From 7ac25503ed693dcdde633b07ac1182f560fa72fe Mon Sep 17 00:00:00 2001 From: igneum-labs <337424239+igneum-labs@users.noreply.github.com> Date: Thu, 8 Oct 2026 08:48:03 +0000 Subject: [PATCH 1/2] attack-pass: AP-F8-1 tail attributed (p4, p8, p10, p34 as per-site bucket concentration at a narrow-window site; the largest-bucket bound named for a next class) Co-Authored-By: Claude Fable 5.1 --- docs/analysis/attack-pass-2026-10.md | 20 +++++++++++++++----- 1 file changed, 15 insertions(+), 5 deletions(-) diff --git a/docs/analysis/attack-pass-2026-10.md b/docs/analysis/attack-pass-2026-10.md index 2212f574d..900090b5f 100644 --- a/docs/analysis/attack-pass-2026-10.md +++ b/docs/analysis/attack-pass-2026-10.md @@ -506,10 +506,10 @@ control, box 2; stream 07a809a7 / 8bdcbdd8, pairing id a788661687db4bb3): FAIL. | p15 | 2.57x | 2, 12 | 4.49 percent | 0.982 | zero through rotl at 0 | | p18 | 2.50x | 6, 30 | 5.55 percent | 0.937 | all-ones through a load | | p56 | 2.01x | 2, 10 | 3.34 percent | 0.994 | unattributed (new over sub-version 1) | -| p10 | 1.50x | 8, 28 | 2.04 percent | 0.979 | unattributed (identical to sub-version 1) | -| p8 | 1.38x | 14, 51 | 1.42 percent | 0.980 | unattributed | -| p34 | 1.25x | 1, 13 | 1.35 percent | 0.997 | one-bit value through sub | -| p4 | 1.22x | 1, 8 | 1.45 percent | 0.981 | unattributed (1.57x on sub-version 1) | +| p10 | 1.50x | 8, 28 | 2.04 percent | 0.979 | bucket concentration at a narrow-window site (r0, window 2^22, offset 1, last writer mad at 20): largest 256-item bucket 5.6x window expectation, index entropy 13.71 of 14 bits, hottest 0x4004da at 362 reads, source none (identical to sub-version 1) | +| p8 | 1.38x | 14, 51 | 1.42 percent | 0.980 | bucket concentration at a narrow-window site (r7, window 2^22, offset 2, last writer xor at 44): largest bucket 3.1x, entropy 13.72 of 14; plus site 6 (instr 33, r3, window 2^23, mad at 30) at 0.834 percent, bucket 3.5x; hottest 0x837de4 at 420 reads, source none | +| p34 | 1.25x | 1, 13 | 1.35 percent | 0.997 | one-bit value through sub (r3, window 2^23, offset 1, last writer sub at 5): largest bucket 3.5x, entropy 14.96 of 15, hottest 0x800010 at 541 reads, saturated source 0.0001 percent | +| p4 | 1.22x | 1, 8 | 1.45 percent | 0.981 | bucket concentration at a narrow-window site (r2, window 2^22, offset 1, last writer mad at 4): largest bucket 4.5x, entropy 13.74 of 14, hottest 0x4000e7 at 355 reads, source none (1.57x on sub-version 1) | Every failing seed is one low-entropy load site. Clean-seed spread of the per-site bucket entropy (848 site rows of sub-version 1's 53 clean seeds): min 0.9865, p1 0.9961, p5 0.9999, so bucket entropy separates only the strong four; @@ -525,7 +525,17 @@ word indices over 2^20 evaluations with the shadow executed against the uniform site ratio 0.9960, p1 0.9990, median 1.0000; the strong five p23 0.8361, p18 0.9274, p19 0.9335, p15 0.9432, p56 0.9654; floor 0.98 sits 0.015 from each side. At 2^24 the weak four (p34 0.9181, p4 0.9614, p8 0.9630, p10 0.9612) share their value with two clean seeds (p44 0.9612, p52 0.9613), so the 2^24 stage is not taken and p4, p8, p10 and -p34 stay the open tail, unattributed. The ratio refuses about 4 percent of candidates that pass every other test +p34 are the tail. The tail attributed (hash lane, 8 October 2026, 09:40 to 09:46 UK, attack-f8 census at 2^24 with +the window-model control and by-site attribution, tree b38b4af6 on the frozen 017e7037; the gate ratios reproduced to +four places, p4 1.2169x, p8 1.3774x, p10 1.5036x, p34 1.2501x, the hot-set verdict clear on the windowed control for +all four): each is a per-site bucket concentration of about a quarter bit (0.26 to 0.29 bits short of 14 on a 2^22 +window; p34 0.04 of 15) at one narrow-window load site whose last writer is mad, xor or sub, with every other site at +its flat share; the ratio tracks the largest-256-item-bucket excess (5.6x gives 1.50x, 3.1x to 4.5x give 1.22x to +1.38x); (c'') passes them at 0.9927 to 0.9963 because distinctness does not see a bucket; the check that would catch +all four is a per-site largest-bucket bound (about 2x window expectation at the 2^20 units), a generator change for a +next class, never for the frozen ones. Meaning per tier: a quarter bit at one site is under the window model's own +spread (the gate line's 61 of 64 stands), so no card or chip gains a cacheable hot set from it; the bound is the next +class's item, not a change to 017e7037 or 1c420786. The ratio refuses about 4 percent of candidates that pass every other test (4,099-program census at 017e7037: mean attempts 2.086 against 1.998, max 17, 0 lossy-sourced load sites of 65,584, 0 exhaustions; suite 103 of 103; devnet epoch-0 at attempt 1, id a785001687d8688a, pairing verified by this lane). RE-GATE VERDICT on sub-version 3 (017e70376489251e18564c0abce7e466e606c8b3; pairing id a785001687d8688a verified; From 29239a2296f9cf4686bb8202d4462385df361a52 Mon Sep 17 00:00:00 2001 From: igneum-labs <337424239+igneum-labs@users.noreply.github.com> Date: Thu, 8 Oct 2026 08:49:21 +0000 Subject: [PATCH 2/2] attack-pass: the status board, F8 row, gate line and re-gate paragraph read the tail as attributed Co-Authored-By: Claude Fable 5.1 --- docs/analysis/attack-pass-2026-10.md | 8 ++++---- 1 file changed, 4 insertions(+), 4 deletions(-) diff --git a/docs/analysis/attack-pass-2026-10.md b/docs/analysis/attack-pass-2026-10.md index 900090b5f..da1ae4705 100644 --- a/docs/analysis/attack-pass-2026-10.md +++ b/docs/analysis/attack-pass-2026-10.md @@ -18,7 +18,7 @@ v5 list at 3.0 percent); F2 PASS, effort-bounded; F3 PASS; F4 PASS against class FIXED-AND-PASSED (the F2 hour skipped by decision); F6 PASS (the worst of 10^5 programs 8.708 ms on the half-core proxy; O-1.14 closed on an i7-9700K); F7 PASS on all three sub-rows (the era VDF in the node, 0 of 6 re-rolls); F8 FIXED-AND-PASSED in class v4 sub-version 3 at 017e7037 (AP-F8-1, AP-F8-2, AP-F8-3 ours and closed; the four-seed -unattributed tail named); F9 PASS on (a) and (c), (b) closed by the same fix; F10 PASS. Frozen generator: class v4 +tail attributed to per-site bucket concentration, 8 October 2026); F9 PASS on (a) and (c), (b) closed by the same fix; F10 PASS. Frozen generator: class v4 sub-version 3, igneum-pow 017e70376489251e18564c0abce7e466e606c8b3, devnet epoch-0 id a785001687d8688a. The freeze tag `cryptanalysis-target-1` is the coordinator's cut on this record; the era VDF precondition is met (F7 a). Main checks every number against the log before quoting it to the founder. @@ -34,7 +34,7 @@ against the log before quoting it to the founder. | F5 | Chip-model sweep + AWS F2 FPGA hour | evidence row 17 holds across the sweep; FPGA row under 27 M reads/s/W | sweep: 2.1x at k=1 GDDR7 reproduces, 3.2x at k=0.5, 4.1x at k=0.3 (matches ledger M32); FPGA row 2.3 to 2.9 G/s, 10 to 20 M reads/s/W (literature). FINDING: the k=0.33 figure is framed as the X9's measured core (M32) and a "measured class" (ladder branch ยง5a); the X9 was withdrawn before launch and never benchmarked. F2 hour SKIPPED: no AWS account | FIXED-AND-PASSED (sweep PASS; AP-F5-1 fixed and re-gated 7 Oct 2026: chip section re-run 2.1x at k=1 unchanged, identity grep 0 hits, site lane concurred); F2 hour SKIPPED-BY-DECISION (the founder, 7 Oct 2026, 09:5x UK; plan 4.2 row F5 is the sweep only at 3714c2a0; the FPGA row stays the JEDEC-ceiling model row labelled unmeasured) | | F6 | Verifier worst case over 10^5 programs + O-1.14 laptop run | worst program under 10 ms cold on the half-core proxy and the laptop | 100,000 programs ranked, 50,000 timed cold one-core (worst 6.194 ms), the worst 200 re-timed and the worst 1,000 timed on the half-core proxy under the per-core lease (core 40 at 3,799.9 MHz): worst 8.708 ms (`attack-f6/87142`), 1.29 ms under the gate, every half-core reading under 9 ms; dr736 fails as it must (15.49). O-1.14 CLOSED on an i7-9700K (v4 6.334 ms cold max, dr736 10.04 fails). Ladder ceiling from the worst program on the half-core proxy: N about 300,000, so rung 2 admissible, rung 3 not. Record `docs/analysis/attack-pass/f6-verifier.md` | PASS | | F7 | Era-draw bias harness + 2^20 era-seed census | no re-roll inside the publish window; no era class with gain over 1.1x over 2^-20 | (b) census PASS at 2^24 seeds (no class over 1.1x, stride bijective, R, pos and M uniform, planted cases fire); (c) 64-bit day-key seeding PASS (0 collisions in 2^17); (a) PASS with the era VDF in the node (era-vdf lane, fork era-vdf-node 394a5902 on release-0.3.20-node c4459193, behind era_vdf_activation_daa; master a4eaf766 carries the spec text, `docs/analysis/era-vdf-2026-10-07.md` and `tools/era-vdf/reroll.mjs`): against the real era cut on three fast-time nodes the re-roll harness fires with the VDF off (6 of 6 cuts) and is silent with it on (0 of 6; the adversary's 5.4 to 6.6 s evaluation against a 1 s block interval, the honest chain 3 to 10 blocks ahead, three nodes agreeing on every era seed); the delay is 517 s on the fastest prover measured (chiavdf NUDUPL over GMP, 208.8K squarings/s) at T = 108,000,000, 259x the 2 s window. Open, not a gate: the verify is 22 ms against the 10 ms target (O-4.6, 0.3.22). Record `docs/analysis/attack-pass/f7-era.md` | PASS (a, b, c) | -| F8 | Uniformity censuses (line-index 2^28, distinct lines, cross-hash histogram) | uniform within the window model of spec 1.13.1, layer 8; the excess beyond it within 6 sigma over 64 seeds; no hot set under 1% of items beyond the model | line index PASS at 2^28. The 6 Oct stream: 31 of 64 seeds over 1.2x (AP-F8-1, the lossy load source). Sub-version 1 (8c728ca3): 11 of 64. Sub-version 2 (07a809a7 / 8bdcbdd8): 9 of 64; AP-F8-2 (exhaustion) closed there, 0 of 10^6. Sub-version 3 (017e7037: the acceptance executing the shadow block, AP-F8-3; the shared-operand rule; (c'') the distinct-index ratio): 60 of 64 under 1.2x, the four over the named unattributed tail at 1.22x to 1.50x with no chip consequence; 0 exhausted in 24,631 chain-shaped seeds, the draw total by construction. Record `docs/analysis/attack-pass/f8-uniform.md` | FIXED-AND-PASSED (sub-version 3, 017e7037, the frozen generator) | +| F8 | Uniformity censuses (line-index 2^28, distinct lines, cross-hash histogram) | uniform within the window model of spec 1.13.1, layer 8; the excess beyond it within 6 sigma over 64 seeds; no hot set under 1% of items beyond the model | line index PASS at 2^28. The 6 Oct stream: 31 of 64 seeds over 1.2x (AP-F8-1, the lossy load source). Sub-version 1 (8c728ca3): 11 of 64. Sub-version 2 (07a809a7 / 8bdcbdd8): 9 of 64; AP-F8-2 (exhaustion) closed there, 0 of 10^6. Sub-version 3 (017e7037: the acceptance executing the shadow block, AP-F8-3; the shared-operand rule; (c'') the distinct-index ratio): 60 of 64 under 1.2x, the four over the named tail at 1.22x to 1.50x, attributed 8 October 2026 to a quarter-bit bucket concentration at one narrow-window site each, with no chip consequence; 0 exhausted in 24,631 chain-shaped seeds, the draw total by construction. Record `docs/analysis/attack-pass/f8-uniform.md` | FIXED-AND-PASSED (sub-version 3, 017e7037, the frozen generator) | | F9 | Acceptance edges (39) + header grinding on an RTX 5090 | zero passing programs with a hot set under 1%; grinding gain under 1% of rate | (a) edges on generator 4 over 10^5 seeds: 34 disagreements in 105,064 candidates (29 const_bit, 4 bias, 1 lane_const), every one a one-bit or sampling-noise property moving the choice to an attempt both stand-ins accept, nothing in the attacker's favour: PASS; (b) hot-set search over 10^6 seeds: 11,696 passing programs (1.17%) concentrate 1% or more of reads on a hot set, worst 17.3%: FINDING, the same or-saturation load-source class as AP-F8-1 found by a second harness (F9-1 merged into AP-F8-1), re-gated on the amended stream; (c) grinding on the 5090: +0.004% at K = 2^14, ceiling +43%: PASS. Record `docs/analysis/attack-pass/f9-grind.md` | (a) PASS; (b) the AP-F8-1 class on the 6 Oct stream, closed by sub-version 3 (F8's census is the re-gate instrument; this harness's hot-share metric counts the era's windows); (c) PASS | | F10 | Ladder signal monotonicity harness | no step without 90% over 7 windows in either direction | known-fail fails, known pass passes; new cases on the exact-share driver: 89% up holds (no step), 89 then 90% down with restarts steps only at 90% after the 7-window cool-down, the floor holds under 100% down (never below rung 0); decision per seed block memoised, identical after a restart, never differs between nodes; 19 of 19 checks per case. Two items to main, not findings: a stale commit string in the ladder lane's igneumd, and proof-synced nodes deciding rung 0 until the witness lands (a precondition line for spec 01). Record `docs/analysis/attack-pass/f10-ladder.md` | PASS | @@ -289,7 +289,7 @@ attack-pass) by the coordinator's exception rule; nothing touches GitHub. |---|---|---|---| | F4 weak-day census | 2^24 chain days from 20,729 under `Shape::for_class(&V5_CLASS)`, box 1, 18:5x to 19:1x UTC | byte-identical to the class v4 census: M2 (DSP-bound) 0 of 2^24 days over 1.1x; M1 (LUT adders) 5,476 days, 3.264e-4, the same bounded tail, worst day 4,819,563 at cost 197 against the median 231; planted weak days fire (mul1all M2 unbounded, mulnaf 1.333x). The day-key draw depends on the mixer shape alone and v5 adds only the state flag, so identity is the expected and the measured result | PASS (v4's reading; AP-F4-1 stays the next-class item) | | F8 hot-set gate (pre-freeze reading) | 64 seeds at 2^24, chain path, v5 with the dn3 state, box 2: hand-started at 18:47 UTC (11 seeds, killed on the coordinator's rule: every hand-started run off the boxes, loads 601 and 401), re-queued through `lease pool 64` at 19:23 UTC (17 more seeds), released at 19:4x UTC on the Counter ASIC lane's yield so the class v5 (c''') census, the 0.3.24 board's critical path, could take the pool | every seed read equals sub-version 3's seed for seed (0.9915x to 1.144x, p10 1.50x), as the v5 lane predicted: the leaves change the words, not the read addresses | READING, not the gate line | -| F8 hot-set gate, the frozen tip (THE GATE LINE) | igneum-pow class-v5 1c420786 (the 0.995 per-site floor (c''') on sub-version 3's rules; binary sha256 0f5c98dc41a1b3aa..., run from a copy); pairing: the library draws the dn3 epoch-0 program as e5a4ac5978462156, the harness validates bit for bit against the library on the dn3 state (0 mismatches on 66 validation lines); 64 seeds p2 to p65 at 2^24 nonces, chain path, the v5 dataset from v5-dn3-epoch0's state.igsd1, window-model control, build-2 under `lease pool` class v5 as two halves of 32 (ended 21:58:43Z and 22:03:21Z) | 61 of 64 under 1.2x of the window model (0.9919x to 1.144x, p75 1.0024x); 3 over, all inside the named four-seed residue and none new: p10 1.5047x (0x4018f5, 346 reads of 2^31, no predicted source), p8 1.3787x (0x839d33, 419), p4 1.2166x (0x400197, 363); p34 0.9997x under the (c''') floor; p23 1.0000x, p19 0.9997x, p15 0.9998x, p18 1.0001x, p56 1.0000x. Seed for seed the ratios equal sub-version 3's within 0.001 except where the floor moved a draw: the state leaves change the words, not the read addresses. Nothing to a chip | PASS (the known residue p4, p8, p10 unattributed and chased) | +| F8 hot-set gate, the frozen tip (THE GATE LINE) | igneum-pow class-v5 1c420786 (the 0.995 per-site floor (c''') on sub-version 3's rules; binary sha256 0f5c98dc41a1b3aa..., run from a copy); pairing: the library draws the dn3 epoch-0 program as e5a4ac5978462156, the harness validates bit for bit against the library on the dn3 state (0 mismatches on 66 validation lines); 64 seeds p2 to p65 at 2^24 nonces, chain path, the v5 dataset from v5-dn3-epoch0's state.igsd1, window-model control, build-2 under `lease pool` class v5 as two halves of 32 (ended 21:58:43Z and 22:03:21Z) | 61 of 64 under 1.2x of the window model (0.9919x to 1.144x, p75 1.0024x); 3 over, all inside the named four-seed residue and none new: p10 1.5047x (0x4018f5, 346 reads of 2^31, no predicted source), p8 1.3787x (0x839d33, 419), p4 1.2166x (0x400197, 363); p34 0.9997x under the (c''') floor; p23 1.0000x, p19 0.9997x, p15 0.9998x, p18 1.0001x, p56 1.0000x. Seed for seed the ratios equal sub-version 3's within 0.001 except where the floor moved a draw: the state leaves change the words, not the read addresses. Nothing to a chip | PASS (the known residue p4, p8, p10, attributed 8 October 2026 to per-site bucket concentration; the largest-bucket bound is a next class's item) | | F9 exhaustion count, the frozen tip (A GATE LINE for the 0.3.24 move) | 10^5 chain-shaped seeds on the v5 chain path (era-composed class, `--chain`) with the dn3 state at igneum-pow class-v5 1c420786, pairing e5a4ac5978462156, build-1, ten chunks of 10,000 under `lease pool 4` (chunks 1, 3, 5 to 9 under class v5; chunks 0, 2, 4 re-leased under class release on the coordinator's order; 14,477 to 14,480 s per chunk, about 1.45 s per seed); binary copied into the run dir; interim line sent at 00:55 UTC (seeds drawn, 0 exhausted, 0 panics, max 30, F1 0 failures), which cleared the move; last chunk written 02:34:54 UTC | 100,000 of 100,000 seeds drawn, 0 exhausted, 0 panics, 0 past attempt index 31, max attempt index 30; histogram by attempt index (0 = accepted on the first draw) 0: 31,454; 1: 21,460; 2: 14,660; 3: 10,263; 4: 7,047; 5: 4,701; 6: 3,297; 7: 2,256; 8: 1,532; 9: 1,027; 10: 702; 11: 509; 12: 365; 13: 216; 14: 153; 15: 103; 16: 80; 17: 56; 18: 39; 19: 20; 20: 24; 21: 9; 22: 6; 23: 9; 24: 3; 25: 4; 26: 2; 27: 1; 29: 1; 30: 1; first-draw acceptance 0.3145, mean attempt index 2.185 (3.185 draws per seed), 4,862 seeds (4.86 percent) at index 8 or above, 255 (0.255 percent) at 16 or above; the 256-attempt cap and the deterministic last resort never reached. Meaning per tier: no epoch seed in 10^5 fails to draw a program, so the liveness halt of AP-F8-2 has no observed case on the frozen tip at this count (the bound it supports is under 3e-5 per seed at 95 percent, about one epoch in 33,000 at worst; a halt a node operator would see as a stuck epoch, a miner as a dead epoch, a holder as a paused chain), and the draw cost stays at about 3.2 candidates per epoch for every node | PASS (0 of 10^5; the record `f9-grind.md`, section (d)) | | F1 shadow redundancy, the frozen tip (A GATE LINE for the 0.3.24 move) | 10^5 class v5 programs through the string-seed path (`generate_from_seed_bytes_program_class`, class V5, every candidate draw through the (c''') floor over 2^20) at igneum-pow class-v5 1c420786, pairing e5a4ac5978462156, build-1, `lease pool 16` class release (cores 8 to 23, re-leased 22:34:05 UTC), binary sha256 bb70bbf69a4b3223... copied into `frozen-1c420786-f1/bin`; 20,774 s of census (5 h 46 min; about 5 core-s per program, the (c''') draw cost), census.csv (sha256 4e34b669f2f5c680..., 100,000 rows) written 04:20 UTC on 8 October 2026 | 100,000 of 100,000 programs; instructions saved min 0.000, mean 0.623, max 4.688 percent (worst `attack-f1/95060` at attempt 0, 6,912 to 6,588 per iteration; `81748`, `66933`, `3006` at the same 4.688; next 4.311); chip-view ops saved mean 0.520, max 4.783; programs over 5 percent 0, over 10 percent 0; soundness: differential mismatches 0 of 100,000 (8 random states each), verifier mismatches 0 of 100,000; 0 panics; histogram of saved, 0.5 percent bins from 0: 55,241; 20,597; 11,762; 9,851; 1,484; 656; 259; 133; 13; 4; 0; 0; draw attempts per program: index 0 31,630, max 30 (the same shape as F9's). Against the v4 10^5 (max 5.078, the AP-F1-1 letter miss): the v5 tip's worst sits 0.39 points under the letter, the two top bins are empty, and the mean is unchanged (0.617 to 0.623), so the v5 leaves add no redundancy and remove the one letter miss. Meaning per tier: the shadow block of every drawn program stays within 5 percent of its naive count under the harness's rules and the honest compiler finds the same shortcuts, so no chip gets a shadow-side discount (a miner on a card pays the full block, a hypothetical ASIC gains nothing here) and the chain's verifier agrees with the harness on every program (0 mismatches), so no node disagrees with another on any drawn block. Harness gap and its fix: section 12 of the record (the running census was the old binary; the flush is in 18a9c04a for every census after it) | PASS (0 of 10^5 over the letter; AP-F1-1 FIXED-AND-PASSED on v5 at this count; the record `f1-shadow.md`, section 13) | | F4 weak-day census, the post-freeze commit | 2^24 chain days at class-v5 8ca66afa (AP-F4-1 in the agreed form: cost A at most 205, k >= 1 or all-ROT-equal rejected, the forty redrawn), the harness on the agreed w32 convention (digits 0 to 31) and median 226; known-failed day 29,337 redrawn under the rule (cost 203 to 228), day 20,729 at 219 unchanged; build-1 `lease pool 12` class adv, 379 s, ended 22:3x UTC | 0 of 2^24 days over 1.1x on M1 (median 226; minimum cost 206 at day 27,016, 1.097x, one adder above the reject line) and 0 on M2; mean 225.79, sd 6.07 (pre-rule: 5.69e-4 over, min 203). The redraw rule removes the LUT tail by construction and the measurement agrees | PASS; AP-F4-1 FIXED-AND-PASSED against class v5 at 8ca66afa | @@ -540,7 +540,7 @@ class's item, not a change to 017e7037 or 1c420786. The ratio refuses about 4 pe 0 exhaustions; suite 103 of 103; devnet epoch-0 at attempt 1, id a785001687d8688a, pairing verified by this lane). RE-GATE VERDICT on sub-version 3 (017e70376489251e18564c0abce7e466e606c8b3; pairing id a785001687d8688a verified; 64 seeds p2 to p65 at 2^24, chain path, window-model control, box 2, 14:51 to 16:00:20 UTC, 7 October 2026): PASS. -60 of 64 under 1.2x (0.9915x to 1.144x); the four over are the named open tail, unattributed and chased: p10 +60 of 64 under 1.2x (0.9915x to 1.144x); the four over are the named tail, attributed 8 October 2026 (per-site bucket concentration, the AP-F8-1 tail paragraph): p10 1.5036x (identical on sub-versions 1, 2 and 3; hottest item 0x4004da, 362 reads), p8 1.3776x (0x837de4, 420), p34 1.2505x (0x800010, 541, the one-bit value through sub at 5), p4 1.2167x (0x4000e7, 355); their hottest items carry 355 to 541 reads of 2^31 (one to two per 2^22 items above the mean), no chip consequence, and the ratio rule reads