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adv-mixer-3 report: Q2 day 20729 closed k=1..8 (k=8 clean), SAT k=4 CNF size

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Co-Authored-By: Claude Fable 5.1 <noreply@anthropic.com>
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igneum-labs 2026-10-07 23:07:15 +00:00
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docs/analysis/cryptanalysis/report-mixer-3.md
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@ -25,7 +25,7 @@ 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 |
| 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..7: 0 and 0, worst z 5.28, -4.60, -4.66, 5.01; day 20733 k = 2: 0 and 0, worst z -4.59; k = 3: 0 and 0, worst z 4.61; k = 4: 0 and 0, worst z 4.67; k = 5..8 and the 2^27 rows running | FINDING at k = 1, PASS from k = 2 on both days (margin: 1 of 8 on random states) |
| 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: 0 and 0, worst z -4.59; k = 3: 0 and 0, worst z 4.61; k = 4: 0 and 0, worst z 4.67; k = 5..8 and the 2^27 rows running | FINDING at k = 1, PASS from k = 2 on both days (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 |
| Q4 | single-bit linear correlations, random states, 2^26 samples | k = 0 (the identity, fired: c = 1.0 on the diagonal) | no cell beyond 6 sigma (band 0.00073) | day 20729 k = 1..7 and day 20733 k = 1..8: worst c between 0.00055 and 0.00062 (z 4.5 to 5.1; the expected maximum of 262,144 normals is 4.8), 0 cells beyond 6 sigma on every row; day 20729 k = 8 running | PASS from k = 1 (BOUND) |
@ -89,6 +89,7 @@ run at k = 1 fired it too: 14,364 holes). The `one` plant is the firing check of
| 20729 | 5 | 2^24 | 0 | 0 | in 360 (word 11) to out 82 (word 2) | 0.49944 (z -4.60) | 0 | inside (queue 17, leased) |
| 20729 | 6 | 2^24 | 0 | 0 | in 354 (word 11) to out 291 (word 9) | 0.49943 (z -4.66) | 0 | inside |
| 20729 | 7 | 2^24 | 0 | 0 | in 226 (word 7) to out 440 (word 13) | 0.50061 (z 5.01) | 0 | inside |
| 20729 | 8 | 2^24 | 0 | 0 | in 354 (word 11) to out 114 (word 3) | 0.50056 (z 4.58) | 0 | inside (the full 8 between reads) |
| 20733 | 2 | 2^24 | 0 | 0 | in 260 (word 8) to out 450 (word 14) | 0.49944 (z -4.59) | 0 | inside |
| 20733 | 3 | 2^24 | 0 | 0 | in 61 (word 1) to out 495 (word 15) | 0.50056 (z 4.61) | 0 | inside |
| 20733 | 4 | 2^24 | 0 | 0 | in 350 (word 10) to out 23 (word 0) | 0.50057 (z 4.67) | 0 | inside |
@ -258,7 +259,7 @@ under a millisecond on one core. The solver at k = 1 is five orders slower than
| 20729 | 1 (queue 08, build-2) | 33,873 | 112,328 | SATISFIABLE | 1,593 s (box at load 500) | the same t |
| 20729 | 2 | 68,624 | 227,767 | TIMEOUT at the one-hour cap (rc 124), 91.8 MB | 3,600 s | none |
| 20729 | 3 | 103,375 | 343,206 | TIMEOUT at the one-hour cap (status 124), 149 MB | 3,600 s | none |
| 20729 | 4 | pending | pending | running since 22:41 UTC (one-hour cap) | | |
| 20729 | 4 | 138,126 | 458,645 | running since 22:41 UTC (one-hour cap) | | |
Reading: the one-application model is a 32-variable problem with 112 k clauses of ripple-carry adders (16
constant multiplies of up to 32 adders each dominate). CaDiCaL needs minutes on it where the honest search needs