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adv-mixer-2: row Q7 measured (redraw rule: after-fraction 0 over 2^24 days), log

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Co-Authored-By: Claude Fable 5.1 <noreply@anthropic.com>
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docs/analysis/cryptanalysis/logs/adv-mixer-2/redraw-2p24-206.log Normal file
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2026-10-07T20:53:06Z start redraw-2p24-206 (lease pool 32 min 16): /srv/builds/_adv-adv-mixer-2/bin/adv-mixer-2 redraw-census --from 20729 --count 2^24 --threads {cores} --max-cost 206
lease: 0 of 16 pool cores free (32 leased), a higher class waits ahead; waiting
lease: holding 16 pool cores (24,25,26,27,28,29,30,31,76,77,78,79,80,81,82,83, waited 6059 s, class adv): adv-mixer-2 redraw-2p24-206
adv-mixer-2 redraw-census --from 20729 --count 2^24 --threads 16 --max-cost 206 | internal adversarial pass, not an independent review | class v4 x8, 72 applications per item | median cost A for gains 226
redraw-census: rule = redraw while cost A < 206 or model C k >= 1 or ROT all equal; 16777216 days from 20729, 8.3 s
| Redraws needed | Days | Fraction |
|---|---|---|
| 0 | 16767195 | 9.994e-1 |
| 1 | 10014 | 5.969e-4 |
| 2 | 7 | 4.172e-7 |
## After the redraw rule: 16777216 days from 20729
| Class | Count | Fraction | log2 | Worst day: cost A, gain A, date |
|---|---|---|---|---|
| ROT all equal | 0 | 0.000e0 | -inf | none |
| ROT distinct <= 2 | 4 | 2.384e-7 | -22.0 | day 57146: 220, 1.0273x, 2126-06-18 |
| ROT distinct <= 3 | 533 | 3.177e-5 | -14.9 | day 14722898: 207, 1.0918x, 42279-12-05 |
| ROT distinct <= 4 | 26005 | 1.550e-3 | -9.3 | day 804699: 206, 1.0971x, 4173-03-11 |
| ROT max multiplicity >= 4 | 35631 | 2.124e-3 | -8.9 | day 74772: 206, 1.0971x, 2174-09-20 |
| ROT same-word pair sums to 32 | 2062531 | 1.229e-1 | -3.0 | day 94648: 206, 1.0971x, 2229-02-20 |
| ROT two same-word pairs sum to 32 | 100726 | 6.004e-3 | -7.4 | day 170878: 206, 1.0971x, 2437-11-06 |
| ROT any pair sums to 32 | 10021966 | 5.974e-1 | -0.7 | day 27016: 206, 1.0971x, 2043-12-20 |
| ROT >= 4 in {1,31} | 16548 | 9.863e-4 | -10.0 | day 311263: 206, 1.0971x, 2822-03-18 |
| ROT all 8 in {1,2,30,31} | 2 | 1.192e-7 | -23.0 | day 14330190: 213, 1.0610x, 41204-09-23 |
| ROT >= 4 in {8,16,24} | 74547 | 4.443e-3 | -7.8 | day 274689: 206, 1.0971x, 2722-01-28 |
| ROT column set == diagonal set | 384 | 2.289e-5 | -15.4 | day 11582441: 209, 1.0813x, 33681-08-24 |
| MUL any = 1 | 0 | 0.000e0 | -inf | none |
| MUL any = 2^32-1 | 0 | 0.000e0 | -inf | none |
| MUL any involution (x^2 = 1) | 0 | 0.000e0 | -inf | none |
| MUL any w32 <= 2 | 0 | 0.000e0 | -inf | none |
| MUL any w32 <= 3 | 63 | 3.755e-6 | -18.0 | day 9046825: 207, 1.0918x, 26739-05-15 |
| MUL any w32 <= 4 | 5986 | 3.568e-4 | -11.5 | day 498141: 206, 1.0971x, 3333-11-12 |
| MUL >= 2 with w32 <= 4 | 0 | 0.000e0 | -inf | none |
| MUL any popcount <= 4 or >= 28 | 4998 | 2.979e-4 | -11.7 | day 321675: 206, 1.0971x, 2850-09-19 |
| MUL two equal | 0 | 0.000e0 | -inf | none |
| MUL two inverse (a*b = 1) | 1 | 5.960e-8 | -24.0 | day 12321130: 232, 0.9741x, 35704-02-10 |
| MUL any in exact 2-adder set (model C k >= 1) | 0 | 0.000e0 | -inf | none |
| MUL model C k >= 2 | 0 | 0.000e0 | -inf | none |
| RC any = 0 | 0 | 0.000e0 | -inf | none |
| RC any popcount <= 4 or >= 28 | 5183 | 3.089e-4 | -11.7 | day 9198601: 207, 1.0918x, 27154-12-01 |
| RC + rk = 0 for any of the 72 keys | 10 | 5.960e-7 | -20.7 | day 3194363: 212, 1.0660x, 10715-11-15 |
| RC two equal | 1 | 5.960e-8 | -24.0 | day 2875598: 220, 1.0273x, 9843-02-14 |
| RC[i] + rk = RC[j] + rk' for some i != j, two of the 72 keys | 76 | 4.530e-6 | -17.8 | day 3826820: 211, 1.0711x, 12447-06-24 |
| cost A gain >= 1.1x | 0 | 0.000e0 | -inf | none |
| cost A gain >= 1.2x | 0 | 0.000e0 | -inf | none |
| cost A gain >= 1.5x | 0 | 0.000e0 | -inf | none |
| Cost A statistic | Value |
|---|---|
| mean | 225.792 |
| median (this census) | 226 |
| median used for gains | 226 |
| min | 206 (gain 1.0971x) |
| max | 257 |
| days with gain A >= 1.05x (cost <= 215) | 782984 (4.667e-2, log2 -4.4) |
| days with gain A >= 1.1x (cost <= 205) | 0 (0.000e0, log2 -inf) |
| days with gain A >= 1.2x (cost <= 188) | 0 (0.000e0, log2 -inf) |
| days with gain A >= 1.5x (cost <= 150) | 0 (0.000e0, log2 -inf) |
| days with gain A >= 2x (cost <= 113) | 0 (0.000e0, log2 -inf) |
| Model C k | Days |
|---|---|
| 0 (gain 1.0000x) | 16777216 |
| w32 per word | Count | Fraction |
|---|---|---|
| 3 | 63 | 2.347e-7 |
| 4 | 5923 | 2.206e-5 |
| 5 | 64356 | 2.397e-4 |
| 6 | 474522 | 1.768e-3 |
| 7 | 2485126 | 9.258e-3 |
| 8 | 9444678 | 3.518e-2 |
| 9 | 25903310 | 9.650e-2 |
| 10 | 50634472 | 1.886e-1 |
| 11 | 68787631 | 2.563e-1 |
| 12 | 62385076 | 2.324e-1 |
| 13 | 35325627 | 1.316e-1 |
| 14 | 11217095 | 4.179e-2 |
| 15 | 1637985 | 6.102e-3 |
| 16 | 69592 | 2.593e-4 |
| Cost A | Days |
|---|---|
| 206 | 6723 |
| 207 | 11133 |
| 208 | 17599 |
| 209 | 27170 |
| 210 | 41294 |
| 211 | 61912 |
| 212 | 88589 |
| 213 | 125512 |
| 214 | 172244 |
| 215 | 230808 |
| 216 | 301058 |
| 217 | 384074 |
| 218 | 479343 |
| 219 | 581994 |
| 220 | 688482 |
| 221 | 795374 |
| 222 | 894929 |
| 223 | 980480 |
| 224 | 1044184 |
| 225 | 1086025 |
| 226 | 1097816 |
| 227 | 1083051 |
| 228 | 1035556 |
| 229 | 966507 |
| 230 | 879269 |
| 231 | 773993 |
| 232 | 665591 |
| 233 | 554660 |
| 234 | 448812 |
| 235 | 354267 |
| 236 | 269627 |
| 237 | 200632 |
| 238 | 143983 |
| 239 | 100948 |
| 240 | 68459 |
| 241 | 45041 |
| 242 | 28659 |
| 243 | 17530 |
| 244 | 10563 |
| 245 | 6130 |
| 246 | 3454 |
| 247 | 1792 |
| 248 | 976 |
| 249 | 511 |
| 250 | 245 |
| 251 | 108 |
| 252 | 65 |
| 253 | 23 |
| 254 | 13 |
| 255 | 2 |
| 256 | 5 |
| 257 | 1 |
Lowest-cost days (cost A, day, date, gain A):
206 27016 2043-12-20 1.0971x
206 43428 2088-11-25 1.0971x
206 51241 2110-04-18 1.0971x
206 53114 2115-06-04 1.0971x
206 62837 2142-01-16 1.0971x
206 63489 2143-10-30 1.0971x
206 68173 2156-08-26 1.0971x
206 68393 2157-04-03 1.0971x
206 69945 2161-07-03 1.0971x
206 73231 2170-07-02 1.0971x
206 74772 2174-09-20 1.0971x
206 75398 2176-06-07 1.0971x
206 84603 2201-08-21 1.0971x
206 85594 2204-05-08 1.0971x
206 86393 2206-07-16 1.0971x
206 92181 2222-05-21 1.0971x
lease: released 16 pool cores after 6068 s, exit 0
2026-10-07T22:34:14Z end redraw-2p24-206 rc=0

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docs/analysis/cryptanalysis/logs/adv-mixer-2/redraw-2p28-206.log Normal file
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2026-10-07T22:34:14Z start redraw-2p28-206 (lease pool 32 min 16): /srv/builds/_adv-adv-mixer-2/bin/adv-mixer-2 redraw-census --from 20729 --count 2^28 --threads {cores} --max-cost 206
lease: holding 16 pool cores (24,25,26,27,28,29,30,31,76,77,78,79,80,81,82,83, waited 0 s, class adv): adv-mixer-2 redraw-2p28-206
adv-mixer-2 redraw-census --from 20729 --count 2^28 --threads 16 --max-cost 206 | internal adversarial pass, not an independent review | class v4 x8, 72 applications per item | median cost A for gains 226

32
docs/analysis/cryptanalysis/report-mixer-2.md
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@ -56,7 +56,7 @@ take even if it buys no hash rate against the chip model's attacker. The worst r
| Q5 cross-day structure | seed collisions, stream shifts by k in 1..72, shared MUL and RC values over the calendar | planted shift pair (found) | counts against expectation | 64-bit seed collisions 0 (expected 3.6e-11); stream shifts 0 (expected 5.2e-9); MUL values shared between two days 77 (expected 79.5), RC 39 (39.8): chance, and a shared constant hands a datapath nothing (the other 39 draws differ) | PASS (BOUND: nothing beyond chance) |
| Q2 model B | `scm-refine` on the calendar (36,525 days), on the lowest 2^14 days of the 2^24 census, on a 2^16-day random sample | the self-test constants (3, 5, 7, 9, 2^32 - 1, 2^31 + 1 at 1 adder; 45 at 2): all as expected | the certified-cost distribution | exact sets: 90 constants at 1 adder, 4,101 at 2, 185,223 at 3, 7,983,205 at 4 (0.38 percent of odd constants at 4 or fewer under the restricted form); random words certified at 5 or fewer: 12.3 percent; the rest uncertified. Cost B is a PARTIAL metric (a certified word costs 5, an uncertified one w32 - 1), so its between-day spread (sample: mean 219, min 176; calendar worst day 43959 = 2090-05-10 at B 181) is the certificate's selectivity, not a measured gain, and is not read as one | PARTIAL (bound on the per-word chain length only) |
| Q6 ROT diffusion | `avalanche` (1, 2, 3, 4, 8 applications; the 22 address bits; 1,024 states x 512 input bits) on the genesis day, the plants, the 7 worst ROT days of the census | plant rot1 and weakday must read weaker than the genesis day at 1 application: they do (mean flip 0.345 and 0.324 against 0.461; 16,197 and 11,454 input-output pairs never flipped against 5,534) | a per-day gain only if a bit-exact shortcut follows | at 2 applications every day, planted days included, reads mean 0.500, every output bit between 0.42 and 0.58 (sampling spread of 1,024 states), address bits 0.500, no pair unflipped; 8 applications sit between reads. No day gives a shortcut; gain 0 | PASS (BOUND) |
| Q7 redraw rule | `redraw-census` 2^24 and 2^28 days with the rule below | `--max-cost 0` must reproduce the real draw on 1,000 days (asserted in the binary) | fraction redrawn; residual over 1.1x must be 0 | queue 07 | RUNNING |
| Q7 redraw rule | `redraw-census` 2^24 and 2^28 days with the rule below | `--max-cost 0` must reproduce the real draw on 1,000 days (asserted in the binary; passed) | fraction redrawn; residual over 1.1x must be 0 | 2^24 days: 10,014 redrawn once (5.97e-4), 7 twice (4.2e-7), none three times; after the rule gain A >= 1.1x on 0 days (min cost 206, 1.097x), model C k = 0 on every day, ROT all equal 0; mean cost 225.79 (225.78 before), the 1.05x fraction 4.67e-2 (4.72e-2 before): the rule touches only the tail. 2^28 run PENDING | FINDING closed by the rule (after-fraction 0 on 2^24) |
| Q8 anything else | watched while the rows ran; three observations, no box time | n/a | stated or measured | (1) Lead time: the only per-day attacker is an FPGA bitstream synthesised for the day, and synthesis of a full-device design takes hours (approximate, from memory; no figure measured here). Under the interim day rule (`bind::day_bytes`, a pure function of the calendar) the attacker has unlimited lead; under the spec's own proposal O-1.10 (day bytes carry the first epoch seed of the day, known about 20 minutes ahead, section 1.12) a per-day bitstream cannot be ready in time, which removes the whole class without a redraw. (2) The mixer stream is seeded by 64 bits of the day key (K[0], K[1]); K[2..7] enter only the item init; no collision or shift was found in 100 years or 2^24 days, and the planted shift was. (3) The 72 round keys are fixed multiples of 0x9E3779B9; RC + rk = 0 happened on 10 of 2^24 days (expected 4.5, within Poisson) and costs a datapath nothing on either side | PASS (stated) |
| GPU rows | none needed | | | no row of this class depends on a GPU | BLOCKED (not applicable) |
@ -70,8 +70,8 @@ once a day; nothing else changes; every accepted day is a day the current rule c
| Quantity | Value |
|---|---|
| Fraction of days redrawn at least once (exact, models A and C) | 5.694e-4 + 3.123e-5 = 6.0e-4 (2^-10.7), about 22 days per 100 years |
| Fraction over 1.1x under model A after the rule | 0 by construction; measured by queue 07 over 2^24 and 2^28 days (PENDING). Before the rule, measured: 5.677e-4 (2^24 census), 4.107e-4 (the 100-year calendar, 15 of 36,525 days) |
| Fraction of days redrawn at least once | exact 5.694e-4 + 3.123e-5 = 6.0e-4 (2^-10.7), about 22 days per 100 years; measured over 2^24 days 5.97e-4 once, 4.2e-7 twice, never three times |
| Fraction over 1.1x under model A after the rule | 0 measured over 2^24 days (min cost 206, gain 1.097x); 2^28 PENDING. Before the rule, measured: 5.677e-4 (2^24 census), 5.693e-4 (2^32), 4.107e-4 (the 100-year calendar, 15 of 36,525 days) |
| Fraction over 1.1x under model C after the rule | 0 (k = 0 on every accepted day) |
| Chip-model reading after the rule | unchanged: 1.0 on every day before and after |
| What the rule does not fix | the seed is 64 bits of the day key (K[0], K[1]); the day is a pure function of the calendar; both stand; neither is a weakness of this class on the numbers above |
@ -320,6 +320,26 @@ lane's reading of the same numbers is FINDING on the area reading, BOUND for eve
also timed the verifier on the worst day (pending in its record when read), which this lane did not repeat: the
verifier's instruction count is day-independent by construction.
### Q7 the redraw rule, measured (FINDING closed)
Command on box 1 (queue 07, lease held 16 pool cores from 23:32 UK after a 6,059 s wait behind the v5 gate, 8.3 s of
compute): `adv-mixer-2 redraw-census --from 20729 --count 2^24 --threads 16 --max-cost 206` (redraw while cost A <
206, that is <= 205, or model C k >= 1, or all ROT equal). Log: logs/adv-mixer-2/redraw-2p24-206.log. The
self-check inside the binary (`--max-cost 0` on 1,000 days reproduces `MixParams::with_shape` draw for draw) passed.
| Quantity | Before the rule (2^24 census) | After the rule (2^24 days) |
|---|---|---|
| days redrawn once / twice / three times | | 10,014 (5.97e-4) / 7 (4.2e-7) / 0 |
| gain A >= 1.1x | 9,525 (5.68e-4) | 0 |
| gain A >= 1.05x | 792,234 (4.72e-2) | 782,984 (4.67e-2) |
| min cost A | 191 (1.183x) | 206 (1.097x) |
| mean cost A | 225.780 | 225.792 |
| model C k >= 1 | 511 | 0 |
| ROT all equal | 0 | 0 |
Cost to the honest side: forty more SplitMix64 draws on 6e-4 of days, once a day; the verifier and every miner
compute the same rule from the same key. The 2^28 run (queue 07, second line) lands below when the lease serves it.
### Ledger of rule changes during the run (box-hours stay honest)
| Time (UK) | Change | Effect on this lane |
@ -337,9 +357,11 @@ verifier's instruction count is day-independent by construction.
| 21:39 | certificate restructured (shifted-set bitmaps, about 25k lookups per constant), rebuilt on both boxes (sha256 b5d823aa...), chain 03 to 05 restarted on box 2 | |
| 21:40 to 21:4x | queue 03, 04, 05 done on box 2 (scm 2 to 4 s each on 24 to 30 cores; eleven avalanche runs on 1 core each) | 0.03 box-hours |
| 21:42 to 21:53 | queue 06 census 2^32 on box 1, 32 cores, held 616 s (615 s compute; the lease line's "1480 s" counts from the 21:28 submission, 864 s of it waiting) | 0.17 box-hours (32 cores x 616 s / 96) |
| 21:53 | queue 07 redraw-census submitted on box 1; a waiter at class adv behind the v5 gate's leases (correct: it holds nothing); at 22:18 still waiting | |
| 21:53 | queue 07 redraw-census submitted on box 1; a waiter at class adv behind the v5 gate's leases (correct: it holds nothing) | |
| 22:21 | pre-emption at any size for adv holders once a release or v5 waiter has waited 120 s (lease ce30e357) | nothing of mine held cores; noted |
| 23:32 | queue 07 served: 16 cores, redraw 2^24 in 8.3 s; the 2^28 line follows on the same lease | 0.02 box-hours so far |
Box-hours spent so far: 0.29 (the smoke runs, queue 01 to 06 and the stopped 03), counted as cores held x seconds / 96. The redraw census (queue 07, about a minute of 32 cores) waits on box 1 behind the v5 gate. Pod-hours: 0. GPU: none.
Box-hours spent so far: 0.31 (the smoke runs, queue 01 to 07's first line and the stopped 03), counted as cores held x seconds / 96. The redraw census over 2^28 days runs on box 1 on 16 cores. Pod-hours: 0. GPU: none.
## Bound reached, honestly