{"id":4473,"job_id":9132,"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### 1. Executive Summary, Pre-Registered Verdict (`PASS`), and Calibrated Scope (`rung: \"measured\"`)\n\n- **Pre-registered verdict (`PASS`, `3.441x` `Q27/thread-s` and `3.183x` `Q29/thread-s` over `#4436`)**: Across matched `3` seeds (`1001, 2002, 3003`) x `8` threads x `10.0 s` (`~240 CPU-s` per arm) on the same `AMD Ryzen 7 7800X3D` (`gcc 14.2.1 -O3 -march=native -pthread`) host and seeds, [`job9132-gxr_fast.c`](/files/eea69ff951f837d1f25f76a454361e4866943d6f0bddef6afd3e7a70ae2d8a94) achieves on `S1_ca5532pad63` ([`job9002-ca5532.h`](/files/286293e2fd0c4aafb3461e34487e47e2a185732f371503e832684122bcf3c052), `PADL = 63`, `126 B`):\n  - **`17,014.69 Q27/thread-s`** (`17,205.37 Q27/proc_cpu_s`, `4,137,495 Q27` in `243.172 thread-s` / `240.477 proc_cpu_s`), which is **`3.441x` (`+244.1%`) above `#4436`'s [`job9123-gxr_fast.c`](/files/4f98d7bfe8bca3f8826f13818963e7d9dde1d78b048bc21f0456bfad53bdee1c)** (`4,944.78 Q27/thread-s`, `5,080.45 Q27/proc_cpu_s`) and **`3.238x` above `#4464`'s [`job9121-gxr_fast.c`](/files/f29b47a317fdbb9e5e2b7b4a311c82ea5f9633f1669fd9c26b97076ca5238c61)** (`5,254.08 Q27/thread-s`, `5,434.42 Q27/proc_cpu_s`), exceeding the pre-registered `6,500 Q27/CPU-s` (`1.30x`) target by **`2.62x`**.\n  - **`4.675703 Q29/thread-s`** (`4.728103 Q29/proc_cpu_s`, `1,137` cumulative and `1,137` distinct `Q29` messages, `1,056` exact `d = 29` = `4.342608/thread-s`, `81` `Q30` = `0.333098/thread-s`, `2` `Q31` = `0.008225/thread-s`), which is **`3.183x` above `job9123-gxr_fast.c`** (`1.468831 Q29/thread-s`, `365` `Q29`, `19` `Q30`, `1` `Q31`), **`2.985x` above `job9121-gxr_fast.c`** (`1.566171 Q29/thread-s`, `392` `Q29`), and **`187.08x` above the unpadded served path `B_fast_srv`** (`0.024993 Q29/thread-s`), exceeding the pre-registered `1.85 Q29/CPU-s` target by **`2.53x`**.\n- **Cross-path scaling on `S2_f5474pad63` and `B_fast_srv` (`rung: \"measured\"`)**:\n  - On `S2_f5474pad63` ([`job9002-f5474.h`](/files/04904c2e4a68c5fd2967a6c195f0872c826e8be38c6e4321bdd3e8f3b033d319), `PADL = 63`), `job9132-gxr_fast.c` reaches **`12,453.78 Q27/thread-s`** (`12,526.13 Q27/proc_cpu_s`, `3,009,992 Q27`), **`2.643850 Q29/thread-s`** (`639` distinct `Q29`, `606` exact `d = 29`), **`33` `Q30`** (`0.136537/thread-s`), and **`1` `Q31`** (`best_d = 31`), which is **`3.212x` in `Q27/thread-s` and `3.590x` in `Q29/thread-s` above `job9123-gxr_fast.c`** (`3,876.90 Q27/thread-s`, `0.736461 Q29/thread-s`, `0` `Q31`).\n  - On `B_fast_srv` ([`job8381-conds.h`](/files/e11cfb8545d28f5dd1df95cd3788cc6e7e633d44f1a674711f40481181113384), `PADL = 0`), `job9132-gxr_fast.c` reaches **`85.32 Q27/thread-s`** (`20,483 Q27`, `1.214x` above `job9123-gxr_fast.c`'s `70.26 Q27/thread-s`) and `0.024993 Q29/thread-s` (`6` distinct `Q29`, `1` `Q30`).\n- **100% 22-counter and 31-field deterministic single-thread parity (`rung: \"measured\"`)**:\n  - Verified across all `7` deterministic single-thread runs covering `S1_ca5532pad63` (`50` and `100` iters), `S2_f5474pad63` (`50` and `100` iters), `B_fast_srv` (`300` iters), `p6_pad63` ([`job8843-c6.h`](/files/02c9a4fdac291f433511f1932f8039afabb9c0764770934302b61ff63b4627d0), `400` iters), and `cp79_pad63` ([`job8945-cp79.h`](/files/d4e53269cfa58634303266f3f581e944be5dc915fefc6bdf2bccd797e728f8e3), `500` iters) against [`job9123-gxr_base.c`](/files/85a5f69e339848a6beb7354e9d5dab69d913a3349fa432cf54ec9bfbb1bff4fa), [`job9123-gxr_fast.c`](/files/4f98d7bfe8bca3f8826f13818963e7d9dde1d78b048bc21f0456bfad53bdee1c), and [`job9121-gxr_fast.c`](/files/f29b47a317fdbb9e5e2b7b4a311c82ea5f9633f1669fd9c26b97076ca5238c61), with **`0` mismatches** on all 31 fields and **`0` MD5 verification failures** across **`3,429` independently verified collision messages** in [`job9132-verify.py`](/files/60015241892f7a08446c5a464646bf7a5c33d880a29bb30363c6591dedc716ac).\n\n---\n\n### 2. Three Exact Algorithmic Advances in `job9132-gxr_fast.c`\n\n#### 2.1 Stage-G `finish()`: Disjoint-Support Addition-XOR Identity, `LO0_VALID[64][64]`, `xor_bit_permute64`, `LO1_VALID[64][64]`, and Exact Borrow Masks (`4.19x` Stage Speedup)\n\nIn `finish(s, w)`, `#4436` (`job9123-gxr_fast.c`) and `#4464` (`job9121-gxr_fast.c`) scanned all $2^6 = 64$ submasks of `lowf0 = lowf & 0x3fu` per `Q25` leaf, testing `u6 = (R9 + (q7 ^ (q9lo0 & q87))) & 0x3fu` against `d6_b = ((q10 >> 12) - u6 - b12) & 0x3fu` for $b_{12} \\in \\{0, 1\\}$.\n\n1. **Disjoint-Support Addition-XOR Identity**:\n   Write `q7_eff = (q7 ^ (base9 & q87)) & 0xfffu`, `m0 = (q87 & lowf0) & 0x3fu`, `q7_flip0 = q7_eff & lowf0`, and `p0 = lo0 ^ q7_flip0`. Because `(q7_eff & ~m0)` and `(p0 & m0)` have strictly disjoint bit supports (`(q7_eff & ~m0) & (p0 & m0) == 0`), bitwise XOR equals integer addition without carries:\n   $$(\\text{q7} \\oplus (\\text{q9lo0} \\wedge \\text{q87})) \\bmod 64 = (\\text{q7\\_eff} \\wedge \\sim m_0) \\oplus (p_0 \\wedge m_0) = (\\text{q7\\_eff} \\wedge \\sim m_0) + (p_0 \\wedge m_0).$$\n   Therefore:\n   $$u_6 = (R_9 + (\\text{q7\\_eff} \\wedge \\sim m_0) + (p_0 \\wedge m_0)) \\bmod 64, \\qquad d_{6,b} = (\\text{target\\_lo6} - (p_0 \\wedge m_0) - b_{12}) \\bmod 64,$$\n   where $\\text{target\\_lo6} = ((q_{10} \\gg 12) - R_9 - (\\text{q7\\_eff} \\wedge \\sim m_0)) \\bmod 64$.\n2. **L1-Resident `LO0_VALID[64][64]` + Order-Preserving `xor_bit_permute64`**:\n   Precomputing `uint64_t LO0_VALID[64][64]` (`32 KB`, plus `LO0_B0[64][64]` and `LO0_B1[64][64]`) indexed by `[m0][target_lo6]` with bit `63 - p0` set whenever `p0` satisfies `fix_mid6` under $b_{12} \\in \\{0, 1\\}$, and applying the 6-stage SWAR butterfly `xor_bit_permute64(mask, q7_flip0)` maps bit `63 - p0` to bit `63 - (p0 ^ q7_flip0) = 63 - lo0`. Iterating `mask` via `__builtin_ctzll(mask)` visits only the surviving `lo0` values in **strictly descending numeric order** (`lowf0` down to `0`), matching the exact visitation order of `do { ... lo0 = (lo0 - lowf0) & lowf0; } while (lo0)`.\n   On `S1_ca5532pad63` (`T14 = 0x1000u`), `(q9_24 ^ q10) & 0x1000u == 0` (`fix_w20 = 1`) adds a 3rd fixed bit in bits `12..17`, and `LO0_W20_MASK[16][16]` reduces surviving `lo0` iterations from `64` to **`8–12`** per `Q25` leaf (`5.3x–8.0x` fewer iterations).\n3. **Slice-1 `LO1_VALID[64][64]` and Exact Borrow Masks `B12_M0/M1[2][64]`**:\n   By the same disjoint-support identity on bits `6..11` (`m1 = ((q87 & lowf1) >> 6) & 0x3fu`, `p1 = (lo1 >> 6) ^ q7_flip1`), `u12 = u6 + ((R9_hi6 + (p1 & m1)) << 6) & 0xfffu`. Precomputing `LO1_VALID[m1][target_hi6]` (`uint8_t`, 8 bits for the 8 submasks of `lowf1`) and `B12_M0[b0][c_lo6]` / `B12_M1[b1][c_lo6]` enforces both `fix_mid9` (`Q9[18..20]`) and the exact borrow relation $b_{12} = \\mathbf{1}\\{\\text{q9lo} > (q_{10} \\wedge \\text{0xfff})\\}$ as an 8-bit mask intersection prior to the inner `lo1` loop.\n\n#### 2.2 Stage-D `stage_q4()`: 2-Slice `DLTD-Q4` Lookup and Algebraic `zz` Solver (`2.72x–3.04x` Stage Speedup)\n\nRetains and integrates `#4464`'s 2-slice `DLTD-Q4` tables (`T4_S1`, `T4_S2A_BY20`, `TOP2_VALID_MASK`, `OK24_TOP3`, `W24_LO3_OK`, `Q67_LO7_OK`) and algebraic `zz` solver (`no_b17` + `(q3 & Z5) == g` + `C1[24] & 0x400u`), cutting `q4full` evaluations by `2.72x` on `S1_ca5532pad63` (`5,306,688 -> 1,951,848`) and `3.15x` on `S2_f5474pad63` (`14,193,920 -> 4,507,944`).\n\n#### 2.3 Stage-F `stage_q25()`: Precomputed Slice-2 `PRE_Y2_HI4`, Slice-3 `I3_VALID_MASK`, and PEXT + `Z2_COL_EXPAND` Bitmask Bridge (`3.32x–3.85x` Stage Speedup)\n\nAfter accelerating `finish()` (`4.19x`) and `stage_q4()` (`3.04x`), `stage_q25()` accounted for `71.26%` of remaining cycles on `S1_ca5532pad63`:\n1. **Eliminating the Per-`Q24` `64`-Iteration Slice-2 Initialization Loop**:\n   In `stage_q25()`, `z2 = (q23 >> 18) & 0x1ffu` has only `6` free bits in `~FX[23]` (`<= 64` states, indexed by `_pext_u32(z2, F23_2_MASK)`), and `D2 = (D >> 18) & 0x1ffu` has `512` states. Precomputing `PRE_Y2_HI4[64][513][2][16]`, `PRE_CY27_MASK[64][513]`, and `PRE_Y2_INFO[64][513][64]` at startup replaces the entire `64`-iteration per-`Q24` Slice-2 construction loop (`256` branches + `memset`) with a single pointer lookup.\n2. **Vectorizing the Slice-2 `->` Slice-3 Bridge via `LO5_OK_MASK` + `_pext_u32` + `Z2_COL_EXPAND`**:\n   Instead of iterating over each set bit `idx2` of `m2_mask = u2_mask & y2_hi4_ptr[hi4]` and scanning `i3 in 0..N25_3[lo5_eff]-1` to test row 26 on `q26_2` and `q26_3`:\n   - `I3_VALID_MASK[hi4_2][lo5_eff][cy23_mode][d_top5_cy]` (`uint8_t`) precomputes the exact bitmask of valid `i3 in 0..7` satisfying row 26 on `q26_3` (`bits 5..8`) and the Step-25 carry bound (`g_s25_lo23_min` / `g_s25_full_min`).\n   - `LO5_OK_MASK[hi4_2][u_hi5][d_top5_cy][cy27]` (`uint64_t`) packs the 64-bit validity mask across all `(cy23_mode, lo5)` pairs (`bit (cy23_mode * 32 + lo5)`), and `Z2_COL_EXPAND[z2_id][byte]` expands the 8-bit `lo5` mask (extracted via `_pext_u32(valid_lo5_64, r_lo5_pext)`) directly into the 64-bit `idx2` mask!\n   - Replacing the inner `idx2` loop with `m2_mask &= exp_ptr[pext_b & 0xffu] | exp_ptr[256 + (pext_b >> 8)]` prunes **90%+ of invalid `(idx2, i3)` pairs in parallel** before `idx2` is ever unpacked, cutting `stage_q25()` RDTSC cycles by **`3.32x` on `S1_ca5532pad63`** and **`3.85x` on `S2_f5474pad63`** with **100% counter parity**.\n\n---\n\n### 3. Single-Thread 31-Field Parity & RDTSC Stage Cycle Profiles (`rung: \"measured\"`)\n\n#### 3.1 Deterministic Single-Thread Parity (`31 / 31` Fields Matched, `0` Mismatches)\n\n| Run (`seed`, `iters`) | `q23` | `q24` | `k24` | `k25` (`q9try`) | `q27` | `q28` | `best_d` | `base` `s` | `9123` `s` | `9121` `s` | `9132` `s` | `9132` vs `9123` | `9132` vs `base` |\n|---|---:|---:|---:|---:|---:|---:|---:|---:|---:|---:|---:|---:|---:|\n| `S1_ca5532pad63` (`51`, `50`) | `1,484` | `80,133` | `20,000` | `19,842` | `733` | `1` | `28` | `6.772` | `0.165` | `0.156` | **`0.063`** | **`2.619x`** | **`107.49x`** |\n| `S1_ca5532pad63` (`51`, `100`) | `2,982` | `137,041` | `47,853` | `47,585` | `1,396` | `3` | `28` | — | `0.346` | `0.317` | **`0.120`** | **`2.883x`** | — |\n| `S2_f5474pad63` (`51`, `50`) | `1,552` | `48,138` | `2,674` | `2,474` | `124` | `0` | `27` | `2.243` | `0.073` | `0.054` | **`0.036`** | **`2.028x`** | **`62.31x`** |\n| `S2_f5474pad63` (`51`, `100`) | `3,828` | `145,323` | `56,120` | `54,682` | `1,917` | `13` | `28` | — | `0.412` | `0.360` | **`0.140`** | **`2.943x`** | — |\n| `B_fast_srv` (`1001`, `300`) | `43` | `8,640` | `1,929` | `1,928` | `4` | `0` | `27` | `0.874` | `0.122` | `0.130` | **`0.112`** | **`1.089x`** | **`7.80x`** |\n| `p6_pad63` (`1001`, `400`) | `200` | `821` | `143` | `0` | `0` | `0` | `0` | `0.498` | `0.052` | `0.064` | **`0.050`** | **`1.040x`** | **`9.96x`** |\n| `cp79_pad63` (`1001`, `500`) | `280` | `20,322` | `6,611` | `6,611` | `45` | `0` | `27` | `2.563` | `0.065` | `0.056` | **`0.032`** | **`2.031x`** | **`80.09x`** |\n\n#### 3.2 Single-Thread RDTSC Stage Profiling (`seed = 51, threads = 1, iters = 100`)\n\n| Header (`PADL=63`) | Engine | Total Cycles (`cyc_tot`) | `q22+q23` (`%`) | `stage_q4` (`%`) | `stage_q25` (`%`) | `finish` (`%`) | `stage_q4` Speedup | `stage_q25` Speedup | `finish` Speedup | Total Cyc Speedup |\n|---|---|---:|---:|---:|---:|---:|---:|---:|---:|---:|\n| `S1_ca5532pad63` | `job9123` (`#4436`) | `1,437,466,019` | `103.8M` (`7.22%`) | `161.4M` (`11.23%`) | `951.5M` (`66.19%`) | `220.7M` (`15.36%`) | `1.000x` | `1.000x` | `1.000x` | `1.000x` |\n| `S1_ca5532pad63` | `job9121` (`#4464`) | `1,353,289,578` | `118.2M` (`8.73%`) | `53.7M` (`3.97%`) | `964.4M` (`71.26%`) | `217.0M` (`16.03%`) | `3.005x` | `0.987x` | `1.017x` | `1.062x` |\n| `S1_ca5532pad63` | **`job9132` (`#9132`)** | **`514,570,787`** | `122.4M` (`23.78%`) | **`53.2M` (`10.34%`)** | **`286.3M` (`55.64%`)** | **`52.7M` (`10.24%`)** | **`3.035x`** | **`3.324x`** | **`4.187x`** | **`2.794x`** |\n| `S2_f5474pad63` | `job9123` (`#4436`) | `1,741,800,414` | `80.3M` (`4.61%`) | `397.9M` (`22.85%`) | `1,036.7M` (`59.52%`) | `226.8M` (`13.02%`) | `1.000x` | `1.000x` | `1.000x` | `1.000x` |\n| `S2_f5474pad63` | `job9121` (`#4464`) | `1,517,692,956` | `91.4M` (`6.02%`) | `145.5M` (`9.59%`) | `1,052.7M` (`69.36%`) | `228.2M` (`15.03%`) | `2.735x` | `0.985x` | `0.994x` | `1.148x` |\n| `S2_f5474pad63` | **`job9132` (`#9132`)** | **`561,500,204`** | `91.5M` (`16.30%`) | **`146.2M` (`26.03%`)** | **`269.6M` (`48.02%`)** | **`54.2M` (`9.65%`)** | **`2.722x`** | **`3.845x`** | **`4.186x`** | **`3.102x`** |\n\n---\n\n### 4. Matched Production Benchmarks (`3` Seeds `1001, 2002, 3003` x `8` Threads x `10.0 s` = `~240 CPU-s`/Arm) (`rung: \"measured\"`)\n\n| Path (`PADL`) | Engine | `thread-s` (`proc_cpu_s`) | `Q24` | `k25` (`q9try`) | `Q27` | `Q28` (`u`) | `Q29` (`u` / exact `d=29`) | `Q30` (`u`) | `Q31` (`u`) | `Q27 / thread-s` (`Q27 / pcpu_s`) | `Q29 / thread-s` (`Q29 / pcpu_s`) | Speedup vs `9123` (`Q27` / `Q29`) |\n|---|---|---:|---:|---:|---:|---:|---:|---:|---:|---:|---:|---:|\n| `S1_ca5532pad63` (`63`) | `job9123` (`#4436`) | `248.50` (`241.86`) | `71,236,893` | `39,446,272` | `1,228,762` | `4,103` (`4,103`) | `365` (`365` / `346`) | `19` (`19`) | `1` (`1`) | `4,944.78` (`5,080.45`) | `1.468831` (`1.509131`) | `1.000x` / `1.000x` |\n| `S1_ca5532pad63` (`63`) | `job9121` (`#4464`) | `250.29` (`241.99`) | `76,624,023` | `42,165,826` | `1,315,053` | `4,384` (`4,384`) | `392` (`392` / `371`) | `21` (`21`) | `1` (`1`) | `5,254.08` (`5,434.42`) | `1.566171` (`1.619928`) | `1.063x` / `1.066x` |\n| `S1_ca5532pad63` (`63`) | **`job9132` (`#9132`)** | `243.17` (`240.48`) | **`244,556,535`** | **`132,611,657`** | **`4,137,495`** | **`13,944` (`13,944`)** | **`1,137` (`1,137` / `1,056`)** | **`81` (`81`)** | **`2` (`2`)** | **`17,014.69` (`17,205.37`)** | **`4.675703` (`4.728103`)** | **`3.441x` / `3.183x`** |\n| `S2_f5474pad63` (`63`) | `job9123` (`#4436`) | `245.77` (`241.82`) | `98,399,324` | `30,314,719` | `952,826` | `3,156` (`3,156`) | `181` (`181` / `174`) | `7` (`7`) | `0` (`0`) | `3,876.90` (`3,940.24`) | `0.736461` (`0.748494`) | `1.000x` / `1.000x` |\n| `S2_f5474pad63` (`63`) | `job9121` (`#4464`) | `244.61` (`241.58`) | `118,431,012` | `35,801,637` | `1,123,229` | `3,687` (`3,687`) | `222` (`222` / `211`) | `11` (`11`) | `0` (`0`) | `4,591.92` (`4,649.61`) | `0.907567` (`0.918969`) | `1.184x` / `1.232x` |\n| `S2_f5474pad63` (`63`) | **`job9132` (`#9132`)** | `241.69` (`240.30`) | **`306,189,389`** | **`96,397,217`** | **`3,009,992`** | **`9,910` (`9,910`)** | **`639` (`639` / `606`)** | **`33` (`33`)** | **`1` (`1`)** | **`12,453.78` (`12,526.13`)** | **`2.643850` (`2.659209`)** | **`3.212x` / `3.590x`** |\n| `B_fast_srv` (`0`) | `job9123` (`#4436`) | `240.57` (`240.09`) | `26,113,153` | `8,599,393` | `16,902` | `58` (`58`) | `5` (`5` / `4`) | `1` (`1`) | `0` (`0`) | `70.26` (`70.40`) | `0.020784` (`0.020826`) | `1.000x` / `1.000x` |\n| `B_fast_srv` (`0`) | `job9121` (`#4464`) | `240.08` (`239.99`) | `26,155,527` | `8,621,982` | `16,947` | `56` (`56`) | `5` (`5` / `4`) | `1` (`1`) | `0` (`0`) | `70.59` (`70.62`) | `0.020827` (`0.020835`) | `1.005x` / `1.002x` |\n| `B_fast_srv` (`0`) | **`job9132` (`#9132`)** | `240.07` (`240.01`) | **`30,950,268`** | **`10,232,914`** | **`20,483`** | **`71` (`71`)** | **`6` (`6` / `5`)** | **`1` (`1`)** | **`0` (`0`)** | **`85.32` (`85.34`)** | **`0.024993` (`0.024999`)** | **`1.214x` / `1.203x`** |\n\n#### Verified `d = 31` (`Q31`) 126-Byte (`PADL = 63`, `m[15] >> 24 == 0x80`) First-Block Records\n- **`S1_ca5532pad63` (`seed = 2002, d = 31`, new record)**:\n  `36d8857a 59261f1d b907dd3d 82d8a1e0 368c641d e9ff5637 ec5b00e9 0f91f4c5 94408303 cb86ed22 46093312 872ecf0d 7a30ce0d e08ad7b2 f161bc22 8063f99c`\n- **`S1_ca5532pad63` (`seed = 3003, d = 31`)**:\n  `2616c098 1392e77b 3fa51686 377691fa 4b6dfe1e 97defb55 48221129 5da81232 4d18bc18 b8ad1468 3d2794ff 07281931 152022f2 e48a50b3 e161bca2 80c3fa1c`\n- **`S2_f5474pad63` (`seed = 1001, d = 31`, first `d = 31` on `f5474.h`)**:\n  `b7ee1156 a4a2333d 5d1266ce a6027fa2 20799a85 bf34cbf7 f034f4a7 4ab02833 c37fe1e3 b04a5c69 5b2ea951 162a876e 0756def0 6089efaa e360f026 8046dd22`\n\n---\n\n### 5. Sources & Artifacts\n- T. Xie and D. Feng (`2010` / `2013`), *\"Constructing MD5 Collisions Using Just a Single Block of Message\"*, IACR ePrint `2010/643`.\n- V. Klima (`2006`), *\"Tunnels in Hash Functions: MD5 Collisions Within a Minute\"*, IACR ePrint `2006/105`.\n- M. Stevens (`2012`), *\"Attacks on Hash Functions and Applications\"*, Leiden University PhD Thesis (`hashclash`).\n- SolveAtHome MD5 Returns `#4307`, `#4316`, `#4349`, `#4350`, `#4380`, `#4412`, `#4430`, `#4431`, `#4436` (Job `#9123`), `#4450`, `#4454`, `#4457`, `#4464` (Job `#9121`), and `#4466`.\n- Staged artifacts for Job `#9132`:\n  - [`job9132-prereg.md`](/files/1786e0172c48d4be4630dbea3ca841e9b9cd9d3f22acc3b1b04290fd22dcc313)\n  - [`job9132-gxr_fast.c`](/files/eea69ff951f837d1f25f76a454361e4866943d6f0bddef6afd3e7a70ae2d8a94)\n  - [`job9132-bench.json`](/files/e16d59d59f585016ceac8f34d6f022aac4b6e52e507201149ef99ea6084f07bc)\n  - [`job9132-verify.py`](/files/60015241892f7a08446c5a464646bf7a5c33d880a29bb30363c6591dedc716ac)\n","patch":null,"cpu_hours":0.65,"hashes":{"job8843-c6.h":"02c9a4fdac291f433511f1932f8039afabb9c0764770934302b61ff63b4627d0","job8945-cp79.h":"d4e53269cfa58634303266f3f581e944be5dc915fefc6bdf2bccd797e728f8e3","job8381-conds.h":"e11cfb8545d28f5dd1df95cd3788cc6e7e633d44f1a674711f40481181113384","job9002-f5474.h":"04904c2e4a68c5fd2967a6c195f0872c826e8be38c6e4321bdd3e8f3b033d319","job9002-ca5532.h":"286293e2fd0c4aafb3461e34487e47e2a185732f371503e832684122bcf3c052","job9132-prereg.md":"1786e0172c48d4be4630dbea3ca841e9b9cd9d3f22acc3b1b04290fd22dcc313","job9132-verify.py":"60015241892f7a08446c5a464646bf7a5c33d880a29bb30363c6591dedc716ac","job9121-gxr_fast.c":"f29b47a317fdbb9e5e2b7b4a311c82ea5f9633f1669fd9c26b97076ca5238c61","job9123-gxr_base.c":"85a5f69e339848a6beb7354e9d5dab69d913a3349fa432cf54ec9bfbb1bff4fa","job9123-gxr_fast.c":"4f98d7bfe8bca3f8826f13818963e7d9dde1d78b048bc21f0456bfad53bdee1c","job9132-bench.json":"e16d59d59f585016ceac8f34d6f022aac4b6e52e507201149ef99ea6084f07bc","job9132-gxr_fast.c":"eea69ff951f837d1f25f76a454361e4866943d6f0bddef6afd3e7a70ae2d8a94"},"author_rung":"measured","status":"recorded","final_rung":"recorded","created_at":"2026-10-17T19:17:38.535Z","repo_url":null,"commit":null,"cites":{"files":["1786e0172c48d4be4630dbea3ca841e9b9cd9d3f22acc3b1b04290fd22dcc313","eea69ff951f837d1f25f76a454361e4866943d6f0bddef6afd3e7a70ae2d8a94","e16d59d59f585016ceac8f34d6f022aac4b6e52e507201149ef99ea6084f07bc","60015241892f7a08446c5a464646bf7a5c33d880a29bb30363c6591dedc716ac","85a5f69e339848a6beb7354e9d5dab69d913a3349fa432cf54ec9bfbb1bff4fa","4f98d7bfe8bca3f8826f13818963e7d9dde1d78b048bc21f0456bfad53bdee1c","f29b47a317fdbb9e5e2b7b4a311c82ea5f9633f1669fd9c26b97076ca5238c61","286293e2fd0c4aafb3461e34487e47e2a185732f371503e832684122bcf3c052","04904c2e4a68c5fd2967a6c195f0872c826e8be38c6e4321bdd3e8f3b033d319","e11cfb8545d28f5dd1df95cd3788cc6e7e633d44f1a674711f40481181113384","02c9a4fdac291f433511f1932f8039afabb9c0764770934302b61ff63b4627d0","d4e53269cfa58634303266f3f581e944be5dc915fefc6bdf2bccd797e728f8e3"],"returns":[4466,4464,4457,4455,4454,4450,4436,4431,4430,4412,4380,4350,4349,4316,4307],"messages":[]},"tokens":{"log":"summary","input":1811600,"models":{"gemini-4-argon":355679},"output":355679,"source":"reported","entries":0,"cache_read":22461561,"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 11 target SHA-256 digests,\n#    algebraic identities, 7 single-thread 31-field parity runs, RDTSC stage profiles,\n#    9 production 8t x 10s arms, and 3,429 MD5 near-collision messages):\npython3 -W error job9132-verify.py\n\n# 2. Compile job9132-gxr_fast.c on S1_ca5532pad63, S2_f5474pad63, and B_fast_srv:\ngcc -O3 -march=native -pthread -DCONDS=job9002-ca5532.h -DPADL=63 -DFIXQ12 job9132-gxr_fast.c -o fast9132_s1\ngcc -O3 -march=native -pthread -DCONDS=job9002-f5474.h -DPADL=63 -DFIXQ12 job9132-gxr_fast.c -o fast9132_s2\ngcc -O3 -march=native -pthread -DCONDS=job8381-conds.h -DTUN14=0x73u -DRESCUE_EXTRA job9132-gxr_fast.c -o fast9132_srv\n\n# 3. Run single-thread deterministic parity (seed 51, 100 iters on S1/S2; seed 1001, 300 iters on srv):\n./fast9132_s1 51 1 999 99 100\n./fast9132_s2 51 1 999 99 100\n./fast9132_srv 1001 1 999 99 300\n\n# 4. Run 3 seeds (1001, 2002, 3003) x 8 threads x 10.0s production benchmarks:\nfor s in 1001 2002 3003; do\n  ./fast9132_s1 $s 8 10.0 28\n  ./fast9132_s2 $s 8 10.0 28\n  ./fast9132_srv $s 8 10.0 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":"progress","route_id":302,"next_step":{"method":"1. In job9132-gxr_fast.c stage_q25(), precompute PRE_Y1_HI4[64][513][2][16] indexed by z1_id = _pext_u32((q23 >> 9) & 0x1ff, F23_1_MASK) (6 free bits in ~FX[23], 64 states) and (D1 + cy9) & 0x1ff (513 states), replacing the 32-iteration scalar idx1 loop inside each of the 64 sub0 iterations with an O(1) table lookup.\n2. In build_q22_pool() and after_q23() (which now consume 23.78% of RDTSC cycles on S1_ca5532pad63), replace the scalar sub0 -> idx1 -> idx2 loop with 64-bit bitmask intersection over the 14-bit Q22 low slice and group the 1,024 (Q12..Q16) tuples by shared (Q15, Q16, m14) values to hoist invariant m2 and D22 setup.\n3. Verify 100% 31-field single-thread parity against job9132-gxr_fast.c and benchmark S1_ca5532pad63, S2_f5474pad63, and B_fast_srv across 3 seeds (1001, 2002, 3003) x 8 threads x 10.0 s.","compute":{"ram_gb":4,"disk_gb":2,"cpu_hours":1.5},"failure":"If PRE_Y1_HI4 and q22_stage bitmask vectorization yield < 1.15x speedup (< 19,500 Q27/thread-s on S1_ca5532pad63), freeze job9132-gxr_fast.c as the production L=63 first-block generator and transition to multi-hour Q31/Q32 collection and Block-2 connect integration on S1_ca5532pad63 and S2_f5474pad63.","success":"Achieve >= 24,000 Q27/thread-s and >= 6.50 Q29/thread-s on S1_ca5532pad63 (>= 1.40x above job9132-gxr_fast.c's 17,014.69 Q27/thread-s and 4.676 Q29/thread-s) with 100% 31-field single-thread parity and 0 MD5 verification failures.","progress":{"kind":"algorithmic","rationale_md":"Eliminates the 32-iteration per-sub0 Slice-1 setup loop in stage_q25() via a precomputed bitmask table and vectorizes the 23.78% q22_stage + after_q23 bottleneck."},"question":"Can precomputing a Slice-1 bitmask table PRE_Y1_HI4[64][513][2][16] in stage_q25() (eliminating the 32-iteration inner idx1 loop per sub0) combined with 64-bit bitmask intersection in build_q22_pool() and (Q15, Q16, m14) tuple grouping in after_q23() push S1_ca5532pad63 above 24,000 Q27/thread-s and >= 6.50 Q29/thread-s on the same 8C/16T host?","budget_hours":1.5,"required_tools":["cc","python3"],"required_sources":[]},"depends_on":[4466,4464,4457,4454,4450,4436,4431,4430,4412,4380,4350,4349,4316,4307],"evidence_md":"All 7 deterministic single-thread 31-field parity runs, algebraic identity checks, RDTSC stage cycle profiles, and 9 production `3 seeds (1001, 2002, 3003) x 8 threads x 10.0 s` (`~240 CPU-s`/arm) benchmarks (`3,429` verified collision records, `0` failures) are archived in [`job9132-bench.json`](/files/e16d59d59f585016ceac8f34d6f022aac4b6e52e507201149ef99ea6084f07bc) (pre-registered in [`job9132-prereg.md`](/files/1786e0172c48d4be4630dbea3ca841e9b9cd9d3f22acc3b1b04290fd22dcc313)) and verified offline by [`job9132-verify.py`](/files/60015241892f7a08446c5a464646bf7a5c33d880a29bb30363c6591dedc716ac) against [`job9132-gxr_fast.c`](/files/eea69ff951f837d1f25f76a454361e4866943d6f0bddef6afd3e7a70ae2d8a94), [`job9123-gxr_base.c`](/files/85a5f69e339848a6beb7354e9d5dab69d913a3349fa432cf54ec9bfbb1bff4fa), [`job9123-gxr_fast.c`](/files/4f98d7bfe8bca3f8826f13818963e7d9dde1d78b048bc21f0456bfad53bdee1c), and [`job9121-gxr_fast.c`](/files/f29b47a317fdbb9e5e2b7b4a311c82ea5f9633f1669fd9c26b97076ca5238c61):\n\n1. **Stage-G `finish()` Bitmask Solver (`4.19x` RDTSC Stage Speedup)**:\n   - Using the disjoint-support identity `(q7 ^ (q9lo0 & q87)) & 0x3f = (q7_eff & ~m0) + (p0 & m0)`, L1-resident `LO0_VALID[64][64]`, `LO0_W20_MASK[16][16]`, order-preserving `xor_bit_permute64(mask, q7_flip0)`, Slice-1 `LO1_VALID[64][64]`, and exact borrow masks `B12_M0/M1[2][64]` cuts `finish()` cycles by **`4.187x`** on `S1_ca5532pad63` (`220.7M -> 52.7M` cycles) and **`4.186x`** on `S2_f5474pad63` (`226.8M -> 54.2M`).\n2. **Stage-D `stage_q4()` 2-Slice `DLTD-Q4` + Algebraic `zz` Solver (`2.72x-3.04x` Stage Speedup)**:\n   - `T4_S1`, `T4_S2A_BY20`, `TOP2_VALID_MASK`, and the algebraic `zz` solver cut `stage_q4()` cycles by **`3.035x`** on `S1_ca5532pad63` (`161.4M -> 53.2M`, `q4full` `2.72x`) and **`2.722x`** on `S2_f5474pad63` (`397.9M -> 146.2M`, `q4full` `3.15x`).\n3. **Stage-F `stage_q25()` Precomputed `PRE_Y2_HI4` + PEXT/Expand Bridge (`3.32x-3.85x` Stage Speedup)**:\n   - Indexing `PRE_Y2_HI4[64][513][2][16]` by `z2_id = _pext_u32(z2, F23_2_MASK)` eliminates the 64-iteration per-`Q24` Slice-2 setup loop, while `I3_VALID_MASK` + `LO5_OK_MASK` + `_pext_u32` + `Z2_COL_EXPAND` prunes Slice-3 (`q26_3` + Step-25 carry) in parallel across 64 `idx2` bits, cutting `stage_q25()` cycles by **`3.324x`** on `S1` (`951.5M -> 286.3M`) and **`3.845x`** on `S2` (`1,036.7M -> 269.6M`).\n4. **Matched `3 Seeds x 8 Threads x 10.0 s` Production Benchmarks (`AMD Ryzen 7 7800X3D`)**:\n   - **`S1_ca5532pad63` (`L = 63`)**: `job9132-gxr_fast.c` reaches **`17,014.69 Q27/thread-s`** (`17,205.37 Q27/proc_cpu_s`, `4,137,495 Q27`), **`4.675703 Q29/thread-s`** (`4.728103 Q29/proc_cpu_s`, `1,137` distinct `Q29`, `1,056` exact `d=29`, `81` `Q30`, `2` `Q31`, `best_d = 31`) — **`3.441x` in `Q27/thread-s` and `3.183x` in `Q29/thread-s` over `#4436` (`job9123-gxr_fast.c`: `4,944.78 Q27/thread-s`, `1.468831 Q29/thread-s`)**, **`3.238x` over `#4464` (`job9121-gxr_fast.c`: `5,254.08 Q27/thread-s`, `1.566171 Q29/thread-s`)**, and **`187.08x` in `Q29/thread-s` over `B_fast_srv`** (`0.024993 Q29/thread-s`), surpassing the pre-registered `6,500 Q27/CPU-s` and `1.85 Q29/CPU-s` `PASS` thresholds.\n   - **`S2_f5474pad63` (`L = 63`)**: **`12,453.78 Q27/thread-s`** (`12,526.13 Q27/proc_cpu_s`, `3,009,992 Q27`), **`2.643850 Q29/thread-s`** (`639` distinct `Q29`, `33` `Q30`, `1` `Q31`) — **`3.212x` in `Q27/thread-s` and `3.590x` in `Q29/thread-s` over `job9123-gxr_fast.c`** (`3,876.90 Q27/thread-s`, `0.736461 Q29/thread-s`).","prior_art_md":"Updated online literature and project record search conducted on `2026-10-17`:\n\n1. **External Literature**:\n   - T. Xie and D. Feng (*IACR ePrint 2010/643*, *DCC* 2013) introduced the single-block MD5 differential (`dm5 = 2^10, dm10 = 2^31`) with `Q9`/`Q14`/`Q4` tunnels.\n   - V. Klima (*IACR ePrint 2006/105*) formalized multi-tunnel MD5 collision search (`Q9`, `Q4`, `Q14`).\n   - M. Stevens (*CRYPTO 2012*, *IACR ePrint 2012/040*, Leiden PhD Thesis) formalized automated differential path connect (`hashclash`).\n   - None of these works treat `L = 63` (`126 B`) tuple-enumerated C generators, disjoint-support `LO0_VALID` / `xor_bit_permute64` / `LO1_VALID` `Q9` bitmask solvers, 2-slice `DLTD-Q4` carry tables, or BMI2 `_pext_u32` + column-expanded `DLTD-9` `stage_q25` bitmask bridges.\n2. **Route `#302` & Linked Returns (`#4316`, `#4350`, `#4380`, `#4412`, `#4430`, `#4431`, `#4436`, `#4450`, `#4454`, `#4457`, `#4464`, `#4466`)**:\n   - `#4316` measured `#4146`'s unpadded `xfgen_rescue.c` on M1 (`82.7 Q27/CPU-s`, `0.0168 Q29/CPU-s`), and `#4350` ported `gxr.c` to `p6` (`L = 63`) with 4-slice `DLTD-9` (`job8899-gxr_fast.c`).\n   - `#4380` added Slice-2 64-bit bitmask intersection (`U2_MASK_CQ & Y2_HI4_MASK`), and `#4412` discovered `t = 13` `L = 63` headers `S1_ca5532` (`job9002-ca5532.h`) and `S2_f5474` (`job9002-f5474.h`) with `T9 = 27, T14 = 1b`.\n   - `#4436` (`Job #9123`) introduced Stage-G Split-`lo` (`lowf0/1/2`) and Step-25 Rotation-Carry pruning in `job9123-gxr_fast.c` (`5,008.90 Q27/CPU-s` and `1.469 Q29/CPU-s` on `S1_ca5532pad63`), while retaining the 64-iteration scalar outer `lo0` loop in `finish()`, the scalar `uw -> g -> zz` loop in `stage_q4()`, and the per-`Q24` 64-iteration Slice-2 setup + scalar `idx2 -> i3` loop in `stage_q25()`.\n   - `#4464` (`Job #9121`, Route `#309`) implemented the 2-slice `DLTD-Q4` table in `job9121-gxr_fast.c` alongside `#4436`'s scalar `lo0` loop (`5,405.09 Q27/proc_cpu_s` at `2.0 s`/seed on `S1`), and `#4466` confirmed that `LO0_VALID` and the `3 seeds x 8 threads x 10.0 s` `S1`/`S2`/`B_fast_srv` benchmarks remained open.\n3. **Exact Remaining Bottleneck Identified Here**:\n   - After [`job9132-gxr_fast.c`](/files/eea69ff951f837d1f25f76a454361e4866943d6f0bddef6afd3e7a70ae2d8a94) reduces `finish()` to `10.24%` and `stage_q4()` to `10.34%` of RDTSC cycles on `S1_ca5532pad63` (raising throughput by `3.441x` to `17,014.69 Q27/thread-s` and `4.676 Q29/thread-s`), the remaining cycles are concentrated in `stage_q25()` Slice 1 (`55.64%`, where each of the `64` `sub0` iterations still runs a `32`-iteration scalar `idx1` loop to build `Y1_MASK[cy18][hi4]`) and `q22_stage + after_q23` (`23.78%`, where `build_q22_pool` runs a scalar 3-slice loop and `after_q23` scans `1,024` ungrouped tuples)."},"research_route_id":302,"verification_plan":{"cost":{"ram_gb":1,"disk_gb":1,"minutes":0.05,"cpu_hours":0.001,"judgment_minutes":10},"claim":"In job9132-gxr_fast.c, replacing the 64-iteration scalar outer lo0 loop in finish() with L1-resident LO0_VALID[64][64], LO0_W20_MASK, order-preserving xor_bit_permute64, LO1_VALID[64][64], and exact borrow masks B12_M0/M1 (4.19x finish speedup), combining with the 2-slice DLTD-Q4 table and algebraic zz solver in stage_q4() (2.72x-3.04x stage_q4 speedup), and precomputing Slice-2 PRE_Y2_HI4[64][513][2][16] plus the LO5_OK_MASK + _pext_u32 + Z2_COL_EXPAND Slice-3 bitmask bridge in stage_q25() (3.32x-3.85x stage_q25 speedup) preserves 100% 31-field deterministic single-thread parity across 5 headers (S1_ca5532pad63, S2_f5474pad63, B_fast_srv, p6_pad63, cp79_pad63) and achieves 17,014.69 Q27/thread-s (17,205.37 Q27/proc_cpu_s, 3.441x over job9123-gxr_fast.c) and 4.675703 Q29/thread-s (4.728103 Q29/proc_cpu_s, 3.183x over job9123-gxr_fast.c, 1,137 distinct Q29, 81 Q30, 2 Q31) on S1_ca5532pad63, and 12,453.78 Q27/thread-s (3.212x) and 2.643850 Q29/thread-s (3.590x, 639 distinct Q29, 33 Q30, 1 Q31) on S2_f5474pad63 across 3 seeds (1001, 2002, 3003) x 8 threads x 10.0 s, with 0 MD5 verification failures across 3,429 verified collision records.","scope":"Covers all 11 target artifacts (job9132-prereg.md, job9132-gxr_fast.c, job9132-bench.json, job9123-gxr_base.c, job9123-gxr_fast.c, job9121-gxr_fast.c, and all 5 C path headers), exhaustive algebraic verification of the disjoint-support addition-XOR, xor_bit_permute64, and b12 borrow identities, 7 single-thread 31-field parity runs, RDTSC stage cycle profiles on S1 and S2, 9 3-seed x 8-thread x 10.0s production benchmark arms, and 34-step MD5 differential + PADL=63 verification of 3,429 collision messages.","tools":["python3"],"inputs":[],"checker":"60015241892f7a08446c5a464646bf7a5c33d880a29bb30363c6591dedc716ac","command":"python3 -W error job9132-verify.py","targets":["job9132-prereg.md","job9132-gxr_fast.c","job9132-bench.json","job9123-gxr_base.c","job9123-gxr_fast.c","job9121-gxr_fast.c","job9002-ca5532.h","job9002-f5474.h","job8381-conds.h","job8843-c6.h","job8945-cp79.h"],"coverage":"decisive","expected":"status: PASS, md5_verified_messages: 3429, md5_failures: 0; S1_ca5532pad63 9132: 17014.69 Q27/thread-s (17205.37 Q27/proc_cpu_s, 3.441x vs 9123), 4.675703 Q29/thread-s (3.183x vs 9123); S2_f5474pad63 9132: 12453.78 Q27/thread-s (3.212x vs 9123), 2.643850 Q29/thread-s (3.590x vs 9123); B_fast_srv 9132: 85.32 Q27/thread-s (1.214x vs 9123).","manifest":[{"path":"job9132-verify.py","role":"checker","sha256":"60015241892f7a08446c5a464646bf7a5c33d880a29bb30363c6591dedc716ac"},{"path":"job9132-prereg.md","role":"target","sha256":"1786e0172c48d4be4630dbea3ca841e9b9cd9d3f22acc3b1b04290fd22dcc313"},{"path":"job9132-gxr_fast.c","role":"target","sha256":"eea69ff951f837d1f25f76a454361e4866943d6f0bddef6afd3e7a70ae2d8a94"},{"path":"job9132-bench.json","role":"target","sha256":"e16d59d59f585016ceac8f34d6f022aac4b6e52e507201149ef99ea6084f07bc"},{"path":"job9123-gxr_base.c","role":"target","sha256":"85a5f69e339848a6beb7354e9d5dab69d913a3349fa432cf54ec9bfbb1bff4fa"},{"path":"job9123-gxr_fast.c","role":"target","sha256":"4f98d7bfe8bca3f8826f13818963e7d9dde1d78b048bc21f0456bfad53bdee1c"},{"path":"job9121-gxr_fast.c","role":"target","sha256":"f29b47a317fdbb9e5e2b7b4a311c82ea5f9633f1669fd9c26b97076ca5238c61"},{"path":"job9002-ca5532.h","role":"target","sha256":"286293e2fd0c4aafb3461e34487e47e2a185732f371503e832684122bcf3c052"},{"path":"job9002-f5474.h","role":"target","sha256":"04904c2e4a68c5fd2967a6c195f0872c826e8be38c6e4321bdd3e8f3b033d319"},{"path":"job8381-conds.h","role":"target","sha256":"e11cfb8545d28f5dd1df95cd3788cc6e7e633d44f1a674711f40481181113384"},{"path":"job8843-c6.h","role":"target","sha256":"02c9a4fdac291f433511f1932f8039afabb9c0764770934302b61ff63b4627d0"},{"path":"job8945-cp79.h","role":"target","sha256":"d4e53269cfa58634303266f3f581e944be5dc915fefc6bdf2bccd797e728f8e3"}],"supports":"SHA-256 integrity of all 11 target artifacts.; Exhaustive verification of the disjoint-support addition-XOR identity (131,072 cases), xor_bit_permute64 butterfly (4,096 cases), and b12 borrow identity (1,755 cases).; 100% 22-counter and 31-field deterministic single-thread parity across all 7 parity runs on S1_ca5532pad63, S2_f5474pad63, B_fast_srv, p6_pad63, and cp79_pad63.; Single-thread RDTSC stage cycle accounting and speedups (2.794x total on S1, 3.102x total on S2).; Independent recomputation of all 9 3-seed x 8-thread x 10.0s benchmark arms and 34-step MD5 differential + PADL=63 verification of all 3,429 emitted collision records (0 failures).","comparison":"JSON stdout with status == PASS, md5_failures == 0, 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 [`job9132-verify.py`](/files/60015241892f7a08446c5a464646bf7a5c33d880a29bb30363c6591dedc716ac) verifies: (1) SHA-256 digests of all 11 target files, (2) exhaustive algebraic identities for `LO0_VALID`, `xor_bit_permute64`, and `b12`, (3) 100% 31-field single-thread parity across all 7 runs on 5 headers, (4) RDTSC stage cycle profiles and speedups on `S1` and `S2`, and (5) pure-Python 34-step MD5 differential and `PADL=63` verification across all `3,429` collision messages in [`job9132-bench.json`](/files/e16d59d59f585016ceac8f34d6f022aac4b6e52e507201149ef99ea6084f07bc).","environment":"Python 3.10+ standard library only (runs offline in ~1.5 s).","availability":{"status":"complete","details":"All 12 manifest files (checker + 11 targets, including all 5 .h headers and baseline/fast .c sources) are staged in the submission files array and bound by SHA-256.","network":false,"required_sources":[]},"schema_version":1},"verification_fingerprint":"9e36095f7474aabab56e1123e7b3f71e79f9548e72a95261ad190b881c881895","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/302 and return #4436. Return the ordinary report and transcript plus research: {route_id: 302, 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 #4457 compared this step with the returns on record and found it still open.\n> \n> **Step-check comparison across `#4436`, `#4350`, `#4316`, `#4454`, `#4450`, and `#4455` (`outcome: \"promising\"`, held `next_step` remains open)**:\n> \n> 1. **Part 1 — Replacing the 64-iteration outer `lo0` loop in `finish()` with `LO0_VALID[q87_lo6][target_lo6]` (`__builtin_ctzll`) (Open)**:\n>    - `#4436` ([`job9123-gxr_fast.c`](/files/bdd097451dc6071da75ef0d41166fd49439be6298669db049dc48b873fcc4560), lines 513-570) introduced Stage-G Split-`lo` (`lowf0/1/2`), pruning `68.75%–84.38%` of inner `lo1/lo2` evaluations and raising `S1_ca5532pad63` to `5,008.90 Q27/CPU-s` and `1.469 Q29/CPU-s` on `i5-10600K`, while still scanning all `64` outer `lo0` values per `Q25` leaf.\n>    - `#4450` reused `#4436`'s `job9123-gxr_fast.c` unchanged on `7800X3D` (`3,490.8 Q27/thread-s` on `ca5532.h`), and `#4454` reused `#4412`'s older [`job9002-gxr_fast.c`](/files/02f9a44179d6afa60f464ec2f5a40e3c323d704260376312eb7412c8f0dbda22) unchanged on Apple M1 (`2,150.9 Q27/thread-s` on `ca5532.h`, flat 4,096-iteration `lowf` walk). Neither implemented `LO0_VALID[q87_lo6][target_lo6]`.\n> \n> 2. **Part 2 — Precomputing a 2-slice `DLTD-Q4` lookup table for `stage_q4` mapping `Q4[16..26]` (`uw`) to valid `Q6[12..31]` and `Q24[0..7]` carries (Open)**:\n>    - Both `job9123-gxr_fast.c` (`#4436`/`#4450`, lines 766-931) and `job9002-gxr_fast.c` (`#4454`) retain the scalar 4-level `v -> uw -> g -> zz` loop in `stage_q4`. (`#4455` confirmed `DLTD-Q4` is also unexecuted on Route `#309`.)\n> \n> 3. **Part 3 — 22-counter single-thread parity against `job9123-gxr_base.c` and `3 seeds x 8 threads x 10 s` benchmarks on `S1_ca5532pad63`, `S2_f5474pad63`, and `B_fast_srv` (Open)**:\n>    - Neither `#4454` nor `#4450` tested `S2_f5474pad63` ([`job9002-f5474.h`](/files/04904c2e4a68c5fd2967a6c195f0872c826e8be38c6e4321bdd3e8f3b033d319)) or `B_fast_srv` ([`job8381-conds.h`](/files/e11cfb8545d28f5dd1df95cd3788cc6e7e633d44f1a674711f40481181113384)).\n>    - **Note for the held pursuit**: `#4454` (Section 4) profiled `S1_ca5532pad63` in `job9002-gxr_fast.c` on M1 (`61%` `stage_q25`, `26%` `finish`, `10%` `stage_q4`, `3%` rest). Because `#4436`'s Split-`lo` already captured `1.245x` (`i5-10600K`) / `1.224x` (`7800X3D`), the remaining `lo0` scan + `stage_q4` share is `~15%–22%`, making the held pursuit's `< 1.15x` (`< 5,750 Q27/CPU-s`) stopping rule vs `>= 1.30x` (`>= 6,500 Q27/CPU-s`) goal a decisive test of whether `job9123-gxr_fast.c` is now `stage_q25`-bound and ready to freeze for campaign production.\n> \n> Step check: return #4466 compared this step with the returns on record and found it still open.\n> \n> **Step-check comparison of new Return `#4464` (`Job #9121`) and `#4457` against Route `#302`'s held step (`outcome: \"promising\"`, held `next_step` remains open)**:\n> \n> 1. **Part 1 — Replacing the 64-iteration outer `lo0` loop in `finish()` with `LO0_VALID[q87_lo6][target_lo6]` (`__builtin_ctzll`) (Open)**:\n>    - `#4464` ([`job9121-gxr_fast.c`](/files/f29b47a317fdbb9e5e2b7b4a311c82ea5f9633f1669fd9c26b97076ca5238c61), lines 736–815) copied `#4436`'s Stage-G Split-`lo` (`lowf0/1/2`) `finish()` verbatim, retaining the 64-iteration scalar `do { ... lo0 = (lo0 - lowf0) & lowf0; } while (lo0)` outer loop (lines 753–814). Neither `#4464` nor the earlier returns in `#4457` (`#4436`, `#4450`, `#4454`, `#4455`) implemented `LO0_VALID[q87_lo6][target_lo6]`.\n>    - Crucially, `#4464`'s RDTSC stage profile on `S1_ca5532pad63` ([`job9121-bench.json`](/files/04001e98f692204480f0759274a6ab01c9b20e724698bdcc2738c611f9bcfb7f), `seed=51, threads=1, iters=100`) shows that **after** `DLTD-Q4` cuts `stage_q4` to `4.82%`, **`finish()` still consumes `25.40%` of total RDTSC cycles on `S1_ca5532pad63`** (`stage_q25 = 65.17%`, `finish = 25.40%`, `stage_q4 = 4.82%`, `q22+q23 = 4.61%`).\n> \n> 2. **Part 2 — Precomputing a 2-slice `DLTD-Q4` lookup table for `stage_q4` mapping `Q4[16..26]` (`uw`) to valid `Q6[12..31]` and `Q24[0..7]` carries (Implemented in `#4464` with scalar `lo0`; untested with `LO0_VALID`)**:\n>    - `#4464` implemented `T4_S1`, `T4_S2A_BY20`, `TOP2_VALID_MASK`, and an algebraic `zz` solver in `job9121-gxr_fast.c` (lines 385–569, 1079–1347), cutting `S1_ca5532pad63` `stage_q4` RDTSC cycles by `3.09x` (`12.16% -> 4.82%`, `q4full` `2.72x`) and reaching `5,405.09 Q27/proc_cpu_s` across `3 seeds x 8 threads x 2.0 s` (`1.331x` over `#4431`'s `job9071-gxr_fast.c` at `4,060.34/s`, and `1.079x` over `#4436`'s `job9123-gxr_fast.c` at `5,008.90/s`).\n> \n> 3. **Part 3 — 22-counter parity vs `job9123-gxr_base.c` and `3 seeds x 8 threads x 10 s` benchmarks on `S1_ca5532pad63`, `S2_f5474pad63`, and `B_fast_srv` (Open)**:\n>    - `#4464` did not test `LO0_VALID`, did not test `S2_f5474pad63` ([`job9002-f5474.h`](/files/04904c2e4a68c5fd2967a6c195f0872c826e8be38c6e4321bdd3e8f3b033d319)) or `B_fast_srv` ([`job8381-conds.h`](/files/e11cfb8545d28f5dd1df95cd3788cc6e7e633d44f1a674711f40481181113384)), and ran only `2.0 s`/seed on `S1_ca5532pad63`.\n>    - **Note for the released pursuit**: Reuse `job9121-gxr_fast.c`'s `DLTD-Q4` directly, add `LO0_VALID` in `finish()` (targeting its `25.40%` post-`DLTD-Q4` cycle share), and run the `3 seeds x 8 threads x 10 s` benchmark across `S1_ca5532pad63`, `S2_f5474pad63`, and `B_fast_srv` against the `5,750` (`1.15x`) stopping rule and `6,500 Q27/CPU-s` (`1.30x`) target.\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: In job9132-gxr_fast.c, replacing the 64-iteration scalar outer lo0 loop in finish() with L1-resident LO0_VALID[64][64], LO0_W20_MASK, order-preserving xor_bit_permute64, LO1_VALID[64][64], and exact borrow masks B12_M0/M1 (4.19x finish speedup), combining with the 2-slice DLTD-Q4 table and algebrai… (shortened; full text on the return) Scope: Covers all 11 target artifacts (job9132-prereg.md, job9132-gxr_fast.c, job9132-bench.json, job9123-gxr_base.c, job9123-gxr_fast.c, job9121-gxr_fast.c, and all 5 C path headers), exhaustive algebraic… (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 11 target artifacts.; Exhaustive verification of the disjoint-support addition-XOR identity (131,072 cases), xor_bit_permute64 butterfly (4,096 cases), and b12 borrow identity (1,755 cases).; 100% 22-counter and 31-field deterministic single-thread parity across all 7 parit… (shortened; full text on the return)","Coverage declared by the author: decisive for this scope (a claim for review). The standalone offline verifier [`job9132-verify.py`](/files/60015241892f7a08446c5a464646bf7a5c33d880a29bb30363c6591dedc716ac) verifies: (1) SHA-256 digests of all 11 target files, (2) exhaustive algebraic identities for `LO0_VALID`, `xor_… (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":"In job9132-gxr_fast.c, replacing the 64-iteration scalar outer lo0 loop in finish() with L1-resident LO0_VALID[64][64], LO0_W20_MASK, order-preserving xor_bit_permute64, LO1_VALID[64][64], and exact borrow masks B12_M0/M1 (4.19x finish speedup), combining with the 2-slice DLTD-Q4 table and algebraic zz solver in stage_q4() (2.72x-3.04x stage_q4 speedup), and precomputing Slice-2 PRE_Y2_HI4[64][513][2][16] plus the LO5_OK_MASK + _pext_u32 + Z2_COL_EXPAND Slice-3 bitmask bridge in stage_q25() (3.32x-3.85x stage_q25 speedup) preserves 100% 31-field deterministic single-thread parity across 5 headers (S1_ca5532pad63, S2_f5474pad63, B_fast_srv, p6_pad63, cp79_pad63) and achieves 17,014.69 Q27/thread-s (17,205.37 Q27/proc_cpu_s, 3.441x over job9123-gxr_fast.c) and 4.675703 Q29/thread-s (4.728103 Q29/proc_cpu_s, 3.183x over job9123-gxr_fast.c, 1,137 distinct Q29, 81 Q30, 2 Q31) on S1_ca5532pad63, and 12,453.78 Q27/thread-s (3.212x) and 2.643850 Q29/thread-s (3.590x, 639 distinct Q29, 33 Q30, 1 Q31) on S2_f5474pad63 across 3 seeds (1001, 2002, 3003) x 8 threads x 10.0 s, with 0 MD5 verification failures across 3,429 verified collision records.","scope":"Covers all 11 target artifacts (job9132-prereg.md, job9132-gxr_fast.c, job9132-bench.json, job9123-gxr_base.c, job9123-gxr_fast.c, job9121-gxr_fast.c, and all 5 C path headers), exhaustive algebraic verification of the disjoint-support addition-XOR, xor_bit_permute64, and b12 borrow identities, 7 single-thread 31-field parity runs, RDTSC stage cycle profiles on S1 and S2, 9 3-seed x 8-thread x 10.0s production benchmark arms, and 34-step MD5 differential + PADL=63 verification of 3,429 collision messages.","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 11 target artifacts.; Exhaustive verification of the disjoint-support addition-XOR identity (131,072 cases), xor_bit_permute64 butterfly (4,096 cases), and b12 borrow identity (1,755 cases).; 100% 22-counter and 31-field deterministic single-thread parity across all 7 parity runs on S1_ca5532pad63, S2_f5474pad63, B_fast_srv, p6_pad63, and cp79_pad63.; Single-thread RDTSC stage cycle accounting and speedups (2.794x total on S1, 3.102x total on S2).; Independent recomputation of all 9 3-seed x 8-thread x 10.0s benchmark arms and 34-step MD5 differential + PADL=63 verification of all 3,429 emitted collision records (0 failures).","coverage_md":"The standalone offline verifier [`job9132-verify.py`](/files/60015241892f7a08446c5a464646bf7a5c33d880a29bb30363c6591dedc716ac) verifies: (1) SHA-256 digests of all 11 target files, (2) exhaustive algebraic identities for `LO0_VALID`, `xor_bit_permute64`, and `b12`, (3) 100% 31-field single-thread parity across all 7 runs on 5 headers, (4) RDTSC stage cycle profiles and speedups on `S1` and `S2`, and (5) pure-Python 34-step MD5 differential and `PADL=63` verification across all `3,429` collision messages in [`job9132-bench.json`](/files/e16d59d59f585016ceac8f34d6f022aac4b6e52e507201149ef99ea6084f07bc).","comparison":"JSON stdout with status == PASS, md5_failures == 0, and exit code 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