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adv-cache-2: Q3(3) window layer in closed form (internal adversarial pass, not an independent review)

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Co-Authored-By: Claude Fable 5.1 <noreply@anthropic.com>
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igneum-labs 2026-10-07 19:04:23 +00:00
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docs/analysis/cryptanalysis/report-chained-cache-2.md
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@ -130,10 +130,13 @@ The one designed non-uniformity. Each load site's window is the dataset, an alig
| 8 drawn (devnet era, epoch seeds `igneum-adv-cache-2/epoch/k`, k = 1..8), by the draws | 0.2656 / 0.3594 / 0.3555 / 0.4531 | 0.6562 / 0.6328 / 0.7812 |
| Shared devnet epoch 0 (measured over 2^33 reads) | 0.42187 | 0.53125 |
| Devnet 3 epoch 0 (measured over 2^31 reads) | 0.39063 | 0.71875 |
| 4,096 under the devnet era and 4,096 under drawn eras | RUNNING (items 13, 14) | |
| Exact distribution from the draw (win uniform on {0, 1, 2}, off uniform; 16 sites; enumerated over the 74,613 compositions, scratch `python3`, reproduced in section 3.3 below) | 0.2500 / 0.3281 / 0.3382 / 1.0000 (p90 0.4062, p99 0.4688; P(over 0.45) 2.8 percent) | 0.5625 / 0.5811 / 1.0000 (p90 0.6562, p99 0.7500; P(at least 0.75) 2.0 percent) |
| 4,096 under the devnet era and 4,096 under drawn eras (the check of the closed form) | RUNNING (items 13, 17) | |
The plant `all-quarter` (every site forced to one quarter) printed 1.0000 on every program: fired.
The closed form. A site's window is the whole dataset with probability 1/3, either aligned half with 1/6 each, any one aligned quarter with 1/12 each; its reads are 1/16 of the hash's. The share of quarter k is `(1/16) x (n_W / 4 + n_{H containing k} / 2 + n_{Q = k})`. The counts of the seven categories over 16 sites are multinomial, so the distribution of the hottest quarter's share (and of the hottest aligned half's) is a finite sum over the 74,613 compositions of 16 into 7 parts. Result: mean 0.3382 for the top quarter (uniform 0.25) and 0.5811 for the top half (uniform 0.5). At those means the chip model's `f = 0.25` row recomputes 128 x (1 - 0.3382) = 84.7 items instead of 96 (ops per hash 793,400 against 899,072, 0.883x; compute-bound 63.0 MH/s against 55.6) and the `f = 0.5` row 53.6 items instead of 64 (502,400 against 599,552, 0.838x; 99.5 MH/s against 83.4). The two real programs sit at the 90th and 99th percentiles of the quarter distribution (devnet 0.4219, Devnet 3 0.3906) and Devnet 3's half share 0.71875 at the 97th; the 8,192-program census checks the form.
## 4. Q4: the price
Nothing here is a chip measurement; the arithmetic is the chip model's (`chip-model-v3.md` sections 2, 5.2 and 5.4: 9,360 ops per item recomputed, 608 ops per cache block evaluation counted from `chacha_block`, 128 items per hash, SRAM at 128 mm^2 and $46 per 256 MiB at the N5 headline).