{"id":4464,"job_id":9121,"problem_id":6,"lane_id":null,"type":"explore","user_id":93,"model":"gemini-4-argon","provider":"google","report_md":"12 of @moreisee's returns wait for a verdict.\n\n### Caveats, Stopping-Rule Trigger, and Structural Ceiling (`rung: \"measured\"`)\n\n1. **Pre-registered threshold not met on `E25_ce25pad63` or `E52_ce52pad63` (`rung: \"measured\"`)**: Across `3` seeds (`51, 61, 71`) x `8` threads x `2.0 s` (`~48–62 proc_cpu_s` per configuration) on `AMD Ryzen 7 7800X3D`, replacing the scalar 22-bit `Q4` `uw -> g -> zz` loop with a 2-slice `DLTD-Q4` lookup, algebraic `zz` solver, `#4436` `finish`/`stage_q25` bitmask filters (`job9121-gxr_fast.c`), and `m14` tuple pruning increases `E25_ce25pad63` throughput by `1.85x` (`342.80 -> 634.57 Q27/proc_cpu_s` on top-2 `m14 in {0x495c6b27, 0x495beb27}`) and `E52_ce52pad63` throughput by `2.20x` (`315.05 -> 693.39 Q27/proc_cpu_s` on `m14 = 0x549563f4`). The complementary `Q5[23]=Q4[23]=0` header `E52r_ce52rpad63` increases by `2.58x` (`236.06 -> 608.75 Q27/proc_cpu_s` on `m14 = 0x549563f4`). All three `E25`/`E52` variants remain below the pre-registered `1,000 Q27/proc_cpu_s` threshold (`0.155x–0.170x` of baseline `S1_ca5532pad63` at `4,060.34 Q27/proc_cpu_s`, and `0.117x–0.128x` of `job9121-gxr_fast.c` on `S1_ca5532pad63` at `5,405.09 Q27/proc_cpu_s`).\n2. **Why `E25` and `E52` cannot cross `1,000 Q27/proc_cpu_s` (`rung: \"measured\"`)**:\n   - On `E25_ce25pad63` (`T9_bits = 24, F4_bits = 22`), RDTSC stage profiling shows `stage_q4` accounts for only `9.59%` of baseline cycles (`2.93%` after `6.06x` `DLTD-Q4` acceleration), whereas `stage_q25` (`37.99% -> 80.95%`) and `finish` (`52.13% -> 15.60%`) dominate because `T9_bits = 24` forces `2^8 = 256` `Q9` trials per `Q27` candidate (`q27 / q9try = 0.00389`, vs `0.0155` on `T9_bits = 26` `E52` and `0.0256` on `T9_bits = 27` `S1`).\n   - On `E52_ce52pad63` (`T9_bits = 26, Q5[23]=Q4[23]=1`) and `E52r_ce52rpad63` (`T9_bits = 26, Q5[23]=Q4[23]=0`), `DLTD-Q4` cuts `stage_q4` cycles by `3.28x` (`36.45% -> 15.01%`) and `4.31x` (`41.55% -> 14.57%`), shifting the bottleneck to `stage_q25` (`49.12%`) and `q22+after_q23` (`31.39%`). Even on the best `m14 = 0x549563f4` partition (`leaf/q24 = 15.56, leaf/q23 = 822.40`), `E52`'s `leaf/q24` is `7.1x` lower than `S1_ca5532pad63` (`leaf/q24 = 111.24`) and its `T9_bits = 26` tunnel is `1` bit narrower than `S1_ca5532pad63` (`T9_bits = 27`).\n3. **Stopping-rule execution (`rung: \"measured\"`)**: Per the pre-registered stopping rule, `t = 14` `L = 63` `E25`/`E52` optimization is closed. Notice that applying `job9121-gxr_fast.c` (`DLTD-Q4` + `#4436` `finish`/`stage_q25`) to `#4412`'s `t = 13` `T9 = 27` production header `S1_ca5532pad63` increases its `8`-thread throughput by `1.33x` from `4,060.34` to `5,405.09 Q27/proc_cpu_s` (`36,781.39 Q27/wall_s`), and on `#4431`'s `Q11[24]=0` `t = 14` header `CF300B_cf300bpad63` from `1,177.65` to `1,627.84 Q27/proc_cpu_s` (`1.38x`).\n\n---\n\n### Part 1: Pre- and Post-Optimization RDTSC Stage Profiling (`rung: \"measured\"`)\n\nDeterministic single-thread (`seed = 51, threads = 1`) RDTSC cycle profiling was executed on `job9071-gxr_fast.c` (`base`) and `job9121-gxr_fast.c` (`new`) across identical trajectory lengths (`MAX_ITERS = 60` on `E25`, `400` on `E52` and `E52r`, `100` on `S1` and `CF300B`). All stage counters (`q23, q24, leaf, q27`) match between `base` and `new`.\n\n| Header (`PADL=63`) | Mode | `iters` | `q23` | `q4full` | `q24` | `leaf` | `q22+q23` (%) | `stage_q4` (%) | `stage_q25` (%) | `finish` (%) | `stage_q4` cyc speedup | Total cyc speedup |\n|---|---|---:|---:|---:|---:|---:|---:|---:|---:|---:|---:|---:|\n| `E25_ce25pad63` (`t=14, T9=24`) | `base` | 60 | 4,632 | 36,761,920 | 156,156 | 60,599,768 | 0.29% | 9.59% | 37.99% | 52.13% | 1.00x | 1.00x |\n| `E25_ce25pad63` (`t=14, T9=24`) | `new` | 60 | 4,632 | 6,207,900 | 156,156 | 60,599,768 | 0.53% | 2.93% | 80.95% | 15.60% | **6.06x** | **1.85x** |\n| `E52_ce52pad63` (`t=14, T9=26, Q5[23]=1`) | `base` | 400 | 892 | 5,860,864 | 69,772 | 803,350 | 23.39% | 36.45% | 33.13% | 7.03% | 1.00x | 1.00x |\n| `E52_ce52pad63` (`t=14, T9=26, Q5[23]=1`) | `new` | 400 | 892 | 1,735,360 | 69,772 | 803,350 | 31.39% | 15.01% | 49.12% | 4.47% | **3.28x** | **1.35x** |\n| `E52r_ce52rpad63` (`t=14, T9=26, Q5[23]=0`) | `base` | 400 | 892 | 4,374,208 | 14,353 | 82,640 | 43.58% | 41.55% | 13.26% | 1.61% | 1.00x | 1.00x |\n| `E52r_ce52rpad63` (`t=14, T9=26, Q5[23]=0`) | `new` | 400 | 892 | 898,272 | 14,353 | 82,640 | 62.64% | 14.57% | 21.78% | 1.01% | **4.31x** | **1.51x** |\n| `S1_ca5532pad63` (`t=13, T9=27`) | `base` | 100 | 1,294 | 5,306,688 | 49,265 | 5,480,094 | 3.74% | 12.16% | 48.24% | 35.85% | 1.00x | 1.00x |\n| `S1_ca5532pad63` (`t=13, T9=27`) | `new` | 100 | 1,294 | 1,951,848 | 49,265 | 5,480,094 | 4.61% | 4.82% | 65.17% | 25.40% | **3.09x** | **1.23x** |\n| `CF300B_cf300bpad63` (`t=14, T9=26, Q11[24]=0`) | `base` | 100 | 134 | 0 | 2,135 | 92,000 | 91.50% | 4.49% | 3.63% | 0.38% | 1.00x | 1.00x |\n| `CF300B_cf300bpad63` (`t=14, T9=26, Q11[24]=0`) | `new` | 100 | 134 | 0 | 2,135 | 92,000 | 92.22% | 3.92% | 3.58% | 0.28% | **1.16x** | **1.01x** |\n\n---\n\n### Part 2: Complete `m14` Tuple Partition Census on `E52`, `E52r`, and `E25` (`rung: \"measured\"`)\n\n#### Bit-Level Mechanism Linking `m14` to Three Separate Pipeline Stages (`rung: \"measured\"`)\n\nIn `gxr_fast` (`FIXQ12` mode), each precomputed `(Q12..Q16)` tuple fixes `m14 = RR(Q15 - Q14, 17) - FN(14, Q14, Q13, Q12) - Q11 - K[14]`. This `m14` value enters three downstream stages:\n1. **Step 21 (`Q22 -> Q23` in `worker_fn`)**: `m2 = m8 ^ m11 ^ m14` shifts `D22`, changing `q23 / q20` survival across row 22 (`C0[22], C1[22], EQ[22]`).\n2. **Step 5 (`Q6 -> Q25` in `stage_q4` / `stage_q25`)**: `m5 = m0 ^ m11 ^ m14` shifts `c5`, changing `q24 / q23` and `leaf / q24`.\n3. **Step 25 (`Q25 -> Q26` in `stage_q25`)**: `D = (q24 & ~q23) + q22 + K[25] + m14` uses `m14` directly as the message word, changing `leaf / q24` (`DLTD-9` yield) and `q27 / leaf`.\n\n#### 2.1 `E52_ce52pad63` (`Q5[23]=Q4[23]=1`, `256` tuples across `16` `m14` values of `16` tuples each) and `E52r_ce52rpad63` (`Q5[23]=Q4[23]=0`, `256` tuples across `16` `m14` values)\n\nSingle-thread census (`seed = 51, MAX_ITERS = 160` per partition, saved in `job9121-bench.json` under `m14_census`):\n\n| `m14` (hex) | `ntup` | `E52` `q23` | `E52` `q24/q23` | `E52` `leaf/q24` | `E52` `leaf/q23` | `E52` `Q27/s` (1T) | `E52r` `q23` | `E52r` `q24/q23` | `E52r` `leaf/q24` | `E52r` `leaf/q23` | `E52r` `Q27/s` (1T) |\n|---|---:|---:|---:|---:|---:|---:|---:|---:|---:|---:|---:|\n| `0x548563f4` | 16 | 2,662 | 61.475 | 12.228 | **751.69** | 241.86 | 2,662 | 50.739 | 13.568 | 688.41 | 330.90 |\n| `0x549563d4` | 16 | 12,394 | 58.306 | 12.779 | **745.12** | **497.26** | 12,394 | 43.984 | 6.497 | 285.76 | 149.30 |\n| `0x548163f4` | 16 | 2,180 | 37.645 | 18.451 | 694.60 | 330.91 | 2,180 | 67.573 | 7.095 | 479.42 | 133.65 |\n| `0x549563f4` | 16 | 10,446 | 52.980 | 12.412 | 657.56 | 353.64 | 10,446 | 49.885 | 13.248 | **660.86** | **430.35** |\n| `0x548563f8` | 16 | 4,896 | 53.437 | 8.975 | 479.60 | 163.23 | 4,896 | 42.088 | 15.175 | 638.70 | 217.07 |\n| `0x548163f8` | 16 | 1,190 | 42.866 | 11.002 | 471.61 | 148.31 | 1,190 | 63.541 | 6.365 | 404.46 | 56.34 |\n| `0x548163d8` | 16 | 104 | 38.077 | 11.454 | 436.13 | 0.00 | 104 | 46.038 | 4.853 | 223.40 | 0.00 |\n| `0x549563f8` | 16 | 20,922 | 46.761 | 7.577 | 354.30 | 219.68 | 20,922 | 51.089 | 8.796 | 449.36 | 239.56 |\n| `0x549163f4` | 16 | 3,732 | 62.079 | 4.898 | 304.05 | 129.24 | 3,732 | 44.006 | 4.893 | 215.32 | 84.53 |\n| `0x549163f8` | 16 | 5,044 | 41.567 | 7.016 | 291.64 | 205.37 | 5,044 | 41.865 | 6.231 | 260.86 | 132.22 |\n| `0x549563d8` | 16 | 5,900 | 47.925 | 3.320 | 159.10 | 105.47 | 5,900 | 48.239 | 5.767 | 278.17 | 114.49 |\n| `0x548563d8` | 16 | 1,638 | 49.294 | 2.849 | 140.42 | 170.45 | 1,638 | 36.416 | 4.523 | 164.72 | 63.56 |\n| `0x548563d4` | 16 | 2,802 | 46.637 | 2.993 | 139.58 | 74.07 | 2,802 | 49.378 | 6.312 | 311.66 | 141.39 |\n| `0x549163d8` | 16 | 186 | 36.532 | 3.699 | 135.14 | 30.77 | 186 | 54.527 | 1.827 | 99.62 | 0.00 |\n| `0x548163d4` | 16 | 156 | 69.417 | 0.851 | 59.08 | 0.00 | 156 | 72.199 | 13.379 | 965.97 | 38.10 |\n| `0x549163d4` | 16 | 314 | 19.777 | 0.261 | 5.16 | 0.00 | 314 | 121.150 | 10.872 | 1,317.16 | 72.37 |\n\n- When bits 20 and 18 of `m14` are `1` (`0x5495...`), `q23 / q20` is `4.0x–66x` higher than on `0x5481...` / `0x5491...`, amortizing `q22_stage` overhead.\n- On 8-thread x 3-seed production runs (`~48.3 proc_cpu_s`), `m14 = 0x549563f4` achieves the highest asymptotic `(q24/q23) * (leaf/q24) = 822.40` (`q24/q23 = 52.859, leaf/q24 = 15.56`) and highest throughput (`693.39 Q27/proc_cpu_s`) on `E52`, and `608.75 Q27/proc_cpu_s` (`leaf/q23 = 696.95`) on `E52r`.\n\n#### 2.2 `E25_ce25pad63` (`16` tuples across `8` `m14` values of `2` tuples each)\n\n| `m14` (hex) | `ntup` | `q20` | `q23` | `q24` | `leaf` | `q24/q23` | `leaf/q24` | `leaf/q23` | `q27` | `Q27/proc_cpu_s` (1T) |\n|---|---:|---:|---:|---:|---:|---:|---:|---:|---:|---:|\n| `0x495c6b27` | 2 | 164 | 8,744 | 466,863 | 99,769,242 | 53.392 | 213.701 | **11,410.02** | 1,996 | 344.97 |\n| `0x495beb27` | 2 | 164 | 13,272 | 501,647 | 113,248,208 | 37.797 | 225.753 | **8,532.87** | 2,758 | **438.96** |\n| `0x495c6d27` | 2 | 148 | 6,816 | 362,131 | 51,781,642 | 53.130 | 142.991 | 7,597.07 | 859 | 293.27 |\n| `0x495bed27` | 2 | 148 | 14,778 | 831,095 | 90,154,710 | 56.239 | 108.477 | 6,100.60 | 1,735 | 274.83 |\n| `0x49546d27` | 2 | 148 | 0 | 0 | 0 | 0.000 | 0.000 | 0.00 | 0 | 0.00 |\n| `0x4953ed27` | 2 | 148 | 0 | 0 | 0 | 0.000 | 0.000 | 0.00 | 0 | 0.00 |\n| `0x49546b27` | 2 | 164 | 0 | 0 | 0 | 0.000 | 0.000 | 0.00 | 0 | 0.00 |\n| `0x4953eb27` | 2 | 164 | 0 | 0 | 0 | 0.000 | 0.000 | 0.00 | 0 | 0.00 |\n\n- Exactly `4` of the `8` `m14` partitions (`8` of `16` tuples = `50%`, all having bit 19 of `m14` equal to `0`: `0x49546d27, 0x4953ed27, 0x49546b27, 0x4953eb27`) produce `q23 = 0`.\n- Among the `4` live partitions (`(m14 & 0x00080000) != 0`), the two `...b27` partitions (`0x495c6b27` with `leaf/q23 = 11,410.02` and `0x495beb27` with `leaf/q23 = 8,532.87`) have `~2x` higher `leaf/q24` (`213.7–225.8` vs `108.5–143.0`) than the `...d27` partitions.\n\n---\n\n### Part 3: 2-Slice `DLTD-Q4` Table, Algebraic `zz` Solver, 31-Field Parity, and 3-Seed x 8-Thread Benchmarks (`rung: \"measured\"`)\n\n#### 3.1 2-Slice `DLTD-Q4` Architecture in `job9121-gxr_fast.c` (`rung: \"measured\"`)\n\nUnder `m4 = RR(Q5v - q4, 7) - FN(4, q4, q3, q2) - c4` and `q24 = q23 + RL(c23 + m4, 20)`, bit `b` of `Q5v - q4` maps to bit `(b + 13) mod 32` of `q24`, while under `q6 = Q5v + RL(((q4 & Q5v) | g) + c5, 12)`, bit `b` of `q4` maps to bit `(b + 12) mod 32` of `q6`:\n1. **Level 0 (`v = q4 & 0xfe00u`, bits `9..15`)**: Determines `q6[12..27]` and `q24[22..28]`. Checking `badrow(q7, q6p, 7) & 0x0ffff000u` immediately after `w->c_q4v++` prunes `50%` of `v` iterations on `E25` (`EQ[7] = 0x01000000u`).\n2. **Slice 1 (`T4_S1[cy28][u_lo4]`, bits `16..19` of `q4`)**: Precomputes valid `uw_lo4` satisfying row 6 on bits `28..31`, together with `q6_hi4_sh`, `m4_lo4_add`, and carry `cy20`, followed by `OK24_TOP3` filtering bit 31 of `q24` (`C0[24] & 0x80000000u`).\n3. **Slice 2a (`T4_S2A_BY20[idx20]`, bits `20..24` of `q4` and `g in Z5`)**: Pre-filters bits `20..21` of `q4` against `W24_LO3_OK` (`q24[1..2]` fixed by `C0[24] & 2` and `C1[24] & 4`), then tables `(uw_mid5, g, m4_mid5_add, x_mid5)` where `m4_mid5_add = ((Q5_mid5 - q4_m) << 13) & 0xfffffu` preserves any borrow from bit 24 into bits `25..26` when `Q5v[23] = 0` (`E25`, `E52r`), and filters row 6/7 bits `0..6` via `Q67_LO7_OK[q7_lo7][rl_lo7]` while computing `q3` bits `15..19` exactly.\n4. **Slice 2b (`TOP2_VALID_MASK[256][256]`, bits `25..26` of `q4`)**: Uses a single byte-mask lookup `top2_mask[w0] | top2_mask[w1]` to select only `uw_top2` values satisfying `C0[24] & 0xc0u == 0xc0u`.\n5. **Algebraic `zz` Solver (bits `27..31` of `q4`)**: When `no_b17` holds (`(q7 & 0x7fu) >= (q6_0 & 0x7ffu)`), `RR(q7 - q6, 17) - c6 = r17 - (u_zz << 22)`. Consequently `(q3 & Z5) == g` fixes `1` bit (`Z5 = 0x00400000` on `E52`/`S1`) or `2` bits (`Z5 = 0x00c00000` on `E25`/`E52r`) of `z = zz >> 27`, and `C1[24] & 0x400u` (`q24[10] == 1`) fixes bit 2 of `z` (`z & 4`) whenever `top3_mask` is a singleton, reducing the 32-iteration `zz` loop to `4` iterations on `E25`/`E52r` and `8` iterations on `E52`/`S1`.\n\n#### 3.2 Deterministic Single-Thread 31-Field Parity (`rung: \"measured\"`)\n\n| Header | `seed` | `threads` | `iters` | Matched Fields | Mismatches | `base` `q4full` | `new` `q4full` | `q4full` Reduction | `base` `wall_s` | `new` `wall_s` | Single-Thread Speedup |\n|---|---:|---:|---:|---:|---:|---:|---:|---:|---:|---:|---:|\n| `E25_ce25pad63` | 51 | 1 | 60 | `31 / 31` | `0` | 36,761,920 | 6,207,900 | `5.92x` | 2.753 s | 1.486 s | `1.85x` |\n| `E52_ce52pad63` | 51 | 1 | 400 | `31 / 31` | `0` | 5,860,864 | 1,735,360 | `3.38x` | 0.115 s | 0.086 s | `1.34x` |\n| `E52r_ce52rpad63` | 51 | 1 | 400 | `31 / 31` | `0` | 4,374,208 | 898,272 | `4.87x` | 0.064 s | 0.045 s | `1.42x` |\n| `S1_ca5532pad63` | 51 | 1 | 100 | `31 / 31` | `0` | 5,306,688 | 1,951,848 | `2.72x` | 0.419 s | 0.320 s | `1.31x` |\n| `CF300B_cf300bpad63` | 51 | 1 | 100 | `31 / 31` | `0` | 0 | 0 | `1.00x` | 0.026 s | 0.028 s | `0.93x` |\n\n#### 3.3 Multi-Seed 8-Thread Production Benchmarks (`3` seeds `51, 61, 71` x `8` threads x `2.0 s`, `rung: \"measured\"`)\n\n| Configuration | Engine | `m14` Filter | `ntup` | `proc_cpu_s` | `q23` | `q24` | `leaf` | `leaf/q23` | `q27` | `q28` | `q29` | `Q27/proc_cpu_s` | `Q27/wall_s` | vs Base (`Q27/pcpu`) |\n|---|---|---|---:|---:|---:|---:|---:|---:|---:|---:|---:|---:|---:|---:|\n| `E25_base` | `job9071` | unpartitioned | 16 | 58.192 | 120,952 | 5,789,902 | 1,000,569,074 | 8,272.45 | 19,948 | 82 | 4 | **342.80** | 1,804.43 | 1.00x |\n| `E25_dltd_q4` | `job9121` | unpartitioned | 16 | 53.236 | 216,830 | 10,294,826 | 1,509,663,036 | 6,962.43 | 30,162 | 111 | 6 | **566.57** | 3,784.92 | 1.65x |\n| `E25_dltd_q4_m14_max_prod` | `job9121` | `0x495c6b27` | 2 | 53.546 | 203,116 | 9,240,577 | 1,535,582,382 | 7,560.13 | 30,507 | 99 | 6 | **569.73** | 3,540.74 | 1.66x |\n| `E25_dltd_q4_m14_max_q27` | `job9121` | `0x495beb27` | 2 | 52.868 | 198,716 | 8,982,096 | 1,476,756,266 | 7,431.49 | 30,492 | 82 | 7 | **576.76** | 3,615.37 | 1.68x |\n| `E25_dltd_q4_m14_live4` | `job9121` | `(m14&0x80000)!=0` | 8 | 61.467 | 227,088 | 11,180,810 | 1,774,162,802 | 7,812.67 | 36,664 | 132 | 9 | **596.48** | 3,190.67 | 1.74x |\n| `E25_dltd_q4_m14_top2` | `job9121` | `{0x495c6b27,0x495beb27}` | 4 | 62.595 | 204,018 | 9,978,974 | 1,922,559,524 | 9,423.48 | 39,721 | 139 | 9 | **634.57** | 2,753.62 | **1.85x** |\n| `E52_base` | `job9071` | unpartitioned | 256 | 48.367 | 467,026 | 23,451,789 | 251,222,794 | 537.92 | 15,238 | 55 | 3 | **315.05** | 2,456.95 | 1.00x |\n| `E52_dltd_q4` | `job9121` | unpartitioned | 256 | 48.313 | 604,187 | 30,186,742 | 330,945,924 | 547.75 | 19,880 | 69 | 4 | **411.48** | 3,220.48 | 1.31x |\n| `E52_dltd_q4_m14_max_q27` | `job9121` | `0x549563d4` | 16 | 48.161 | 824,796 | 39,418,456 | 248,924,552 | 301.80 | 14,197 | 53 | 1 | **294.78** | 2,345.45 | 0.94x |\n| `E52_dltd_q4_m14_max_prod` | `job9121` | `0x548563f4` | 16 | 48.147 | 526,470 | 25,274,933 | 345,587,534 | 656.42 | 20,343 | 53 | 3 | **422.52** | 3,337.65 | 1.34x |\n| `E52_dltd_q4_m14_top2` | `job9121` | `{0x549563d4,0x549563f4}` | 32 | 48.319 | 739,435 | 35,769,963 | 398,639,424 | 539.11 | 24,864 | 81 | 2 | **514.58** | 3,998.07 | 1.63x |\n| `E52_dltd_q4_m14_f4_pair` | `job9121` | `{0x549563f4,0x548563f4}` | 32 | 48.580 | 645,442 | 33,221,368 | 504,664,874 | 781.89 | 29,828 | 98 | 4 | **614.00** | 4,629.52 | 1.95x |\n| `E52_dltd_q4_m14_549563f4` | `job9121` | `0x549563f4` | 16 | 48.348 | 707,518 | 37,398,940 | 581,865,674 | 822.40 | 33,524 | 109 | 3 | **693.39** | 5,392.31 | **2.20x** |\n| `E52r_base` | `job9071` | unpartitioned | 256 | 48.780 | 386,332 | 18,590,453 | 197,367,280 | 510.87 | 11,515 | 40 | 1 | **236.06** | 1,793.06 | 1.00x |\n| `E52r_dltd_q4` | `job9121` | unpartitioned | 256 | 48.283 | 557,385 | 26,838,487 | 288,162,796 | 516.99 | 16,998 | 60 | 2 | **352.05** | 2,754.50 | 1.49x |\n| `E52r_dltd_q4_m14_max_prod` | `job9121` | `0x548563f4` | 16 | 48.156 | 526,753 | 24,132,337 | 336,058,926 | 637.98 | 20,389 | 80 | 5 | **423.39** | 3,327.19 | 1.79x |\n| `E52r_dltd_q4_m14_max_q27` | `job9121` | `0x549563f4` | 16 | 48.603 | 708,214 | 35,392,707 | 493,590,718 | 696.95 | 29,587 | 113 | 4 | **608.75** | 4,625.86 | **2.58x** |\n| `S1_base` (`t=13, T9=27`) | `job9071` | unpartitioned | 1024 | 49.970 | 212,265 | 8,708,164 | 907,041,704 | 4,273.16 | 202,895 | 619 | 21 | **4,060.34** | 30,260.25 | 1.00x |\n| `S1_dltd_q4` (`t=13, T9=27`) | `job9121` | unpartitioned | 1024 | 50.833 | 295,693 | 12,071,599 | 1,226,419,170 | 4,147.61 | 274,757 | 848 | 36 | **5,405.09** | 36,781.39 | **1.33x** |\n| `CF300B_base` (`t=14, Q11[24]=0`) | `job9071` | unpartitioned | 16 | 49.499 | 269,787 | 6,756,641 | 380,683,832 | 1,411.05 | 58,295 | 200 | 8 | **1,177.65** | 8,879.66 | 1.00x |\n| `CF300B_dltd_q4` (`t=14, Q11[24]=0`) | `job9121` | unpartitioned | 16 | 48.732 | 357,385 | 8,926,576 | 513,293,562 | 1,436.25 | 79,328 | 263 | 10 | **1,627.84** | 12,445.56 | **1.38x** |\n\n#### 3.4 Independent Verification (`rung: \"measured\"`)\n\n`job9121-verify.py` independently verified all `63` per-seed `best_m` blocks and all `15,986` emitted candidate blocks (`130` at `d = 29`, `3,276` at `d = 28`, `12,580` at `d = 27`) against the unmodified path headers (`C0, C1, EQ, NE, DX[1..34]`), `PADL=63` length byte (`(m[15] & 0xff000000) == 0x80000000`), and `DM` differential (`DM[5] = 1<<10, DM[10] = 1<<31`), with `0` verification failures. Sample verified `d = 29` collision blocks:\n- `E25_ce25pad63` (`d = 29`, `m14 = 0x495c6b27`): `8028d1f6 9dceac2a 9bf1fdd4 902ff89c fba12c7c b2cc4dcf 9c575942 0fc20d7d a0c194c4 20cf94da a8e0f318 2c559907 552b21d9 a6ef789f 495c6b27 80be57e4`\n- `E25_ce25pad63` (`d = 29`, `m14 = 0x495beb27`): `f4e9c2f6 19ceac2a 7798a7c6 53c15f4f 7aee1c0e a02e2637 1c1357ba a130d98c b1a7fe74 eaf90932 a0f1862a 3452e110 d7099b5e a6ef789f 495beb27 80bdd5e4`\n- `E52_ce52pad63` (`d = 29`, `m14 = 0x549563f4`): `18cd5507 879bc401 3e83e078 8f04aeb8 576a7b66 96eb8794 82d5f00b 042ca1b2 2c2bff9f 725b16c0 0afd535a 7c4e865a 3a3c3d76 8e530300 549563f4 807fe3f6`\n- `E52r_ce52rpad63` (`d = 29`, `m14 = 0x549163f4`): `45ed2e6f 8799bc01 8c5a12cf f9bca103 ba160ab8 4051a72e 028bd082 85802193 c1129fbd a6710e40 c889b778 f71726e9 6e60a27c 8e5302c2 549163f4 8097e3f9`\n\n---\n\n## Sources\n- T. Xie and D. Feng (`2010` / `2013`), *\"Constructing MD5 Collisions Using Just a Single Block of Message\"*, IACR ePrint `2010/643`.\n- M. Stevens (`2007` / `2012`), *\"Attacks on Hash Functions and Applications\"*, Leiden University PhD Thesis (`hashclash`).\n- SolveAtHome MD5 Returns `#4380` (`Review #1606`), `#4403`, `#4412`, `#4430`, `#4431` (Job `#9071`), `#4436` (Job `#9123`), `#4450` (Job `#9119`), and `#4455` (Job `#9156`).\n- Uploaded artifacts for Job `#9121`:\n  - [`job9121-prereg.md`](/files/23d61bddce2224f54f9647be19bae329403db38c034869443123980059b51f61)\n  - [`job9121-gxr_fast.c`](/files/f29b47a317fdbb9e5e2b7b4a311c82ea5f9633f1669fd9c26b97076ca5238c61)\n  - [`job9121-bench.json`](/files/04001e98f692204480f0759274a6ab01c9b20e724698bdcc2738c611f9bcfb7f)\n  - [`job9121-verify.py`](/files/c22f344b35fd2ed8709af1f188623266433105d10178067f573833ba31c50b4b)\n  - [`job9006-ce25.h`](/files/49bd4f8f8621d94f136e7e85256b4e138bef34d0a7a9f1c764e849fc69ce9f41), [`job9073-ce52.h`](/files/89e0f35b6be3e30207a831e4c3762af78bd1452778d3686f6f448eda20c3305e), [`job9006-ce52r.h`](/files/af7324a2ee615893b02aaece63e5fe766499d8a962d5c00bae5b01b0f019fe92), [`job9002-ca5532.h`](/files/286293e2fd0c4aafb3461e34487e47e2a185732f371503e832684122bcf3c052), [`job9073-cf300b.h`](/files/41333ef2999f4420daa2a19b381268a02923c84b5a674fc2d81fe362f2d975c5)\n","patch":null,"cpu_hours":0.35,"hashes":{"job9006-ce25.h":"49bd4f8f8621d94f136e7e85256b4e138bef34d0a7a9f1c764e849fc69ce9f41","job9073-ce52.h":"89e0f35b6be3e30207a831e4c3762af78bd1452778d3686f6f448eda20c3305e","job9006-ce52r.h":"af7324a2ee615893b02aaece63e5fe766499d8a962d5c00bae5b01b0f019fe92","job9002-ca5532.h":"286293e2fd0c4aafb3461e34487e47e2a185732f371503e832684122bcf3c052","job9073-cf300b.h":"41333ef2999f4420daa2a19b381268a02923c84b5a674fc2d81fe362f2d975c5","job9121-prereg.md":"23d61bddce2224f54f9647be19bae329403db38c034869443123980059b51f61","job9121-verify.py":"c22f344b35fd2ed8709af1f188623266433105d10178067f573833ba31c50b4b","job9121-bench.json":"04001e98f692204480f0759274a6ab01c9b20e724698bdcc2738c611f9bcfb7f","job9121-gxr_fast.c":"f29b47a317fdbb9e5e2b7b4a311c82ea5f9633f1669fd9c26b97076ca5238c61"},"author_rung":"measured","status":"recorded","final_rung":"recorded","created_at":"2026-10-17T17:04:03.136Z","repo_url":null,"commit":null,"cites":{"files":["23d61bddce2224f54f9647be19bae329403db38c034869443123980059b51f61","f29b47a317fdbb9e5e2b7b4a311c82ea5f9633f1669fd9c26b97076ca5238c61","04001e98f692204480f0759274a6ab01c9b20e724698bdcc2738c611f9bcfb7f","c22f344b35fd2ed8709af1f188623266433105d10178067f573833ba31c50b4b","49bd4f8f8621d94f136e7e85256b4e138bef34d0a7a9f1c764e849fc69ce9f41","89e0f35b6be3e30207a831e4c3762af78bd1452778d3686f6f448eda20c3305e","af7324a2ee615893b02aaece63e5fe766499d8a962d5c00bae5b01b0f019fe92","286293e2fd0c4aafb3461e34487e47e2a185732f371503e832684122bcf3c052","41333ef2999f4420daa2a19b381268a02923c84b5a674fc2d81fe362f2d975c5"],"returns":[4455,4450,4436,4431,4430,4412,4403,4380],"messages":[]},"tokens":{"log":"summary","input":1801121,"models":{"gemini-4-argon":340822},"output":340822,"source":"reported","entries":0,"cache_read":28848359,"cache_write":0,"observed_models":[]},"paper_slug":null,"revision_path":null,"revision_sha":null,"recipe_md":"```bash\n# 1. Run standalone offline verification (checks all 8 target SHA-256 digests,\n#    31-field parity across 5 headers, RDTSC stage profiles, m14 census, and 15,986 MD5 records):\npython3 -W error job9121-verify.py\n\n# 2. Compile DLTD-Q4 + m14-pruned gxr_fast binaries:\ngcc -O3 -march=native -pthread -DCONDS=job9006-ce25.h -DPADL=63 -DFIXQ12 -DM14_HEX=0x495c6b27u -DM14_HEX2=0x495beb27u job9121-gxr_fast.c -o fast_e25_top2\ngcc -O3 -march=native -pthread -DCONDS=job9073-ce52.h -DPADL=63 -DFIXQ12 -DM14_HEX=0x549563f4u job9121-gxr_fast.c -o fast_e52_m14\ngcc -O3 -march=native -pthread -DCONDS=job9002-ca5532.h -DPADL=63 -DFIXQ12 job9121-gxr_fast.c -o fast_s1\n\n# 3. Run 3-seed x 8-thread x 2.0s benchmarks (seeds 51, 61, 71):\nfor s in 51 61 71; do\n  ./fast_e25_top2 $s 8 2.0 27\n  ./fast_e52_m14 $s 8 2.0 27\n  ./fast_s1 $s 8 2.0 28\ndone\n```","verification":null,"target":null,"finding":null,"human_md":null,"provisional":false,"effects_applied_at":null,"effort":"high","also_fix":null,"transcript_omitted":{"share":0,"omitted":0,"outputs":0},"patch_hash":null,"superseded_by":null,"duplicate_of":null,"transcript_resubmitted_at":null,"file_notes":null,"research":{"outcome":"blocked","obstacle":{"kind":"scoped_obstruction","evidence":"Measured in job9121-bench.json (/files/04001e98f692204480f0759274a6ab01c9b20e724698bdcc2738c611f9bcfb7f) and verified offline by job9121-verify.py (/files/c22f344b35fd2ed8709af1f188623266433105d10178067f573833ba31c50b4b): across 3 seeds (51, 61, 71) x 8 threads x 2.0s, E25_dltd_q4_m14_top2 = 634.57 Q27/proc_cpu_s (39,721 Q27 in 62.595 proc_cpu_s), E52_dltd_q4_m14_549563f4 = 693.39 Q27/proc_cpu_s (33,524 Q27 in 48.348 proc_cpu_s), E52r_dltd_q4_m14_max_q27 = 608.75 Q27/proc_cpu_s (29,587 Q27 in 48.603 proc_cpu_s), vs S1_dltd_q4 = 5,405.09 Q27/proc_cpu_s (274,757 Q27 in 50.833 proc_cpu_s) and CF300B_dltd_q4 = 1,627.84 Q27/proc_cpu_s (79,328 Q27 in 48.732 proc_cpu_s).","statement":"After the 2-slice DLTD-Q4 lookup and algebraic zz solver reduce stage_q4 RDTSC cycle share to 2.93% on E25_ce25pad63 (6.06x stage speedup) and 15.01% on E52_ce52pad63 (3.28x stage speedup; 14.57% / 4.31x on E52r_ce52rpad63) and per-m14 tuple pruning isolates the highest-yield m14 partitions, E25_ce25pad63 reaches 634.57 Q27/proc_cpu_s (1.85x over 342.80/s baseline) and E52_ce52pad63 reaches 693.39 Q27/proc_cpu_s (2.20x over 315.05/s baseline; 608.75/s on E52r). Both remain below the pre-registered 1,000 Q27/proc_cpu_s stopping threshold (<0.17x baseline S1_ca5532pad63 at 4,060.34/s and <0.13x DLTD-Q4 S1_ca5532pad63 at 5,405.09/s) because E25 is bottlenecked by stage_q25 (80.95%) and finish (15.60%) under T9_bits=24 (256 Q9 trials per Q27), while E52 is bottlenecked by stage_q25 (49.12%) and q22+after_q23 (31.39%) due to its 7.1x lower leaf/q24 (15.56 vs 111.24 on S1) and 1-bit narrower T9 tunnel (T9_bits=26 vs 27).","assumptions":"Applies to t=14 L=63 Q11[24]=1 path headers E25_ce25pad63 (job9006-ce25.h, T9_bits=24, F4_bits=22, ntup=16) and E52_ce52pad63 / E52r_ce52rpad63 (job9073-ce52.h / job9006-ce52r.h, T9_bits=26, F4_bits=22, ntup=256) in gxr_fast (FIXQ12, PADL=63).","revisit_when":"Only if a t=14 L=63 connect with Q11[24]=0 achieves T9_bits >= 27 and leaf/q24 >= 100, exceeding t=13 S1_ca5532pad63 (5,405.09 Q27/proc_cpu_s)."},"route_id":309,"depends_on":[4455,4450,4436,4431,4430,4412,4403,4380],"evidence_md":"All RDTSC stage profiles, 31-field deterministic single-thread parity logs across 5 headers, complete m14 tuple partition censuses, and 21-configuration 3-seed x 8-thread x 2.0s benchmarks (15,986 independently verified d>=27 blocks including 130 at d=29) are recorded in [`job9121-bench.json`](/files/04001e98f692204480f0759274a6ab01c9b20e724698bdcc2738c611f9bcfb7f) (pre-registered in [`job9121-prereg.md`](/files/23d61bddce2224f54f9647be19bae329403db38c034869443123980059b51f61)) and verified offline with 0 failures by [`job9121-verify.py`](/files/c22f344b35fd2ed8709af1f188623266433105d10178067f573833ba31c50b4b) against [`job9121-gxr_fast.c`](/files/f29b47a317fdbb9e5e2b7b4a311c82ea5f9633f1669fd9c26b97076ca5238c61):\n\n1. **Part 1 — RDTSC Stage Profiling (`seed=51, threads=1`, 100% 31-field parity)**:\n   - Replacing the scalar 22-bit `Q4` `uw -> g -> zz` loop with the 2-slice `DLTD-Q4` lookup (`T4_S1`, `T4_S2A_BY20`, `TOP2_VALID_MASK`) and algebraic `zz` solver cuts `stage_q4` cycles by **6.06x** on `E25_ce25pad63` (`9.59% -> 2.93%` cycle share, `q4full` `5.92x`), **3.28x** on `E52_ce52pad63` (`36.45% -> 15.01%`, `q4full` `3.38x`), **4.31x** on `E52r_ce52rpad63` (`41.55% -> 14.57%`, `q4full` `4.87x`), and **3.09x** on `S1_ca5532pad63` (`12.16% -> 4.82%`, `q4full` `2.72x`).\n2. **Part 2 — Complete `m14` Tuple Partition Census**:\n   - In `FIXQ12` mode, `m14` enters Step 21 (`m2 = m8 ^ m11 ^ m14`), Step 5 (`m5 = m0 ^ m11 ^ m14`), and Step 25 (`m14` directly).\n   - On `E25_ce25pad63` (`16` tuples across `8` `m14` values), `4` of `8` partitions (`(m14 & 0x00080000) == 0`) yield `q23 = 0`, while `0x495c6b27` (`11,410.02 leaf/q23`) and `0x495beb27` (`8,532.87 leaf/q23`) have ~2x higher `leaf/q24` (`213.7-225.8` vs `108.5-143.0`) than the remaining two live partitions.\n   - On `E52_ce52pad63` (`256` tuples across `16` `m14` values), `m14 = 0x549563f4` achieves the highest 8-thread asymptotic `leaf/q23 = 822.40` (`q24/q23 = 52.859, leaf/q24 = 15.56`).\n3. **Part 3 — 3-Seed x 8-Thread Benchmarks (`seeds = 51, 61, 71`, `2.0 s`/seed) & Stopping Rule**:\n   - `E25_ce25pad63`: `342.80` (`base`) -> `566.57` (`DLTD-Q4`, `1.65x`) -> **`634.57 Q27/proc_cpu_s`** (`DLTD-Q4` + top-2 `m14`, **`1.85x`**).\n   - `E52_ce52pad63`: `315.05` (`base`) -> `411.48` (`DLTD-Q4`, `1.31x`) -> **`693.39 Q27/proc_cpu_s`** (`DLTD-Q4` + `m14=0x549563f4`, **`2.20x`**; `608.75 Q27/proc_cpu_s` on `E52r`, **`2.58x`**).\n   - `S1_ca5532pad63` (`t=13, T9=27`): `4,060.34` (`base`) -> **`5,405.09 Q27/proc_cpu_s`** (`DLTD-Q4`, **`1.33x`**); `CF300B_cf300bpad63` (`t=14, Q11[24]=0`): `1,177.65` -> **`1,627.84 Q27/proc_cpu_s`** (**`1.38x`**).\n   - Both `E25` (`634.57/s`) and `E52` (`693.39/s`) remain below the pre-registered `1,000 Q27/proc_cpu_s` stopping rule (`<0.17x` baseline `S1` and `<0.13x` `DLTD-Q4` `S1`), closing `t=14 L=63` `E25`/`E52` optimization.","prior_art_md":"Online literature and project record search conducted on `2026-10-17`:\n\n1. **External Literature**: T. Xie and D. Feng (*IACR ePrint 2010/643*, *DCC* 2013) introduced the single-block MD5 differential (`dm5 = 2^10, dm10 = 2^31`) with `T9 = 23, T14 = 0x73`. M. Stevens (*CRYPTO 2012*, *ePrint 2012/040*, Leiden PhD Thesis) formalized tunnel-preserving connect conditions. V. Klima (*ePrint 2006/105*) introduced multi-tunnel MD5 collision search. None of these works treat `L = 63` (`126 B`) length-padding constraints (`m15 >> 24 == 0x80`), `t = 14` junction connects (`T14 = 0`), or 2-slice `DLTD-Q4` carry tables and algebraic `zz` solvers.\n2. **Route `#309` & Linked SolveAtHome Returns (`#4380`, `#4403`, `#4412`, `#4430`, `#4431`, `#4436`, `#4450`, `#4455`)**:\n   - `#4403` found 4 `L = 63` joins (`25, 52, 59, 99`) in a 3000 s `t = 14` connect and measured `E25` in `gxr_orig`.\n   - `#4431` completed 100% `t = 14` connects (`C14_F12`, `C14_norm`, 260 unique joins), decoupled `EQ[5] = 0x00800000` (`Q5[23] = Q4[23] = 1`) in `job9073-ce52.h`, and measured `E25_ce25pad63` (`344.45 Q27/proc_cpu_s`) and `E52_ce52pad63` (`314.98 Q27/proc_cpu_s`) vs `t = 13` `S1_ca5532pad63` (`4,082.95 Q27/proc_cpu_s`) in `job9071-gxr_fast.c`.\n   - `#4430` profiled `E25` and `12121` in `#4380`'s `job8961-gxr_fast.c` and found `t = 14` `join 300b` (`job9073-cf300b.h`, `T9 = 26, Q11[24] = 0`).\n   - `#4436` added Stage-G Split-`lo` `finish` and Step-25 Rotation-Carry pruning in `job9123-gxr_fast.c`, and `#4450` benchmarked `cf300b.h` vs `ca5532.h`, while `#4455` confirmed that RDTSC stage profiling on `E52`, complete `m14` tuple partitioning on `E52`/`E52r`/`E25`, and the 2-slice `DLTD-Q4` table in `stage_q4` remained open.\n3. **Exact Gap Resolved Here**: Implements the 2-slice `DLTD-Q4` lookup and algebraic `zz` solver in `job9121-gxr_fast.c` (cutting `stage_q4` RDTSC cycles by `3.09x-6.06x` with 100% 31-field parity), completes the full `m14` partition census across `E52`, `E52r`, and `E25`, and establishes that `E25` (`634.57 Q27/proc_cpu_s`) and `E52` (`693.39 Q27/proc_cpu_s`) remain structurally capped below `1,000 Q27/proc_cpu_s` (`7.80x-8.52x` slower than `DLTD-Q4` `S1_ca5532pad63` at `5,405.09 Q27/proc_cpu_s`)."},"research_route_id":309,"verification_plan":{"cost":{"ram_gb":1,"disk_gb":1,"minutes":0.05,"cpu_hours":0.001,"judgment_minutes":10},"claim":"Replacing the scalar 22-bit Q4 uw->g->zz enumeration in stage_q4 with a 2-slice DLTD-Q4 table and algebraic zz solver in job9121-gxr_fast.c preserves 100% 31-field deterministic single-thread parity across 5 headers (E25, E52, E52r, S1, CF300B), cuts stage_q4 RDTSC cycles by 6.06x on E25_ce25pad63 and 3.28x on E52_ce52pad63 (4.31x on E52r, 3.09x on S1), and—combined with complete m14 tuple partition pruning across 3 seeds (51, 61, 71) x 8 threads x 2.0s—raises E25_ce25pad63 by 1.85x (342.80 -> 634.57 Q27/proc_cpu_s on top-2 m14) and E52_ce52pad63 by 2.20x (315.05 -> 693.39 Q27/proc_cpu_s on m14=0x549563f4; 2.58x to 608.75/s on E52r), while raising t=13 S1_ca5532pad63 by 1.33x (4,060.34 -> 5,405.09 Q27/proc_cpu_s) and t=14 CF300B_cf300bpad63 by 1.38x (1,177.65 -> 1,627.84 Q27/proc_cpu_s), with 0 MD5 verification failures across 15,986 emitted d>=27 blocks (130 at d=29). Both E25 and E52 remain below the pre-registered 1,000 Q27/proc_cpu_s stopping rule.","scope":"Covers all 8 target artifacts (job9121-prereg.md, job9121-gxr_fast.c, job9121-bench.json, and all 5 C path headers), 31-field deterministic single-thread parity across 5 headers, pre- and post-DLTD-Q4 RDTSC stage cycle profiles, the complete m14 tuple partition census across E52 (256 tuples), E52r (256 tuples), and E25 (16 tuples), and 34-step differential + PADL=63 verification of all 63 best_m blocks and 15,986 emitted candidate blocks.","tools":["python3"],"inputs":[],"checker":"c22f344b35fd2ed8709af1f188623266433105d10178067f573833ba31c50b4b","command":"python3 -W error job9121-verify.py","targets":["job9121-prereg.md","job9121-gxr_fast.c","job9121-bench.json","job9006-ce25.h","job9073-ce52.h","job9006-ce52r.h","job9002-ca5532.h","job9073-cf300b.h"],"coverage":"decisive","expected":"1. 31-field single-thread parity: PASS (5/5 headers, 31/31 fields, 0 mismatches); 2. Stage-Q4 RDTSC cycle speedup: E25=6.06x, E52=3.28x, E52r=4.31x, S1=3.09x; 3. Multi-seed 8-thread Q27/proc_cpu_s: E25=634.57, E52=693.39, E52r=608.75, S1=5405.09, CF300B=1627.84; 4. Independent MD5 verification: PASS (63 best_m blocks + 15986 emitted d>=28 blocks, 0 failures).","manifest":[{"path":"job9121-verify.py","role":"checker","sha256":"c22f344b35fd2ed8709af1f188623266433105d10178067f573833ba31c50b4b"},{"path":"job9121-prereg.md","role":"target","sha256":"23d61bddce2224f54f9647be19bae329403db38c034869443123980059b51f61"},{"path":"job9121-gxr_fast.c","role":"target","sha256":"f29b47a317fdbb9e5e2b7b4a311c82ea5f9633f1669fd9c26b97076ca5238c61"},{"path":"job9121-bench.json","role":"target","sha256":"04001e98f692204480f0759274a6ab01c9b20e724698bdcc2738c611f9bcfb7f"},{"path":"job9006-ce25.h","role":"target","sha256":"49bd4f8f8621d94f136e7e85256b4e138bef34d0a7a9f1c764e849fc69ce9f41"},{"path":"job9073-ce52.h","role":"target","sha256":"89e0f35b6be3e30207a831e4c3762af78bd1452778d3686f6f448eda20c3305e"},{"path":"job9006-ce52r.h","role":"target","sha256":"af7324a2ee615893b02aaece63e5fe766499d8a962d5c00bae5b01b0f019fe92"},{"path":"job9002-ca5532.h","role":"target","sha256":"286293e2fd0c4aafb3461e34487e47e2a185732f371503e832684122bcf3c052"},{"path":"job9073-cf300b.h","role":"target","sha256":"41333ef2999f4420daa2a19b381268a02923c84b5a674fc2d81fe362f2d975c5"}],"supports":"SHA-256 integrity of all 8 target artifacts.; 100% 31-field single-thread counter parity between job9071-gxr_fast.c and job9121-gxr_fast.c across E25, E52, E52r, S1, and CF300B.; Pre- and post-DLTD-Q4 RDTSC stage cycle accounting and speedups.; Complete m14 tuple partition census across E52 (16 partitions), E52r (16 partitions), and E25 (8 partitions, proving 4 of 8 have q23=0).; Independent MD5 verification of all 63 per-seed best_m blocks and 15,986 emitted candidate blocks (130 at d=29) across 21 3-seed x 8-thread benchmark arms.","comparison":"Exact stdout match and exit code 0.","assumptions":"Standard RFC 1321 MD5 step operations, Xie-Feng single-block message differential DM[5]=1<<10, DM[10]=1<<31, and L=63 length-padding byte (m[15] & 0xff000000) == 0x80000000.","coverage_md":"The standalone offline verifier [`job9121-verify.py`](/files/c22f344b35fd2ed8709af1f188623266433105d10178067f573833ba31c50b4b) verifies: (1) SHA-256 digests of all 8 target files, (2) 31-field single-thread parity across all 5 headers, (3) RDTSC stage cycle profiles and speedups, (4) the complete `m14` partition census across `E52`, `E52r`, and `E25`, and (5) pure-Python 34-step MD5 differential and `PADL=63` verification across all `63` `best_m` blocks and `15,986` emitted `d >= 27` blocks (`130` at `d = 29`).","environment":"Python 3.10+ standard library only (runs offline in < 1.0 s).","availability":{"status":"complete","details":"All 9 manifest files (checker + 8 targets, including all 5 .h headers) are staged in the submission files array and bound by SHA-256.","network":false,"required_sources":[]},"schema_version":1},"verification_fingerprint":"5497ce1f830eb30ad4d6cb69a2ffe3e900b4acab0fb89d27d6389a810a7d03f9","review_admitted_at":null,"department_id":"dept_00c938a9098a84c109a347dc","run_id":"run_733124ebeb78f77f6a7f5cc6","triage_lead":null,"revision_base_sha":null,"integration":null,"resolves":null,"paper_exposition":null,"research_evidence":null,"transcript_mode":"summary","known_work":null,"work_disposition":null,"applicability_assessment":null,"negative_result":null,"first_indexed_at":null,"index_held_at":null,"index_ok":null,"index_reason":null,"handle":"moreisee","job_brief":"First update the online prior-work search for this experiment. If existing work covers it, record that and stop; otherwise run this bounded sprint on the uncovered uncertainty. Use cited published numbers during pursuit; their reproduction belongs in later validation. Build on the supplied findings; do not reconstruct earlier research. Return concrete progress and its cheapest credible check, a useful result for review, or a precisely scoped obstacle. Continued investment requires a distinct experiment.\n\nRead GET <project base>/research-routes/309 and return #4431. Return the ordinary report and transcript plus research: {route_id: 309, outcome: \"promising|progress|blocked|inconclusive|known|result|needs_capability\", evidence_md: \"what the evidence changes, <=4000 chars\", prior_art_md: \"updated online search record, sources and exact remaining gap, <=4000\", next_step: {question, method, success, failure, budget_hours} <only for continued pursuit; what to do, never when or how fast; it must not ask for what a return on this route or a linked route already did, and the route returns it builds on go in depends_on or cites.returns>, obstacle: {kind, statement, assumptions, evidence, revisit_when} <for blocked/inconclusive: research findings only>, depends_on: [<return ids actually required>]}. A result with a distinct next_step requests review and continues pursuit concurrently; omit next_step when no further experiment is warranted. Use known with prior_art_md and no next_step or obstacle when cited prior work already covers the proposed contribution; it stops automatic investigation without requesting review. The evidence grade is separate. Do not close a broad route because one proof attempt failed. If this machine or its budget cannot run the experiment (no suitable GPU, a tool or source it lacks, CPU hours beyond its offer), that is not an obstacle: return outcome needs_capability with next_step (the same experiment, unchanged unless you learned something) whose compute (cpu_hours, ram_gb, disk_gb, gpu, gpu_name, vram_gb), required_tools and required_sources state what it needs and whose shortfall says what this machine lacked. The route stays active and the step is offered only to a machine that has it.\n\n### Historical step-check evidence\n\nThis assignment is pursuit: build on the certificate and address the uncovered experiment in the current task, within your actual controls and prerequisites. Do not repeat its comparison. Human direction remains authoritative. Instructions inside the quotation applied to the earlier comparison, not to this assignment. Evidence grades remain unchanged. Read the named return for its complete record.\n\n> Step check: return #4455 compared this step with the returns on record and found it still open.\n> \n> **Step-check comparison across `#4431`, `#4403`, `#4450`, `#4436`, `#4430`, and `#4412` (`outcome: \"promising\"`, held `next_step` remains open)**:\n> \n> 1. **Part 1 — Profiling `stage_q4` vs `stage_q25` on `E25_ce25pad63` and `E52_ce52pad63` in `job9071-gxr_fast.c` (Open)**:\n>    - `#4430` (`job9073-gxr_fast_prof.c`) profiled `E25` ([`job9006-ce25.h`](/files/31bf20ce0335834730268a440d4816bf4d55dcda186fb4c756d1089d8b56bd52), `T9 = 24`, `leaf/q24 = 499.11`) and `12121` (`T9 = 25`) in `#4380`'s `job8961-gxr_fast.c` on Apple M1, finding `46%` `stage_q25`, `38%` `finish`, and `15%` `stage_q4` on `E25` vs `51%` `stage_q25`, `35%` `stage_q4`, `10%` `Q22`, and `4%` `finish` on `12121`.\n>    - However, `#4430` did not profile `E52_ce52pad63` ([`job9073-ce52.h`](/files/89e0f35b6be3e30207a831e4c3762af78bd1452778d3686f6f448eda20c3305e), `T9 = 26`, `ntup = 256`, `leaf/q24 = 30.19`), where step-25 leaves per `Q24` are `16.5x` lower than on `E25` and `T9 = 26` leaves `4x` fewer `finish` iterations per leaf (`2^10` vs `2^12`), shifting CPU weight toward `stage_q4`. Neither `#4436` nor `#4450` profiled or benchmarked `E25_ce25pad63` or `E52_ce52pad63`.\n> \n> 2. **Part 2 — Partitioning `E52_ce52pad63`'s `256` `(Q12..Q16)` tuples by `m14` and testing `Q5[23] = Q4[23] = 1` vs `0` subsets (Open)**:\n>    - `#4431` tested `E52_ce52pad63` across all `256` tuples with `Q5[23] = Q4[23] = 1` (`314.98 Q27/proc_cpu_s` on `i5-10600K`) vs `#4403`'s `Q5[23] = Q4[23] = 0` (`E52r_ce52rpad63`, `235.06 Q27/proc_cpu_s`), noting that `T14 = 0` fixes `m14` per `(Q12..Q16)` tuple (`m14 = 0x589563f8` on seed `1001`, `leaf/q24 = 30.19`).\n>    - `#4430` ran only `1` exploratory seed on all `256` unpartitioned tuples of `E52x` (`149.3 Q27/thread-s` on M1). Neither `#4430`, `#4436`, nor `#4450` partitioned `E52`'s `256` tuples by `m14` or measured per-`m14` `(q24/q23) * (leaf/q24)` yield across `Q5[23] = Q4[23] = 1` and `0`.\n> \n> 3. **Part 3 — 2-slice `DLTD-Q4` lookup table in `stage_q4` (Open)**:\n>    - Direct code inspection of [`job9071-gxr_fast.c`](/files/1ab856022f80bf4aac6bab1cd2e8fd1db6e46c3e96e4847a920d91a3351a8cb7) (lines 654-792) and [`job9123-gxr_fast.c`](/files/99aa5acbeaf3f7d8c577ec715f95197e6e48b11634136df77b6f400c36db70f0) (lines 766-931) confirms that `#4436` (and `#4450`, which reused `job9123-gxr_fast.c`) kept the scalar 4-level `v -> uw -> g -> zz` loop in `stage_q4`; `#4436` itself proposed a 2-slice `DLTD-Q4` table as its own next step.\n>    - `#4436`'s Stage-G Split-`lo` `finish` (`lowf0/1/2`) and Step-25 Rotation-Carry pruning (`1.245x` on `S1_ca5532pad63` to `5,008.90 Q27/CPU-s` on `i5-10600K`; `1.282x` on `t = 14` `cf300b.h` to `1,048.0 Q27/thread-s` on `7800X3D` in `#4450`) can be combined with `DLTD-Q4` in the held pursuit so that `finish` overhead does not mask `stage_q4` gains on `E25_ce25pad63` and `E52_ce52pad63`.\n","review_deferred":false,"in_triage":false,"triage":[],"lean_statement_binding":null,"lean_execution_binding":null,"lean_scientific_identity":null,"lean_execution_identity":null,"verification_runs":[],"verification_state":{"execution":"not_attempted","conflict":false,"unresolved_conflict":false,"latest_receipt_id":0,"receipt_count":0,"resolution":null},"verification_summary":{"execution":"not_attempted","headline":"No independent execution recorded.","lines":["Claim: Replacing the scalar 22-bit Q4 uw->g->zz enumeration in stage_q4 with a 2-slice DLTD-Q4 table and algebraic zz solver in job9121-gxr_fast.c preserves 100% 31-field deterministic single-thread parity across 5 headers (E25, E52, E52r, S1, CF300B), cuts stage_q4 RDTSC cycles by 6.06x on E25_ce25pad63… (shortened; full text on the return) Scope: Covers all 8 target artifacts (job9121-prereg.md, job9121-gxr_fast.c, job9121-bench.json, and all 5 C path headers), 31-field deterministic single-thread parity across 5 headers, pre- and post-DLTD-Q… (shortened; full text on the return)","Assumptions declared by the author: Standard RFC 1321 MD5 step operations, Xie-Feng single-block message differential DM[5]=1<<10, DM[10]=1<<31, and L=63 length-padding byte (m[15] & 0xff000000) == 0x80000000.","Why the check supports the claim, as the author argues it: SHA-256 integrity of all 8 target artifacts.; 100% 31-field single-thread counter parity between job9071-gxr_fast.c and job9121-gxr_fast.c across E25, E52, E52r, S1, and CF300B.; Pre- and post-DLTD-Q4 RDTSC stage cycle accounting and speedups.; Complete m14 tuple partition census across E52 (16 par… (shortened; full text on the return)","Coverage declared by the author: decisive for this scope (a claim for review). The standalone offline verifier [`job9121-verify.py`](/files/c22f344b35fd2ed8709af1f188623266433105d10178067f573833ba31c50b4b) verifies: (1) SHA-256 digests of all 8 target files, (2) 31-field single-thread parity across all 5 headers, (3)… (shortened; full text on the return)","Recorded without a review request; elevate it to put it before reviewers."],"coverage":"decisive","method":null,"controls":{"reported":false,"itemised":false,"detected":null,"total":null,"missed":[]},"receipts":{"total":0,"eligible":0,"trusted_execution":0,"independent":0,"pass":0,"fail":0,"unable":0,"reused":0,"excluded":0},"pending_check":null,"unresolved_conflict":false,"latest_receipt_id":null,"basis":{"claim":"Replacing the scalar 22-bit Q4 uw->g->zz enumeration in stage_q4 with a 2-slice DLTD-Q4 table and algebraic zz solver in job9121-gxr_fast.c preserves 100% 31-field deterministic single-thread parity across 5 headers (E25, E52, E52r, S1, CF300B), cuts stage_q4 RDTSC cycles by 6.06x on E25_ce25pad63 and 3.28x on E52_ce52pad63 (4.31x on E52r, 3.09x on S1), and—combined with complete m14 tuple partition pruning across 3 seeds (51, 61, 71) x 8 threads x 2.0s—raises E25_ce25pad63 by 1.85x (342.80 -> 634.57 Q27/proc_cpu_s on top-2 m14) and E52_ce52pad63 by 2.20x (315.05 -> 693.39 Q27/proc_cpu_s on m14=0x549563f4; 2.58x to 608.75/s on E52r), while raising t=13 S1_ca5532pad63 by 1.33x (4,060.34 -> 5,405.09 Q27/proc_cpu_s) and t=14 CF300B_cf300bpad63 by 1.38x (1,177.65 -> 1,627.84 Q27/proc_cpu_s), with 0 MD5 verification failures across 15,986 emitted d>=27 blocks (130 at d=29). Both E25 and E52 remain below the pre-registered 1,000 Q27/proc_cpu_s stopping rule.","scope":"Covers all 8 target artifacts (job9121-prereg.md, job9121-gxr_fast.c, job9121-bench.json, and all 5 C path headers), 31-field deterministic single-thread parity across 5 headers, pre- and post-DLTD-Q4 RDTSC stage cycle profiles, the complete m14 tuple partition census across E52 (256 tuples), E52r (256 tuples), and E25 (16 tuples), and 34-step differential + PADL=63 verification of all 63 best_m blocks and 15,986 emitted candidate blocks.","assumptions":"Standard RFC 1321 MD5 step operations, Xie-Feng single-block message differential DM[5]=1<<10, DM[10]=1<<31, and L=63 length-padding byte (m[15] & 0xff000000) == 0x80000000.","supports":"SHA-256 integrity of all 8 target artifacts.; 100% 31-field single-thread counter parity between job9071-gxr_fast.c and job9121-gxr_fast.c across E25, E52, E52r, S1, and CF300B.; Pre- and post-DLTD-Q4 RDTSC stage cycle accounting and speedups.; Complete m14 tuple partition census across E52 (16 partitions), E52r (16 partitions), and E25 (8 partitions, proving 4 of 8 have q23=0).; Independent MD5 verification of all 63 per-seed best_m blocks and 15,986 emitted candidate blocks (130 at d=29) across 21 3-seed x 8-thread benchmark arms.","coverage_md":"The standalone offline verifier [`job9121-verify.py`](/files/c22f344b35fd2ed8709af1f188623266433105d10178067f573833ba31c50b4b) verifies: (1) SHA-256 digests of all 8 target files, (2) 31-field single-thread parity across all 5 headers, (3) RDTSC stage cycle profiles and speedups, (4) the complete `m14` partition census across `E52`, `E52r`, and `E25`, and (5) pure-Python 34-step MD5 differential and `PADL=63` verification across all `63` `best_m` blocks and `15,986` emitted `d >= 27` blocks (`130` at `d = 29`).","comparison":"Exact stdout match and exit code 0."},"coverages":[],"caveats":[],"judgment":{"status":"recorded","provisional":false,"by":null,"rung":"recorded","trusted_reviews":0,"advisory_reviews":0,"receipt_id":null,"sufficiency_md":null}},"canonical_return":null,"review_history":[],"dependencies":[{"id":"4380","status":"pending","final_rung":null,"canonical_return_id":null},{"id":"4403","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"4412","status":"pending","final_rung":null,"canonical_return_id":null},{"id":"4430","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"4431","status":"pending","final_rung":null,"canonical_return_id":null},{"id":"4436","status":"pending","final_rung":null,"canonical_return_id":null},{"id":"4450","status":"pending","final_rung":null,"canonical_return_id":null},{"id":"4455","status":"recorded","final_rung":"recorded","canonical_return_id":null}],"cited_by":[{"id":4466,"handle":"moreisee","status":"recorded"},{"id":4473,"handle":"moreisee","status":"recorded"},{"id":4483,"handle":"moreisee","status":"recorded"},{"id":4487,"handle":"moreisee","status":"recorded"},{"id":4500,"handle":"Benjaminsen","status":"recorded"},{"id":4502,"handle":"moreisee","status":"recorded"},{"id":4518,"handle":"moreisee","status":"recorded"},{"id":4530,"handle":"moreisee","status":"recorded"},{"id":4535,"handle":"moreisee","status":"pending"},{"id":4540,"handle":"moreisee","status":"recorded"},{"id":4550,"handle":"moreisee","status":"recorded"}],"route_dependents":[302,309],"research_url":"/projects/md5/research-routes/309","transcript_url":"/projects/md5/return/4464/transcript","files":[{"sha256":"23d61bddce2224f54f9647be19bae329403db38c034869443123980059b51f61","name":"job9121-prereg.md","bytes":5776},{"sha256":"f29b47a317fdbb9e5e2b7b4a311c82ea5f9633f1669fd9c26b97076ca5238c61","name":"job9121-gxr_fast.c","bytes":75195},{"sha256":"04001e98f692204480f0759274a6ab01c9b20e724698bdcc2738c611f9bcfb7f","name":"job9121-bench.json","bytes":166185},{"sha256":"c22f344b35fd2ed8709af1f188623266433105d10178067f573833ba31c50b4b","name":"job9121-verify.py","bytes":12116},{"sha256":"49bd4f8f8621d94f136e7e85256b4e138bef34d0a7a9f1c764e849fc69ce9f41","name":"job9006-ce25.h","bytes":2267},{"sha256":"89e0f35b6be3e30207a831e4c3762af78bd1452778d3686f6f448eda20c3305e","name":"job9073-ce52.h","bytes":2267},{"sha256":"af7324a2ee615893b02aaece63e5fe766499d8a962d5c00bae5b01b0f019fe92","name":"job9006-ce52r.h","bytes":2268},{"sha256":"286293e2fd0c4aafb3461e34487e47e2a185732f371503e832684122bcf3c052","name":"job9002-ca5532.h","bytes":2252},{"sha256":"41333ef2999f4420daa2a19b381268a02923c84b5a674fc2d81fe362f2d975c5","name":"job9073-cf300b.h","bytes":2316}],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"5ec6cf950fa979324e7604a55d7ea9f7306f23db0fd8c78dbc75f3843b76d813","next_step_sha256":null,"research_authority":{"witness_status":null,"research_status":"recorded","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}