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attack-pass F4: reconciled with adv-mixer-2 (the carry digit at position 32 counted here and not there; agreed median 226, 15 days a century, worst 2050-04-28 at 1.113x; the rule takes adv-mixer-2's form)

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Co-Authored-By: Claude Fable 5.1 <noreply@anthropic.com>
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igneum-labs 2026-10-07 20:39:42 +00:00
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5
docs/analysis/attack-pass-2026-10.md
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@ -558,6 +558,11 @@ redraw day 22,633; no pack changes. Landed (Counter ASIC lane, 7 October 2026, 1
(`docs/design/class-v5-stored-state.md` section 11) with F4's harness as its gate, re-gated by this lane against the (`docs/design/class-v5-stored-state.md` section 11) with F4's harness as its gate, re-gated by this lane against the
v5 branch once its `accept.rs` carries it. The brief's rank 3 (funding.md B2, the untested all-equal ROT draw of v5 branch once its `accept.rs` carries it. The brief's rank 3 (funding.md B2, the untested all-equal ROT draw of
MEMHARD.md) now reads "a bounded tail, measured", with the F4 record as the source. MEMHARD.md) now reads "a bounded tail, measured", with the F4 record as the source.
Reconciled with adv-mixer-2's independent census (7 October 2026, 21:5x UK; F4 record section 9): the same class
and cost form; this record's NAF counted the carry digit at position 32, which a 32-bit multiplier never pays, so the
agreed figures are adv-mixer-2's: median 226, a 1.1x gain at cost A at most 205, 5.69e-4 of days (2^-10.8), 15 days
a century, worst 2050-04-28 (day 29,337) at 1.113x; the DSP-bound readings agree at 0; the redraw rule for the next
class takes adv-mixer-2's form (cost A at most 205, or k >= 1, or the eight ROT equal).
Status: F4 PASS against v4; AP-F4-1 FIXED-AND-PASSED against v5 once the lane's accept.rs carries the rule and the Status: F4 PASS against v4; AP-F4-1 FIXED-AND-PASSED against v5 once the lane's accept.rs carries the rule and the
census passes against it. census passes against it.

30
docs/analysis/attack-pass/f4-weakday.md
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@ -307,3 +307,33 @@ under 4 in `census-100y.md`); the `ROT` rule redraws one, day 57,146 (2 distinct
* It did not search optimal single-constant multiplication costs (not computable at 2^28 scale); NAF is the standard * It did not search optimal single-constant multiplication costs (not computable at 2^28 scale); NAF is the standard
canonical bound and the ratio between days is what the gate asks. canonical bound and the ratio between days is what the gate asks.
* It did not census the era draw (F7) or the spec's intent for the 64-bit seeding (F7); the fact is stated in section 1. * It did not census the era draw (F7) or the spec's intent for the 64-bit seeding (F7); the fact is stated in section 1.
## 9. Reconciliation with adv-mixer-2's independent census (7 October 2026, 21:5x UK; main's order through the
crypto-engage coordinator: the two tables side by side, the median each used, one agreed figure)
Both censuses read the same class, the FPGA LUT multiplier-adder area (no chip or GPU gain), with the same cost form,
64 + the sum over the sixteen MUL of (signed-digit weight - 1). They differ in one convention. This harness's
`naf_weight` (src/main.rs line 72) computes the canonical NAF of the constant as a `u64` and counts every digit,
including the carry digit at position 32 that a 32-bit odd constant carries with probability 1/3; adv-mixer-2's
`w32` counts the digits at positions 0 to 31 only, because a multiplier modulo 2^32 is never built with a digit at
position 32. Checked on 2^18 random odd constants: mean weight 11.442 with the carry digit against 11.109 without
(P(digit at 32) = 0.3334), cost 231.1 against 225.7. So this record charged every day about 5 adders a 32-bit
multiplier never pays, unevenly per day, which is the whole of 231 against 226 and of 12 against 15 days a century.
| Quantity | This record (M1, carry digit counted) | adv-mixer-2 (model A, w32 modulo 2^32) | Agreed |
|---|---|---|---|
| Cost form | 64 + sum(NAF(MUL_i) - 1), NAF over u64 | 64 + sum(w32(MUL_i) - 1), digits 0 to 31 | adv-mixer-2's: the digit at position 32 costs nothing in a 32-bit multiply |
| Median per application | 231 (census over 2^24 chain days; mean 231.113) | 226 (exact, 16-fold convolution over all 2^31 odd constants; the log's provisional 231 superseded) | 226 |
| Threshold for a 1.1x gain | cost under 210 (NAF sum under 163) | cost A at most 205 | cost A at most 205 |
| Fraction of days over 1.1x | 3.264e-4 (5,476 of 2^24); exact expectation 3.243e-4 | 5.677e-4 (2^24 census); exact 5.694e-4 | 5.69e-4, about 2^-10.8, against the 2^-20 gate |
| Days over 1.1x per century (36,525 public days) | 12 | 15, listed in its Q4 | 15 |
| Worst public day | 29,337 (2050-04-28), cost 206, 1.121x | 29,337 (2050-04-28), cost A 203, 1.113x | 29,337, 1.113x |
| Genesis day 20,729 | cost 226, 0.978x | cost A 219, 1.032x | 219 |
| DSP-bound metric | M2: 0 days with k >= 2 in 2^28; k >= 1 at 1.067x | model C: P(k >= 1) 3.12e-5 (1.067x), P(k >= 2) 4.57e-10 (1.143x) | agree: under the gate at every k |
| Redraw rule for the next class | reject NAF sum under 163 (cost under 211), redraw from the next stream values | cost A at most 205, or k >= 1, or the eight ROT equal: continue the same SplitMix64 stream and draw the forty again | adv-mixer-2's form and numbers |
Verdict unchanged: PASS against class v4 on the DSP-bound reading (M2 and model C agree at 0), the LUT tail bounded
and measured; the agreed numbers above replace this record's M1 figures wherever quoted, and AP-F4-1's rule on the
v5 list takes adv-mixer-2's form. Harness note: `attack-f4 plant` and `day` default `--median` to 221 when the flag is
absent (the plant lines of the class v5 run this evening read "median 221" for that reason); every census line in
this record was run with `--median 231` and is restated against 226 above.