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adv-mixer-3 report: Q1 day 20733 closed k=1..8 (uniform at the real first read on both days)

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Co-Authored-By: Claude Fable 5.1 <noreply@anthropic.com>
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igneum-labs 2026-10-07 23:37:17 +00:00
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docs/analysis/cryptanalysis/report-mixer-3.md
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@ -24,7 +24,7 @@ Plant rule: a tool is trusted once it has fired on a known-failed shape. Which s
| Q | Method | Known-failed shape | Gate | Result (numbers) | Status |
|---|---|---|---|---|---|
| Q1 | exhaustive round-0 line-index census, all 2^32 t, k = 0..8 | k = 0 (the init: one bin holds 2^32, fired on both days) | chi-square z within 6, no empty bin | day 20729: uniform at k = 1 (z -1.13), 2 (-0.68), 3 (-0.39), 4 (-0.47), 5 (-1.47), 6 (-0.30), 7 (-1.04), 8 (1.13, the real first read); day 20733 uniform at k = 1 (z -0.71), its k = 2..8 running under the lock; day 20730 (queue 07) uniform at k = 2, 3, 4, 8 | PASS to k = 8 on day 20729 (BOUND: the index histogram is uniform from k = 1), RUNNING |
| Q1 | exhaustive round-0 line-index census, all 2^32 t, k = 0..8 | k = 0 (the init: one bin holds 2^32, fired on both days) | chi-square z within 6, no empty bin | day 20729: uniform at k = 1 (z -1.13), 2 (-0.68), 3 (-0.39), 4 (-0.47), 5 (-1.47), 6 (-0.30), 7 (-1.04), 8 (1.13, the real first read); day 20733 uniform at k = 1..8 (z -0.71, -1.09, -1.31, -0.20, 1.27, 1.12, 1.25, -0.28); day 20730 (queue 07) uniform at k = 2, 3, 4, 8 | PASS to k = 8 on both days (BOUND: the index histogram is uniform from k = 1) (BOUND: the index histogram is uniform from k = 1), RUNNING |
| Q2 | single-bit avalanche, random states, 2^24 (and 2^27) states | `one` at k = 8 (fired: 1959 holes); `weak` fires at k = 1 only, not at k = 8 (see Q2) | no cell beyond 6 sigma | day 20729 k = 1: 354 holes, 129,726 cells beyond 6 sigma, worst p = 1.000; day 20733 k = 1: 266 holes, 136,797 cells; day 20729 k = 2 at 2^24: 0 holes, 0 cells beyond 6 sigma, worst z -4.74 (band 0.0015); k = 3: 0 and 0, worst z -5.28; k = 4..8: 0 and 0, worst z 5.28, -4.60, -4.66, 5.01, 4.58 (day 20729 closed k = 1..8); day 20733 k = 2..8: 0 and 0, worst z -4.59, 4.61, 4.67, 4.78, 4.55, -4.58, -4.65 (closed k = 1..8); the 2^27 rows at k = 2, 3 running | FINDING at k = 1, PASS from k = 2 on both days, both days complete to k = 8 (margin: 1 of 8 on random states) |
| Q2b | t-bit avalanche on the round-0 input (32 bits in), 2^24 (and 2^28) states | k = 0 (the init alone, fired: 12,439 holes) | no cell beyond 6 sigma | k = 1: 0 holes, 218 cells beyond 6 sigma, worst p = 0.7427 (t bit 31 to state bit 53), 18 line-index cells beyond 6 sigma. k = 2..8 at 2^24: 0 cells beyond 6 sigma, worst z 3.7 to 4.7 (the maximum of 16,384 normals is about 4.1); k = 2, 3, 4 at 2^28 states: 0 cells beyond 6 sigma, worst z -4.30, 4.76, -4.64, band 0.00018. Day 20733: k = 1 has 502 cells beyond 6 sigma, worst p = 0.7595 (t bit 31 to state bit 127); k = 2..8 at 2^24: 0 cells, worst z 3.9 to 4.6; its 2^28 rows running | FINDING at k = 1 on both days, PASS from k = 2 on both days (margin: 1 of 8) |
| Q3 | differential multiplicity, 576 low-weight input differences, 2^20 pairs each | `nomul` at k = 1 (fired: 17,289 deterministic output bits at 4,096 pairs) | no multiplicity 4 or more, no deterministic bit | k = 1: 695 deterministic output bits over the 576 differences (max 35 in one difference) on day 20729, 537 (max 40) on 20733; k = 2..7: 0 deterministic bits, max multiplicity 1, no pair with 2 zero words, both days; k = 8 running | FINDING at k = 1 (deterministic bits), PASS from k = 2 |
@ -62,6 +62,13 @@ Command (build-1), per k: `adv-mixer-3 index --day 20729 --apps k --threads 64`.
| 20730 | 8 | -1.29 | 0 | 867 | 1188 | 0.73 | 1.00 | pending | uniform |
| 20733 | 0 | 6.2e12 | 4194303 | 0 | 2^32 | 7.8e11 | 2.4e10 | n/a | NON-UNIFORM (plant) |
| 20733 | 1 | -0.71 | 0 | 863 | 1202 | 0.11 | -0.60 | pending | uniform |
| 20733 | 2 | -1.09 | 0 | 840 | 1187 | -0.84 | 0.58 | pending | uniform (queue 17, leased) |
| 20733 | 3 | -1.31 | 0 | 862 | 1199 | -1.45 | -1.25 | pending | uniform |
| 20733 | 4 | -0.20 | 0 | 862 | 1180 | 0.27 | 0.72 | pending | uniform |
| 20733 | 5 | 1.27 | 0 | 865 | 1190 | 1.02 | 1.45 | pending | uniform |
| 20733 | 6 | 1.12 | 0 | 865 | 1187 | -0.36 | -1.22 | pending | uniform |
| 20733 | 7 | 1.25 | 0 | 858 | 1197 | 1.30 | -0.21 | pending | uniform |
| 20733 | 8 | -0.28 | 0 | 859 | 1183 | -0.23 | -0.21 | pending | uniform (the real first read) |
Reading: after one application the 2^32 round-0 inputs already spread over the 2^22 lines as a uniform draw
would (Poisson 1024 per bin: min 871, max 1191 are the expected extremes over 4 million bins). The multiply layer