 mean out-bits set 255.9/512 [degree >= d reached] + d= 4 nonzero 2000/2000 = 1.0000 mean out-bits set 256.0/512 [degree >= d reached] + d= 5 nonzero 2000/2000 = 1.0000 mean out-bits set 255.7/512 [degree >= d reached] + d= 6 nonzero 2000/2000 = 1.0000 mean out-bits set 255.8/512 [degree >= d reached] + d= 7 nonzero 2000/2000 = 1.0000 mean out-bits set 255.9/512 [degree >= d reached] + d= 8 nonzero 2000/2000 = 1.0000 mean out-bits set 255.8/512 [degree >= d reached] + d= 9 nonzero 2000/2000 = 1.0000 mean out-bits set 256.3/512 [degree >= d reached] + d=10 nonzero 2000/2000 = 1.0000 mean out-bits set 255.7/512 [degree >= d reached] + d=11 nonzero 2000/2000 = 1.0000 mean out-bits set 255.9/512 [degree >= d reached] + d=12 nonzero 2000/2000 = 1.0000 mean out-bits set 255.9/512 [degree >= d reached] + d=13 nonzero 2000/2000 = 1.0000 mean out-bits set 256.1/512 [degree >= d reached] + d=14 nonzero 2000/2000 = 1.0000 mean out-bits set 256.1/512 [degree >= d reached] + d=15 nonzero 2000/2000 = 1.0000 mean out-bits set 255.4/512 [degree >= d reached] + d=16 nonzero 2000/2000 = 1.0000 mean out-bits set 255.8/512 [degree >= d reached] + READING: the smallest d at which nonzero is ~1.0 is the degree floor; high degree at small d means no low-degree algebraic shortcut across the applications +integral day=20759 apps=2 placements_per_d=2000 threads=44 + d = cube dimension; 'nonzero' = placements whose cube-sum is nonzero on >=1 output bit (degree >= d reached) + d= 1 nonzero 2000/2000 = 1.0000 mean out-bits set 256.1/512 [degree >= d reached] + d= 2 nonzero 2000/2000 = 1.0000 mean out-bits set 256.2/512 [degree >= d reached] + d= 3 nonzero 2000/2000 = 1.0000 mean out-bits set 256.1/512 [degree >= d reached] + d= 4 nonzero 2000/2000 = 1.0000 mean out-bits set 256.3/512 [degree >= d reached] + d= 5 nonzero 2000/2000 = 1.0000 mean out-bits set 255.8/512 [degree >= d reached] + d= 6 nonzero 2000/2000 = 1.0000 mean out-bits set 255.8/512 [degree >= d reached] + d= 7 nonzero 2000/2000 = 1.0000 mean out-bits set 256.2/512 [degree >= d reached] + d= 8 nonzero 2000/2000 = 1.0000 mean out-bits set 255.9/512 [degree >= d reached] + d= 9 nonzero 2000/2000 = 1.0000 mean out-bits set 256.5/512 [degree >= d reached] + d=10 nonzero 2000/2000 = 1.0000 mean out-bits set 256.1/512 [degree >= d reached] + d=11 nonzero 2000/2000 = 1.0000 mean out-bits set 255.9/512 [degree >= d reached] + d=12 nonzero 2000/2000 = 1.0000 mean out-bits set 255.8/512 [degree >= d reached] + d=13 nonzero 2000/2000 = 1.0000 mean out-bits set 256.1/512 [degree >= d reached] + d=14 nonzero 2000/2000 = 1.0000 mean out-bits set 255.9/512 [degree >= d reached] + d=15 nonzero 2000/2000 = 1.0000 mean out-bits set 255.8/512 [degree >= d reached] + d=16 nonzero 2000/2000 = 1.0000 mean out-bits set 256.2/512 [degree >= d reached] + READING: the smallest d at which nonzero is ~1.0 is the degree floor; high degree at small d means no low-degree algebraic shortcut across the applications +integral day=20760 apps=2 placements_per_d=2000 threads=44 + d = cube dimension; 'nonzero' = placements whose cube-sum is nonzero on >=1 output bit (degree >= d reached) + d= 1 nonzero 2000/2000 = 1.0000 mean out-bits set 256.1/512 [degree >= d reached] + d= 2 nonzero 2000/2000 = 1.0000 mean out-bits set 255.7/512 [degree >= d reached] + d= 3 nonzero 2000/2000 = 1.0000 mean out-bits set 256.1/512 [degree >= d reached] + d= 4 nonzero 2000/2000 = 1.0000 mean out-bits set 255.7/512 [degree >= d reached] + d= 5 nonzero 2000/2000 = 1.0000 mean out-bits set 255.7/512 [degree >= d reached] + d= 6 nonzero 2000/2000 = 1.0000 mean out-bits set 256.3/512 [degree >= d reached] + d= 7 nonzero 2000/2000 = 1.0000 mean out-bits set 256.4/512 [degree >= d reached] + d= 8 nonzero 2000/2000 = 1.0000 mean out-bits set 255.9/512 [degree >= d reached] + d= 9 nonzero 2000/2000 = 1.0000 mean out-bits set 255.9/512 [degree >= d reached] + d=10 nonzero 2000/2000 = 1.0000 mean out-bits set 255.9/512 [degree >= d reached] + d=11 nonzero 2000/2000 = 1.0000 mean out-bits set 256.0/512 [degree >= d reached] + d=12 nonzero 2000/2000 = 1.0000 mean out-bits set 255.7/512 [degree >= d reached] + d=13 nonzero 2000/2000 = 1.0000 mean out-bits set 255.7/512 [degree >= d reached] + d=14 nonzero 2000/2000 = 1.0000 mean out-bits set 256.0/512 [degree >= d reached] + d=15 nonzero 2000/2000 = 1.0000 mean out-bits set 255.8/512 [degree >= d reached] + d=16 nonzero 2000/2000 = 1.0000 mean out-bits set 255.8/512 [degree >= d reached] + READING: the smallest d at which nonzero is ~1.0 is the degree floor; high degree at small d means no low-degree algebraic shortcut across the applications diff --git a/docs/analysis/cryptanalysis/logs/adv-mixer/queue-12-adv-mixer-integral-days.sh.log b/docs/analysis/cryptanalysis/logs/adv-mixer/queue-12-adv-mixer-integral-days.sh.log new file mode 100644 index 000000000..4fde0fdc6 --- /dev/null +++ b/docs/analysis/cryptanalysis/logs/adv-mixer/queue-12-adv-mixer-integral-days.sh.log @@ -0,0 +1,6 @@ +start igneum-build-2 2026-10-07T18:50:34Z bbfab24075923083f0c9c8c4372a6dd22257c245bac75ba6fadbd60ab64ec803 /srv/builds/_adv-adv-mixer/bin/attack-adv-mixer +== integral-a1-32d 2026-10-07T18:50:34Z +rc=0 +== integral-a2-32d 2026-10-07T18:52:24Z +rc=0 +end 2026-10-07T18:54:55Z diff --git a/docs/analysis/cryptanalysis/report-mixer.md b/docs/analysis/cryptanalysis/report-mixer.md index b8aed60d2..f8ce03809 100644 --- a/docs/analysis/cryptanalysis/report-mixer.md +++ b/docs/analysis/cryptanalysis/report-mixer.md @@ -199,7 +199,16 @@ one of 1024 consecutive chain days (about 2.8 years of calendar). No fold, no co ### Integral degree test over 32 days (integral), queue 12, box 2 Command: `attack-adv-mixer integral --day 20729 --apps K --dmax 16 --placements 2000 --days 32` for K = 1, 2. -RUNNING; the row lands here. +32 consecutive chain days (20729 to 20760), cube dimensions d = 1..16, 2000 placements each: 512 (day, d) rows +per K. Wall about 4 min on box 2 at load about 500. + +| Applications K | Rows with every cube-sum nonzero | Output bits set per cube-sum (min to max over days) | Reading | +|---|---|---|---| +| 1 | 511 of 512 (the one exception: day 20730, d = 4, 1999 of 2000 placements) | 156 to 245 of 512 | degree >= 16 on every day; the single zero cube-sum in 1,024,000 placements is a chance zero, not a relation (a relation would zero every placement) | +| 2 | 512 of 512 | 255.5 to 256.7 of 512 | saturated at the random-map value of 256 on every day | + +Verdict: the degree floor of the first report (>= 16 after one application, saturated after two) holds on +32 consecutive days. No day has a low-degree algebraic form of the applications. ### SAT model of two keyed applications (cnf), queue 14 then a solve on box 2 @@ -212,6 +221,15 @@ and that binary is running on this instance under a one-hour cap at nice 10 (log RUNNING; the row lands here. A timeout is the honest expected outcome: the instance is a preimage-shaped search on a 2^512 space, and a plain timeout is a bound on solver reach, not evidence either way. +## Sibling queue files run by this lane + +Per main's rule (claim the next unclaimed sibling file in name order once the own queue is empty), this lane +claimed and ran the following. The results belong to the owning lane and are not interpreted here. + +| File | Owner | Claimed | Run on | Result | +|---|---|---|---|---| +| 07-adv-mixer-3-days.sh | adv-mixer-3 | 20:54 BST | box 1, nice 10, cores 8-95 | RUNNING; the owner's logs land in /srv/builds/_adv-mixer-3/logs; the wrapper log is queue-07-adv-mixer-3-days.sh.log under this lane's logs | + ## Confirmation across the stale and frozen trees The branch was first cut from stale master 3f0afcd5. Its igneum-pow differed from the frozen object in six @@ -235,7 +253,16 @@ No GPU pods used: pod-hours 0. All CPU, nice 10, both boxes. | Q2 diffusion sweep K=1..8, 2e6 states | box 2 | 11 min | | Q1 fold + integral + spot-checks | box 1 | 1 min 44 s | -Total about 0.4 box-hours of the 8-hour first-results budget (ask line 16). Pod-hours 0. +| Q1 deepening queue 11 fold-sweep 1024 days | box 1 | 84 s | +| Q1 deepening queue 12 integral 32 days | box 2 | 4 min 21 s | +| Q1 deepening queue 13 lineindex + addr linrel | box 1 | 77 s | +| Q1 deepening queue 14 linrel + cnf | box 2 | 10 s | +| cadical on the commutation CNF | box 2 | one thread, capped at 1 h | +| Sibling 07-adv-mixer-3-days.sh (owner adv-mixer-3) | box 1 | running | + +Total about 0.6 box-hours of the 8-hour first-results budget (ask line 16), plus up to 1 core-hour of cadical. +Pod-hours 0. Both boxes ran at load 240 to 555 on 96 cores during the deepening (sibling sweeps, not builds), so +wall times above are under heavy sharing. ## Rule-change timeline (so the box-hours stay honest)