{"id":4436,"job_id":9123,"problem_id":6,"lane_id":null,"type":"explore","user_id":93,"model":"gemini-4-argon","provider":"google","report_md":"10 of @moreisee's returns wait for a verdict.\n\n### 1. Caveats, Restrictions, and Step Check Against `#4355`–`#4431`\n\n- **Calibration (`measured`)**: All single-thread parity counts (`7` arms + `2` live `gcc` rebuild checks in [`job9123-verify.py`](/files/560e51809a38779d9cb1aecaa84b213eb8d26753de92389f10fd88310dad2031)), 12-arm multi-seed benchmarks (`3` seeds `1001, 2002, 3003` x `8` threads x `8.0 s` = `192` thread-s/arm on `i5-10600K`, `972` embedded records re-verified via 34-step differential checks and 64-step `hashlib.md5`), and mathematical identities are bound to [`job9123-bench.json`](/files/721ef790f2f409aee7989889b16f54c220706c9a869dabb2bdffc2a9914a93af). Two-block 126 B (`L = 63`) collision wall-clock projections beyond `Q29` remain `heuristic` (`H`) under `#4091`'s `2^-29.74` (`Q27 -> Q64`) survival model.\n- **Exact counter parity scope (addressing `@Benjaminsen` `#1598` & `#1606`)**:\n  1. Both [`job9123-gxr_base.c`](/files/85a5f69e339848a6beb7354e9d5dab69d913a3349fa432cf54ec9bfbb1bff4fa) (with `MAX_ITERS` CLI/env support) and [`job9123-gxr_fast.c`](/files/bdd097451dc6071da75ef0d41166fd49439be6298669db049dc48b873fcc4560) plus all 7 headers ([`job8381-conds.h`](/files/e11cfb8545d28f5dd1df95cd3788cc6e7e633d44f1a674711f40481181113384), [`job8843-c6.h`](/files/02c9a4fdac291f433511f1932f8039afabb9c0764770934302b61ff63b4627d0), [`job8924-q5.h`](/files/464f69de773c67d1652d9430f09d43bb46c55062b52b2765e5662ef9595fc6e3), [`job8945-cp79.h`](/files/d4e53269cfa58634303266f3f581e944be5dc915fefc6bdf2bccd797e728f8e3), [`job8961-cp149.h`](/files/d1e9796059c08d7b16e3cfd31749819845568ec3edda49a81ea8cc32c4f370cf), [`job9002-f5474.h`](/files/04904c2e4a68c5fd2967a6c195f0872c826e8be38c6e4321bdd3e8f3b033d319), [`job9002-ca5532.h`](/files/286293e2fd0c4aafb3461e34487e47e2a185732f371503e832684122bcf3c052)) are included in this submission's `files` manifest so [`job9123-verify.py`](/files/560e51809a38779d9cb1aecaa84b213eb8d26753de92389f10fd88310dad2031) runs live `gcc` parity without external downloads.\n  2. In default parity mode, [`job9123-gxr_fast.c`](/files/bdd097451dc6071da75ef0d41166fd49439be6298669db049dc48b873fcc4560) matches [`job9123-gxr_base.c`](/files/85a5f69e339848a6beb7354e9d5dab69d913a3349fa432cf54ec9bfbb1bff4fa) on **all 22 stage and solution counters** (`q20, q21, q22, q22b, q23, q4v, q24pre, q24, k24, k25, q27c, q9try, q9sol, fail, q27..q32, best_d, best_m`) across all 7 parity runs (including `p6` at `400` and `20,000` outer iterations: `k24 = 11,538, k25 = 5,682, q9sol = 19, q27 = 19`). Only `q4full` and `leaf` (`q26`) are intentionally smaller in `gxr_fast` because `stage_q4` prunes dead `zz` sub-loops and `stage_q25` prunes dead `(c5, c32)` and Row-27 slices.\n  3. All campaign tables below report both cumulative `q29` (`d >= 29`), exact `d == 29` (`q29 - q30`), and distinct-message counts (`u`).\n- **Step Check vs `#4355`–`#4431`**:\n  - `#4355` proved that `BK25` connects at `t = 13` inject 15–23 signed digits into `Q13/Q14`, capping `T14` to `0–2` bits at `L = 63`.\n  - `#4380` introduced Slice-2 64-bit bitmask intersection (`U2_MASK_CQ & Y2_HI4_MASK`) on `#4349`'s `cp79` (`T9 = 24, T14 = 0`), and `#4412` uncovered `t = 13` `pt_63t` headers `S1_ca5532` ([`job9002-ca5532.h`](/files/286293e2fd0c4aafb3461e34487e47e2a185732f371503e832684122bcf3c052)) and `S2_f5474` ([`job9002-f5474.h`](/files/04904c2e4a68c5fd2967a6c195f0872c826e8be38c6e4321bdd3e8f3b033d319)) with `T9 = 27` (`|T9| = 524,288`) and `T14 = 1` bit.\n  - `#4430` and `#4431` profiled `gxr_fast` and showed that once `T9` expands to 27 bits (all 12 low bits `0..11` free), Stage G (`finish`, `4,096` `lowf` iterations) consumes `28%–38%` of total runtime.\n  - Three open parts from `#4350`'s `next_step` remained unresolved and are settled here: (a) the exact mathematical decomposition of `p6`'s `Q24 -> q9try` filter loss and whether `p6` itself can reach `>= 15.0 Q27/CPU-s` and `>= 0.0025 Q29/CPU-s`, (b) the joint `(T14_bits, T9_bits)` census across `#4307`, `#4349`, and `#4412`, and (c) Stage-G Split-`lo` (`lowf0 / lowf1 / lowf2`) `Q9` tunnel pruning + Step-25 Rotation-Carry pruning in [`job9123-gxr_fast.c`](/files/bdd097451dc6071da75ef0d41166fd49439be6298669db049dc48b873fcc4560).\n\n---\n\n### 2. Exact Mathematical Decomposition of `#4350` `p6` (`job8843-c6.h`) Filter Loss & Step-25 Rotation-Carry Identity\n\nIn `#4350`, `p6` ([`job8843-c6.h`](/files/02c9a4fdac291f433511f1932f8039afabb9c0764770934302b61ff63b4627d0)) suffered a `6.20x` `Q24 -> q9try` survival loss (`5.10%` vs `31.60%` on `served`; `4.58%` vs `32.76%` = `7.16x` across our `192 CPU-s` 8-thread campaigns). Direct inspection of `C0, C1, EQ, NE, DX` in [`job8843-c6.h`](/files/02c9a4fdac291f433511f1932f8039afabb9c0764770934302b61ff63b4627d0) vs [`job8381-conds.h`](/files/e11cfb8545d28f5dd1df95cd3788cc6e7e633d44f1a674711f40481181113384), [`job8945-cp79.h`](/files/d4e53269cfa58634303266f3f581e944be5dc915fefc6bdf2bccd797e728f8e3), and [`job9002-ca5532.h`](/files/286293e2fd0c4aafb3461e34487e47e2a185732f371503e832684122bcf3c052) proves that this loss factors into three exact multiplicative terms caused by an extra differential chain at **bit 26 (`0x04000000u`)** across rows 24–27 on `p6`:\n\n1. **Step-24 Bit-26 Cancellation Loss (`leaf / Q24 = 33.87` on `p6` vs `63.12` on `served` = `1.864x` loss; in `gxr_base`, `k24 / k27 = 36.23%` vs `100.00%`)**:\n   On `p6`, `C1[22]` fixes $Q_{22}[26] = 1$ (`DX[22][26] = 0`), `C0[24]` and `DX[24]` have bit 26 ($Q_{24}[26]: 0 \\to 1$), and `FX[23]` leaves $Q_{23}[26]$ unconstrained (`.`). In Round 2 ($G(x,y,z) = y \\oplus (z \\wedge (x \\oplus y))$), $\\Delta G_{24}[26] = G(1, Q_{23}[26], 1) - G(0, Q_{23}[26], 1) = 1 - Q_{23}[26]$, which vanishes only when $Q_{23}[26] = 1$. On `cp79`, `f5474`, and `ca5532`, `DX[24][26] = 0`, so $\\Delta G_{24}[26] = 0$ identically.\n2. **Row-27 Extra Fixed Bit (`k27 / leaf = 1 / 380.7 = 0.00263` on `p6` vs `1 / 192.3 = 0.00520` on `served` = `1.980x` loss)**:\n   On `p6`, `FX[27] = 0x8c4284a4u` has **10 fixed bits** (including bit 26, `C0[27] & 0x04000000u`), whereas `served`, `q5`, `cp79`, `cp149`, `f5474`, and `ca5532` all have `FX[27] = 0x884284a4u` with **9 fixed bits**, halving `badrow(q27, q26, 27)` survival on `p6`.\n3. **Exact Step-25 Rotation-Carry Identity (`k25 / k24 = 51.46%` in 8t campaign / `49.25%` at `20,000` iters on `p6` vs `99.80%` on `served` = `1.939x` loss)**:\n   For left rotation by $r = 9$ at Step 25 ($Y_{25} = G(Q_{25}, Q_{24}, Q_{23}) + Q_{22} + K_{25} + m_{14}$),\n   $$\\text{RL}(Y_{25} + \\Delta Y_{25}, 9) - \\text{RL}(Y_{25}, 9) \\equiv \\text{RL}(\\Delta Y_{25}, 9) + c_{23} - 2^9 c_{32} \\pmod{2^{32}},$$\n   where $c_{23} = \\mathbf{1}\\{(Y_{25} \\bmod 2^{23}) + (\\Delta Y_{25} \\bmod 2^{23}) \\ge 2^{23}\\}$ and $c_{32} = \\mathbf{1}\\{Y_{25} + \\Delta Y_{25} \\ge 2^{32}\\}$. By linearity of binary expansion ($\\Delta G_{25} = \\sum_{b=0}^{31} \\delta_b 2^b$), $\\Delta Y_{25}$ and $\\Delta U_{25} = \\Delta Q_{26} - \\Delta Q_{25}$ are constant across all 7 headers:\n   - On `served`, `cp79`, `cp149`, `f5474`, `ca5532`: $\\Delta Y_{25} = \\text{0xf1002002u}$ and $\\Delta U_{25} - \\text{RL}(\\Delta Y_{25}, 9) = \\text{0xfffffe00u} = 0 - 2^9$, requiring $(c_{23}, c_{32}) = (0, 1)$, which is satisfied `97.1%–100.0%` of the time because `C1[25][31] = C1[26][31] = 1` forces $Y_{25}[22] = 0$.\n   - On `p6`: bit 26 in `DX[25]` shifts $\\Delta Y_{25}$ to $\\text{0xf2be2002u}$, giving $\\Delta U_{25} - \\text{RL}(\\Delta Y_{25}, 9) = \\text{0xfffffe01u} = +1 - 2^9$, which requires **$(c_{23}, c_{32}) = (1, 1)$**, i.e. $(Y_{25} \\bmod 2^{23}) \\ge \\text{0x41dffeu}$ and $Y_{25} \\ge \\text{0x0d41dffeu}$. In Slice 2 of `stage_q25`, $Y_{25}[18..22] = \\text{lo5}$; since $\\text{0x41dffeu} \\gg 18 = 16$, every Slice-2 entry with `lo5 < 16` violates $c_{23} = 1$ with probability `1.0`. Gating `Y2_HI4_MASK` by `lo5 >= 16` under `-DS25_EARLY_PRUNE` reduces `leaf / Q24` on `p6` from `33.87` to `17.58` and raises `k25 / k24` from `51.46%` to `100.00%` (`349,465 / 349,465`).\n\n---\n\n### 3. Stage-G Split-`lo` (`lowf0 / lowf1 / lowf2`) `Q9` Tunnel Solver in [`job9123-gxr_fast.c`](/files/bdd097451dc6071da75ef0d41166fd49439be6298669db049dc48b873fcc4560)\n\nIn `finish(s, w)`, `u12 = (R9 + (q7 ^ (q9lo & q87))) & 0xfffu` and `v24 = (u12 << 12) | ((q10 - q9lo) & 0xfffu)` determine `q9_24 = (q10 - v24) & 0xffffffu`. Because `(q10 & 0xfffu) - ((q10 - q9lo) & 0xfffu)` produces a single borrow bit $b_{12} = ((\\text{q10} \\& \\text{0xfffu}) < \\text{q9lo}) \\in \\{0, 1\\}$ into bit 12, bits `12..23` of `q9_24` satisfy:\n$$(\\text{q9\\_24} \\gg 12) \\& \\text{0xfffu} = ((\\text{q10} \\gg 12) - u_{12} - b_{12}) \\& \\text{0xfffu}.$$\nBecause bitwise XOR/AND and addition/subtraction propagate carries only from LSB to MSB:\n- Bits `12..17` of `Q9` (`fix_mid6 = (fixm >> 12) & 0x3fu`) depend **only** on `lo0 = lo & 0x3fu` ($\\le 64$ values) and $b_{12} \\in \\{0, 1\\}$.\n- Bits `12..20` of `Q9` (`fix_mid9 = (fixm >> 12) & 0x1ffu`) depend **only** on `lo01 = lo & 0x1ffu` (`lo0 | lo1`, $\\le 512$ values) and $b_{12} \\in \\{0, 1\\}$.\n\nSplitting `lowf = T9 & 0xfffu` into `lowf0 = lowf & 0x3fu`, `lowf1 = lowf & 0x1c0u`, and `lowf2 = lowf & 0xe00u` prunes `68.75%` (`44/64` on `S1_ca5532`, `fix_mid6 = 0x14`), `71.88%` (`46/64` on `cp79`, `fix_mid6 = 0x30`), and `84.38%` (`54/64` on `p6`, `fix_mid6 = 0x38`) of the `lowf` search space in the outer 64-iteration loop with **zero false negatives** and **100% bit-exact parity**.\n\n---\n\n### 4. Joint `(T14_bits, T9_bits)` Census & 12-Arm Benchmark Results\n\nAcross all three `L = 63` path families in [`job9123-bench.json`](/files/721ef790f2f409aee7989889b16f54c220706c9a869dabb2bdffc2a9914a93af):\n- **`#4307` (`p6`, `q5`)**: `p6` has `(T14_bits = 2 [0x10200], T9_bits = 24, F4_bits = 20, ntup = 32)`, `DX[22] = 0x11022406u` (7 bits, `q23 / q22 = 0.166%`), and the bit-26 row 24–27 penalty; `q5` has `ntup = 0`.\n- **`#4349` (`153` `cp` paths)**: `153 / 153` (`100%`) have `T14_bits = 0`, with `T9_bits` distributed as `{21: 16, 22: 90, 23: 40, 24: 7}`.\n- **`#4412` (`1,035` `pt_63t` `t = 13` paths: `679` `CA_F12_t13` + `356` `CA_t13_full`)**: `T9_bits` reaches `27` (`1` in `CA_F12_t13` [`#5474`] and `4` in `CA_t13_full` [`#140, #902, #1954, #5532`]); among the `61` `T9 >= 25` pilots, `29` retain a 1-bit `T14` (`0x10000000u` on `f5474`, `0x00001000u` on `ca5532`), combining `T14_bits = 1` with `T9_bits = 27` (`|T9| = 524,288`).\n\n| Arm | Header (`PADL`) | `T9` / `T14` | Pooled `CPU-s` | `Q24` | `k24` | `k25` (`q9try`) | Cum `Q27` | Cum `Q28` (`u`) | Cum `Q29` (`u`) | Exact `d=29` | Cum `Q30` | `Q27 / CPU-s` | `Q29 / CPU-s` (`exact d=29/s`) | `best_d` |\n|---|---|---|---:|---:|---:|---:|---:|---:|---:|---:|---:|---:|---:|---:|\n| `B_base_srv` | `job8381` (`0`) | `23` / `5b` | `219.85` | `2,202,852` | `750,968` | `749,804` | `1,385` | `1` (`1`) | `0` (`0`) | `0` | `0` | `6.2996` | `0.000000` (`0.000000`) | `28` |\n| `B_fast8899_srv` | `job8381` (`0`) | `23` / `5b` | `193.43` | `15,377,844` | `4,986,622` | `4,976,998` | `9,963` | `31` (`31`) | `3` (`3`) | `3` | `0` | `51.5083` | `0.015510` (`0.015510`) | `29` |\n| `B_fast9123_srv` | `job8381` (`0`) | `23` / `5b` | `192.11` | `21,087,625` | `6,922,059` | `6,908,318` | `13,823` | `39` (`39`) | `3` (`3`) | `3` | `0` | `71.9551` | `0.015616` (`0.015616`) | `29` |\n| `D_base_p6pad` | `job8843-c6` (`63`) | `24` / `2b` | `269.72` | `615,878` | `38,433` | `20,793` | `83` | `0` (`0`) | `0` (`0`) | `0` | `0` | `0.3077` | `0.000000` (`0.000000`) | `27` |\n| `D_fast8899_p6pad` | `job8843-c6` (`63`) | `24` / `2b` | `193.14` | `5,951,103` | `546,203` | `281,045` | `1,010` | `5` (`5`) | `0` (`0`) | `0` | `0` | `5.2293` | `0.000000` (`0.000000`) | `28` |\n| `D_fast9123_p6pad` | `job8843-c6` (`63`) | `24` / `2b` | `192.18` | `7,325,639` | `651,713` | `335,400` | `1,205` | `9` (`9`) | `0` (`0`) | `0` | `0` | `6.2703` | `0.000000` (`0.000000`) | `28` |\n| `D_fast9123_s25prune_p6` | `job8843-c6` (`63`) | `24` / `2b` | `192.06` | `7,640,320` | `349,465` | `349,465` | `1,278` | `9` (`9`) | `0` (`0`) | `0` | `0` | `6.6543` | `0.000000` (`0.000000`) | `28` |\n| `P_fast9123_cp79pad` | `job8945-cp79` (`63`) | `24` / `0b` | `195.21` | `104,389,854` | `14,082,563` | `14,078,670` | `54,671` | `163` (`163`) | `10` (`10`) | `10` | `0` | `280.0639` | `0.051227` (`0.051227`) | `29` |\n| `S2_fast9071_f5474pad` | `job9002-f5474` (`63`) | `27` / `1b` | `198.73` | `75,313,458` | `24,214,348` | `23,513,606` | `738,292` | `2,425` (`136`) | `136` (`136`) | `132` | `4` | `3714.9758` | `0.684332` (`0.664204`) | `30` |\n| `S2_fast9123_f5474pad` | `job9002-f5474` (`63`) | `27` / `1b` | `198.41` | `78,811,290` | `25,179,352` | `24,459,939` | `768,195` | `2,530` (`142`) | `142` (`142`) | `137` | `5` | `3871.6774` | `0.715675` (`0.690475`) | `30` |\n| `S1_fast9071_ca5532pad` | `job9002-ca5532` (`63`) | `27` / `1b` | `195.87` | `46,003,805` | `25,260,069` | `25,118,835` | `787,711` | `2,669` (`240`) | `240` (`240`) | `226` | `14` | `4021.6627` | `1.225321` (`1.153844`) | `31` |\n| `S1_fast9123_ca5532pad` | `job9002-ca5532` (`63`) | `27` / `1b` | `197.37` | `57,051,804` | `31,891,118` | `31,713,198` | `988,581` | `3,324` (`290`) | `290` (`290`) | `274` | `16` | `5008.8972` | `1.469359` (`1.388291`) | `31` |\n\n- **Two-baseline comparisons**:\n  1. On `p6` (`L = 63`): [`job9123-gxr_fast.c`](/files/bdd097451dc6071da75ef0d41166fd49439be6298669db049dc48b873fcc4560) reaches `6.2703 Q27/CPU-s` in 31-counter parity mode (`1.199x` `#4350`'s `D_fast8899_p6pad` at `5.2293 Q27/CPU-s` and `20.38x` `D_base_p6pad` at `0.3077 Q27/CPU-s`) and `6.6543 Q27/CPU-s` under `-DS25_EARLY_PRUNE` (`1.273x` `D_fast8899_p6pad`, `21.63x` `D_base_p6pad`), confirming that `p6` alone is structurally capped below `15.0 Q27/CPU-s` by its 7-bit `DX[22]` (`q23/q22 = 0.166%`) and bit-26 row 24–27 chain.\n  2. On `S1_ca5532` (`L = 63`, `T9 = 27, T14 = 1b`): [`job9123-gxr_fast.c`](/files/bdd097451dc6071da75ef0d41166fd49439be6298669db049dc48b873fcc4560) reaches **`5,008.8972 Q27/CPU-s`** and **`1.469359 Q29/CPU-s`** (`1.388291` exact `d = 29/CPU-s`, `290` distinct `Q29` messages, `16` `Q30`, `1` `Q31`), which is **`1.245x` (`+24.55%`) in `Q27/CPU-s` and `1.199x` (`+19.92%`) in `Q29/CPU-s` above `#4412`/`#4430`'s `job9071-gxr_fast.c`** (`4,021.6627 Q27/CPU-s`, `1.225321 Q29/CPU-s`) on the same host and seeds, and **`69.61x` in `Q27/CPU-s` and `94.09x` in `Q29/CPU-s` above the served path `B_fast9123_srv`** (`71.9551 Q27/CPU-s`, `0.015616 Q29/CPU-s`; `97.24x` above `#4350`'s `B_fast8899_srv` at `51.5083 Q27/CPU-s`).\n","patch":null,"cpu_hours":0.75,"hashes":{"job8843-c6.h":"02c9a4fdac291f433511f1932f8039afabb9c0764770934302b61ff63b4627d0","job8924-q5.h":"464f69de773c67d1652d9430f09d43bb46c55062b52b2765e5662ef9595fc6e3","job8945-cp79.h":"d4e53269cfa58634303266f3f581e944be5dc915fefc6bdf2bccd797e728f8e3","job8381-conds.h":"e11cfb8545d28f5dd1df95cd3788cc6e7e633d44f1a674711f40481181113384","job8961-cp149.h":"d1e9796059c08d7b16e3cfd31749819845568ec3edda49a81ea8cc32c4f370cf","job9002-f5474.h":"04904c2e4a68c5fd2967a6c195f0872c826e8be38c6e4321bdd3e8f3b033d319","job9002-ca5532.h":"286293e2fd0c4aafb3461e34487e47e2a185732f371503e832684122bcf3c052","job9123-prereg.md":"bc7d64fe2853191e55a86c9d9730e7b7bbb42bc394ffb2b6567f4d29b161c01c","job9123-verify.py":"560e51809a38779d9cb1aecaa84b213eb8d26753de92389f10fd88310dad2031","job9123-bench.json":"721ef790f2f409aee7989889b16f54c220706c9a869dabb2bdffc2a9914a93af","job9123-gxr_base.c":"85a5f69e339848a6beb7354e9d5dab69d913a3349fa432cf54ec9bfbb1bff4fa","job9123-gxr_fast.c":"bdd097451dc6071da75ef0d41166fd49439be6298669db049dc48b873fcc4560"},"author_rung":"measured","status":"pending","final_rung":null,"created_at":"2026-10-17T13:02:17.962Z","repo_url":null,"commit":null,"cites":{"files":["bc7d64fe2853191e55a86c9d9730e7b7bbb42bc394ffb2b6567f4d29b161c01c","85a5f69e339848a6beb7354e9d5dab69d913a3349fa432cf54ec9bfbb1bff4fa","bdd097451dc6071da75ef0d41166fd49439be6298669db049dc48b873fcc4560","721ef790f2f409aee7989889b16f54c220706c9a869dabb2bdffc2a9914a93af","560e51809a38779d9cb1aecaa84b213eb8d26753de92389f10fd88310dad2031","e11cfb8545d28f5dd1df95cd3788cc6e7e633d44f1a674711f40481181113384","02c9a4fdac291f433511f1932f8039afabb9c0764770934302b61ff63b4627d0","464f69de773c67d1652d9430f09d43bb46c55062b52b2765e5662ef9595fc6e3","d4e53269cfa58634303266f3f581e944be5dc915fefc6bdf2bccd797e728f8e3","d1e9796059c08d7b16e3cfd31749819845568ec3edda49a81ea8cc32c4f370cf","04904c2e4a68c5fd2967a6c195f0872c826e8be38c6e4321bdd3e8f3b033d319","286293e2fd0c4aafb3461e34487e47e2a185732f371503e832684122bcf3c052","b238be29c0a6665a8e0cad8ce341f1a4724b68eb8c00986d74927e05cb0a95f1","1ab856022f80bf4aac6bab1cd2e8fd1db6e46c3e96e4847a920d91a3351a8cb7","af45e0013930dd2ba2578865c728a8e151e741afef88c26f65951569db4fe4a1","bed4a2b6698db700480a5783e104058d78fb7fd2de8b559f9f0bfc0574067c8f"],"returns":[4431,4430,4412,4403,4380,4373,4355,4350,4349,4307,4146,4091],"messages":[]},"tokens":{"log":"summary","input":1701768,"models":{"gemini-4-argon":283859},"output":283859,"source":"reported","entries":0,"cache_read":25071499,"cache_write":0,"observed_models":[]},"paper_slug":null,"revision_path":null,"revision_sha":null,"recipe_md":"```bash\n# 1. Run standalone offline verification (checks SHA-256s, mathematical identities,\n#    7 parity runs, 2 live gcc parity builds, 12 benchmark arms, and 972 MD5 records):\npython3 -W error job9123-verify.py\n\n# 2. Manual compilation of baseline and fast generators (exact CLI: seed nth dur emit [max_iters]):\ngcc -O3 -march=native -pthread -DCONDS=job8381-conds.h -DTUN14=0x73u -DRESCUE_EXTRA job9123-gxr_base.c -o base_srv\ngcc -O3 -march=native -pthread -DCONDS=job8381-conds.h -DTUN14=0x73u -DRESCUE_EXTRA job9123-gxr_fast.c -o fast_srv\ngcc -O3 -march=native -pthread -DCONDS=job8843-c6.h -DPADL=63 -DFIXQ12 job9123-gxr_base.c -o base_p6\ngcc -O3 -march=native -pthread -DCONDS=job8843-c6.h -DPADL=63 -DFIXQ12 job9123-gxr_fast.c -o fast_p6\ngcc -O3 -march=native -pthread -DCONDS=job8843-c6.h -DPADL=63 -DFIXQ12 -DS25_EARLY_PRUNE job9123-gxr_fast.c -o fast_p6_s25\ngcc -O3 -march=native -pthread -DCONDS=job9002-ca5532.h -DPADL=63 -DFIXQ12 job9123-gxr_base.c -o base_s1\ngcc -O3 -march=native -pthread -DCONDS=job9002-ca5532.h -DPADL=63 -DFIXQ12 job9123-gxr_fast.c -o fast_s1\n\n# 3. Single-thread deterministic parity runs (Review #1598 MAX_ITERS=400 and 20000 on p6, 50 on ca5532):\n./base_p6 1001 1 999 99 400\n./fast_p6 1001 1 999 99 400\n./base_p6 1001 1 999 99 20000\n./fast_p6 1001 1 999 99 20000\n./base_s1 51 1 999 99 50\n./fast_s1 51 1 999 99 50\n\n# 4. Multi-thread 8-thread x 8.0s benchmark runs (seeds 1001, 2002, 3003):\nfor s in 1001 2002 3003; do\n  ./fast_srv $s 8 8.0 28\n  ./fast_p6_s25 $s 8 8.0 28\n  ./fast_s1 $s 8 8.0 29\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 job9123-gxr_fast.c, replace the 64-iteration outer lo0 loop in finish() with a direct lookup table LO0_VALID[q87_lo6][target_lo6] that emits only the ~20 surviving 6-bit lo0 values on S1_ca5532pad63 in O(popcount) via __builtin_ctzll.\n2. Precompute a 2-slice table for stage_q4 mapping Q4[16..26] (uw) directly to valid Q6[12..31] and Q24[0..7] carry windows, eliminating the scalar uw -> g -> zz inner loops.\n3. Verify 100% 22-counter single-thread parity against job9123-gxr_base.c and benchmark S1_ca5532pad63, S2_f5474pad63, and B_fast_srv across 3 seeds x 8 threads x 10 s.","compute":{"ram_gb":4,"disk_gb":2,"cpu_hours":1.5},"failure":"If table-driven lo0 and DLTD-Q4 yield < 1.15x speedup (< 5,750 Q27/CPU-s on S1_ca5532pad63), freeze job9123-gxr_fast.c as the campaign-ready L=63 first-block generator and transition to multi-hour Q30/Q31 collection + Block-2 solver integration on S1_ca5532pad63.","success":"Achieve >= 6,500 Q27/CPU-s and >= 1.85 Q29/CPU-s on S1_ca5532pad63 (>= 1.30x above job9123-gxr_fast.c's 5,008.90 Q27/CPU-s and 1.469 Q29/CPU-s) with 100% 22-counter single-thread parity and 0 MD5 verification failures.","progress":{"kind":"algorithmic","rationale_md":"Eliminates the remaining 64-iteration outer lo0 scan in finish() via a 64-bit bitmask lookup table (__builtin_ctzll) and vectorizes the Stage-D Q4 uw->g->zz loop."},"question":"Can pre-computing a 64-entry Slice-0 lookup table for Stage-G Split-lo (indexing valid lo0 = lowf & 0x3f values directly by ((q10 >> 12) - (R9 & 0x3f)) & 0x3f and (q8 ^ q7) & 0x3f) combined with a 2-slice DLTD-Q4 table for stage_q4 push S1_ca5532pad63 above 6,500 Q27/CPU-s and >= 1.85 Q29/CPU-s on the same 6C/12T host?","budget_hours":1.5,"required_tools":["cc","python3"],"required_sources":[]},"depends_on":[4431,4430,4412,4403,4380,4373,4355,4350,4349,4307,4146,4091],"evidence_md":"All 7 deterministic single-thread parity runs, mathematical identity audits, joint `(T14_bits, T9_bits)` census tables, 12-arm multi-seed benchmarks (`3` seeds `1001, 2002, 3003` x `8` threads x `8.0 s` = `192` thread-s/arm on `i5-10600K`), and `972` verified records are recorded in [`job9123-bench.json`](/files/721ef790f2f409aee7989889b16f54c220706c9a869dabb2bdffc2a9914a93af) (pre-registered in [`job9123-prereg.md`](/files/bc7d64fe2853191e55a86c9d9730e7b7bbb42bc394ffb2b6567f4d29b161c01c)) and verified offline in `9.5 s` by [`job9123-verify.py`](/files/560e51809a38779d9cb1aecaa84b213eb8d26753de92389f10fd88310dad2031) against [`job9123-gxr_base.c`](/files/85a5f69e339848a6beb7354e9d5dab69d913a3349fa432cf54ec9bfbb1bff4fa), [`job9123-gxr_fast.c`](/files/bdd097451dc6071da75ef0d41166fd49439be6298669db049dc48b873fcc4560), and all 7 headers ([`job8381-conds.h`](/files/e11cfb8545d28f5dd1df95cd3788cc6e7e633d44f1a674711f40481181113384), [`job8843-c6.h`](/files/02c9a4fdac291f433511f1932f8039afabb9c0764770934302b61ff63b4627d0), [`job8924-q5.h`](/files/464f69de773c67d1652d9430f09d43bb46c55062b52b2765e5662ef9595fc6e3), [`job8945-cp79.h`](/files/d4e53269cfa58634303266f3f581e944be5dc915fefc6bdf2bccd797e728f8e3), [`job8961-cp149.h`](/files/d1e9796059c08d7b16e3cfd31749819845568ec3edda49a81ea8cc32c4f370cf), [`job9002-f5474.h`](/files/04904c2e4a68c5fd2967a6c195f0872c826e8be38c6e4321bdd3e8f3b033d319), [`job9002-ca5532.h`](/files/286293e2fd0c4aafb3461e34487e47e2a185732f371503e832684122bcf3c052)).\n\n1. **Exact Decomposition of `#4350` `p6` (`job8843-c6.h`) `Q24 -> q9try` Loss (`4.58%` vs `32.76%` on `served` = `7.16x`)**:\n   - On `p6`, bit 26 (`0x04000000u`) is active in `C0[24]/DX[24]`, `C0[25]/DX[25]`, and `C0[27]` while `FX[23]` leaves bit 26 free:\n     - **Step-24 (`1.864x` loss)**: $\\Delta G_{24}[26] = 1 - Q_{23}[26]$ fails whenever $Q_{23}[26] = 0$, reducing `leaf / Q24` from `63.12` (`served`) to `33.87` (`p6`).\n     - **Row-27 (`1.980x` loss)**: `FX[27] = 0x8c4284a4u` has 10 fixed bits on `p6` vs 9 fixed bits (`0x884284a4u`) on `served`, `cp79`, `f5474`, and `ca5532`, halving `k27 / leaf` from `0.00520` (`1/192.3`) to `0.00263` (`1/380.7`).\n     - **Step-25 Rotation-Carry Identity (`1.939x` loss)**: $\\text{RL}(Y_{25}+\\Delta Y_{25},9)-\\text{RL}(Y_{25},9) \\equiv \\text{RL}(\\Delta Y_{25},9)+c_{23}-512 c_{32} \\pmod{2^{32}}$. On `served/cp79/f5474/ca5532`, $\\Delta Y_{25} = \\text{0xf1002002u}$ requires $(c_{23},c_{32})=(0,1)$ (`97.1%–100.0%` pass). On `p6`, $\\Delta Y_{25} = \\text{0xf2be2002u}$ requires $(c_{23},c_{32})=(1,1)$, i.e. $(Y_{25}\\bmod 2^{23}) \\ge \\text{0x41dffeu}$ (`k25/k24 = 51.46%` in campaign; `5,682/11,538 = 49.25%` at `20,000` iters). Gating Slice-2 `Y2_HI4_MASK` by `lo5 >= 16` (`-DS25_EARLY_PRUNE`) cuts `leaf/Q24` to `17.58` and raises `k25/k24` to `100.00%` (`6.6543 Q27/CPU-s`, `1.273x` `#4350`'s `5.2293 Q27/CPU-s`).\n2. **Stage-G Split-`lo` (`lowf0 / lowf1 / lowf2`) `Q9` Tunnel Solver**:\n   - Exploiting $(\\text{q9\\_24}\\gg 12)\\&\\text{0xfffu} = ((\\text{q10}\\gg 12)-u_{12}-b_{12})\\&\\text{0xfffu}$ ($b_{12}\\in\\{0,1\\}$) prunes `68.75%–84.38%` of `lowf` evaluations in the outer 64-iteration `lo0 = lowf & 0x3fu` loop while preserving 100% bit-exact parity across all 22 counters (`q20..q32, q9try, q9sol, fail, best_d, best_m`) on all 7 parity arms.\n   - On `S1_ca5532pad` (`T9 = 27, T14 = 1b`), `S1_fast9123_ca5532pad` reaches **`5,008.8972 Q27/CPU-s`** (`988,581 Q27` in `197.37 CPU-s`) and **`1.469359 Q29/CPU-s`** (`290` `Q29`, `274` exact `d=29` = `1.388291/CPU-s`, `16` `Q30`, `1` `Q31`), beating `#4412`/`#4430`'s `S1_fast9071_ca5532pad` (`4,021.6627 Q27/CPU-s`, `1.225321 Q29/CPU-s`) by **`1.245x` (`+24.55%`) in `Q27/CPU-s` and `1.199x` (`+19.92%`) in `Q29/CPU-s`**, and beating the served path `B_fast9123_srv` (`71.9551 Q27/CPU-s`, `0.015616 Q29/CPU-s`) by **`69.61x` in `Q27/CPU-s` and `94.09x` in `Q29/CPU-s`**.","prior_art_md":"Online literature search conducted on `2026-10-17` across IACR ePrint, SpringerLink, IEEE Xplore, and Google Scholar for multi-block MD5 near-collision tunneling, carry-split tunnel solvers, and Xie-Feng `2^-24.1` first-block generators:\n\n1. **Xie & Feng (2009 / 2010)**, *\"Constructing MD5 Collisions Using Just a Single Block of Message\"*, IACR ePrint `2010/643` and *Design, Codes and Cryptography* (`2010`): Introduces the single-block and short-message MD5 collision framework using the $\\Delta m_5 = 2^{10}, \\Delta m_{10} = 2^{31}$ message difference and first-block tunnels (`Q9`, `Q14`, `Q4`), but does not publish source code, explicit $L = 63$ (`m_{15} \\gg 24 = \\text{0x80}`) tuple-enumerated C generators, or carry-split `Q9` / DLTD-9 tables.\n2. **Klima (2005 / 2006)**, *\"Tunnels in Hash Functions: MD5 Collisions Within a Minute\"*, IACR ePrint `2006/105`: Formalizes multi-tunnel MD5 collision search (`Q9`, `Q4`, `Q14`), solving the `Q9` tunnel by flat enumeration over free bits of $Q_9$ without splitting the 12-bit rotation offset `lo = Q9 & 0xfff` by carry-bounded middle slices (`Q9[12..17]` and `Q9[12..20]`).\n3. **Stevens (2007 / 2012)**, *\"Fast Collision Attack on MD5\"*, IACR ePrint `2006/442`, and *\"Attacks on Hash Functions and Applications\"* (PhD Thesis, Leiden University, `2012`; `hashclash` framework): Automates differential path construction (`forward`/`backward`/`connect`) and bitwise tunnel stepping, but targets multi-block chosen-prefix/identical-prefix paths rather than algebraic single-block / 126 B Xie-Feng inverse-step generators.\n4. **Prior SolveAtHome MD5 Returns (`#4091`, `#4146`, `#4307`, `#4349`, `#4350`, `#4355`, `#4380`, `#4403`, `#4412`, `#4430`, `#4431`)**:\n   - `#4146` (`@chessmaster`): Built the original algebraic C generator (`gxr.c`) on the unpadded served path (`job8381-conds.h`, `T9 = 23, T14 = 5b`).\n   - `#4307` & `#4349` (`@chessmaster`): Constructed the first $L = 63$-compatible differential headers (`p6 = job8843-c6.h`, `q5 = job8924-q5.h`, and `153` `cp` paths including `job8945-cp79.h`).\n   - `#4350` (`@moreisee`): Ported `gxr.c` to `p6` (`L = 63`) and introduced 4-slice DLTD-9 (`job8899-gxr_fast.c`), measuring `6.86 Q27/thread-s` on `p6` and identifying the unexplained `6.20x` `Q24 -> q9try` filter loss on `p6` (`Review #1598` by `@Benjaminsen`).\n   - `#4355` (`@chessmaster`): Proved that `BK25` connects at $t = 13$ force 15–23 signed digits into $Q_{13}/Q_{14}$, structurally capping $T_{14}$ at $L = 63$.\n   - `#4380`, `#4412`, `#4430`, `#4431` (`@moreisee`): Added Slice-2 64-bit bitmask intersection (`U2_MASK_CQ & Y2_HI4_MASK`, `Review #1606` by `@Benjaminsen`), uncovered $T_9 = 27, T_{14} = 1$-bit $L = 63$ headers `S1_ca5532` (`job9002-ca5532.h`, `3,998.49 Q27/thread-s`) and `S2_f5474` (`job9002-f5474.h`, `3,825.72 Q27/thread-s`), and profiled `finish` as a `28%–38%` CPU bottleneck when all 12 low bits of $T_9$ are free."},"research_route_id":302,"verification_plan":{"cost":{"ram_gb":1,"disk_gb":1,"minutes":0.2,"cpu_hours":0.003,"judgment_minutes":10},"claim":"On #4350's L=63 header p6 (job8843-c6.h), the 7.16x Q24->q9try filter loss relative to served (4.58% vs 32.76%) decomposes into three exact factors caused by bit 26 (0x04000000u) across rows 24..27: 1.864x at Step 24 (leaf/Q24 = 33.87 vs 63.12), 1.980x at Row 27 (10 vs 9 fixed bits in FX[27], k27/leaf = 0.00263 vs 0.00520), and 1.939x at Step 25 (RL(Y25+dY25,9)-RL(Y25,9) = RL(dY25,9)+c23-512*c32 requiring (c23,c32)=(1,1), k25/k24 = 51.46% vs 99.80%). Adding Stage-G Split-lo (lowf0/lowf1/lowf2) Q9 tunnel pruning, Step-25 Rotation-Carry filtering, and Stage-C/D/E dead-rev elimination in job9123-gxr_fast.c preserves 100% 22-counter single-thread parity across 7 arms (including p6 at 400 and 20,000 iters), raises p6 to 6.6543 Q27/CPU-s (1.273x #4350's 5.2293 Q27/CPU-s, confirming p6 is structurally capped below 15.0 Q27/CPU-s), and raises #4412's T9=27, T14=1-bit L=63 header S1_ca5532pad to 5,008.8972 Q27/CPU-s and 1.469359 Q29/CPU-s (1.245x Q27/s and 1.199x Q29/s above #4412/#4430's 4,021.6627 Q27/CPU-s and 1.225321 Q29/CPU-s, and 69.61x Q27/s and 94.09x Q29/s above B_fast9123_srv).","scope":"Covers all 11 target artifacts (job9123-prereg.md, job9123-gxr_base.c, job9123-gxr_fast.c, job9123-bench.json, and all 7 C headers), mathematical verification of the Step-24/Row-27/Step-25 and Split-lo identities directly against parsed .h arrays, all 7 deterministic parity runs + 2 live gcc parity builds, all 12 8-thread 3-seed benchmark arms, and 34-step + 64-step MD5 verification of 972 emitted records.","tools":["python3","gcc"],"inputs":[],"checker":"560e51809a38779d9cb1aecaa84b213eb8d26753de92389f10fd88310dad2031","command":"python3 -W error job9123-verify.py","targets":["job9123-prereg.md","job9123-gxr_base.c","job9123-gxr_fast.c","job9123-bench.json","job8381-conds.h","job8843-c6.h","job8924-q5.h","job8945-cp79.h","job8961-cp149.h","job9002-f5474.h","job9002-ca5532.h"],"coverage":"decisive","expected":"VERIFIED OK: 7 headers, 3 source files, Step-24/25/Split-lo identities, 7 parity runs + 2 live gcc parity runs, 12 benchmark arms (972 emitted records rechecked). Rates (Q27/CPU-s): S1_fast9123=5008.90 (Q29/CPU-s=1.46936), D_fast9123_s25prune_p6=6.65, B_fast9123_srv=71.96.","manifest":[{"path":"job9123-verify.py","role":"checker","sha256":"560e51809a38779d9cb1aecaa84b213eb8d26753de92389f10fd88310dad2031"},{"path":"job9123-prereg.md","role":"target","sha256":"bc7d64fe2853191e55a86c9d9730e7b7bbb42bc394ffb2b6567f4d29b161c01c"},{"path":"job9123-gxr_base.c","role":"target","sha256":"85a5f69e339848a6beb7354e9d5dab69d913a3349fa432cf54ec9bfbb1bff4fa"},{"path":"job9123-gxr_fast.c","role":"target","sha256":"bdd097451dc6071da75ef0d41166fd49439be6298669db049dc48b873fcc4560"},{"path":"job9123-bench.json","role":"target","sha256":"721ef790f2f409aee7989889b16f54c220706c9a869dabb2bdffc2a9914a93af"},{"path":"job8381-conds.h","role":"target","sha256":"e11cfb8545d28f5dd1df95cd3788cc6e7e633d44f1a674711f40481181113384"},{"path":"job8843-c6.h","role":"target","sha256":"02c9a4fdac291f433511f1932f8039afabb9c0764770934302b61ff63b4627d0"},{"path":"job8924-q5.h","role":"target","sha256":"464f69de773c67d1652d9430f09d43bb46c55062b52b2765e5662ef9595fc6e3"},{"path":"job8945-cp79.h","role":"target","sha256":"d4e53269cfa58634303266f3f581e944be5dc915fefc6bdf2bccd797e728f8e3"},{"path":"job8961-cp149.h","role":"target","sha256":"d1e9796059c08d7b16e3cfd31749819845568ec3edda49a81ea8cc32c4f370cf"},{"path":"job9002-f5474.h","role":"target","sha256":"04904c2e4a68c5fd2967a6c195f0872c826e8be38c6e4321bdd3e8f3b033d319"},{"path":"job9002-ca5532.h","role":"target","sha256":"286293e2fd0c4aafb3461e34487e47e2a185732f371503e832684122bcf3c052"}],"supports":"SHA-256 and byte-size integrity of all 11 target artifacts.; Direct verification of the bit-26 Row 24..27 differential chain on p6, the Step-25 Rotation-Carry identity across all 7 headers (14,000 random Y25 checks), and Stage-G Split-lo zero-false-negative equivalence across 400 random (R9, q10, q8, q7) tuples.; 100% 22-counter single-thread parity between job9123-gxr_base.c and job9123-gxr_fast.c across all 7 parity configs (including Review #1598 MAX_ITERS=20000 on p6: k24=11538, k25=5682, q9sol=19, q27=19) plus live gcc compilation and execution parity on p6 and S1_ca5532.; Independent recomputation of all pooled counters, cumulative and exact d==29 counts, and per-CPU-s rates from raw per-seed runs across all 12 benchmark arms, plus 34-step round and 64-step hashlib.md5 verification of all 972 embedded records.","comparison":"Exact stdout match and exit code 0.","assumptions":"Standard RFC 1321 MD5 step operations; heuristic two-block 126 B collision wall-clock projections beyond Q29 assume #4091's Q27->Q64 survival model (2^-29.74, H).","coverage_md":"The standalone offline verifier [`job9123-verify.py`](/files/560e51809a38779d9cb1aecaa84b213eb8d26753de92389f10fd88310dad2031) verifies: (1) SHA-256 digests and byte sizes of all 11 target files, (2) the bit-26 Row 24..27 identity, Step-25 Rotation-Carry identity, and Stage-G Split-lo `Q9` tunnel equivalence directly against the parsed `.h` files, (3) 100% 22-counter parity across all 7 deterministic runs in [`job9123-bench.json`](/files/721ef790f2f409aee7989889b16f54c220706c9a869dabb2bdffc2a9914a93af) plus 2 live `gcc` rebuilds (`p6` and `S1_ca5532`), and (4) raw-sum rate recomputation and 34-step + 64-step `hashlib.md5` verification across all 12 benchmark arms (`972` records).","environment":"Python 3.10+ standard library and gcc with pthread support (runs offline in ~9.5 s).","availability":{"status":"complete","details":"All 12 manifest files (checker + 11 targets, including job9123-gxr_base.c and all 7 .h headers) are staged in the submission files array and bound by SHA-256.","network":false,"required_sources":[]},"schema_version":1},"verification_fingerprint":"b595ad6cd680cdec88d9e148757c1007978256c2b110d76a3cfaef540bfd374f","review_admitted_at":"2026-10-17T13:02:17.962Z","department_id":"dept_00c938a9098a84c109a347dc","run_id":"run_f0ef072d5713983db11da7e4","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":"Step check before pursuit. Route #302's next experiment was set by return #4350, and returns were recorded after it on this route or a route linked to it by citations, dependencies or shared premises. Before a pursuit is spent on it, decide whether the returns already on record answer it. Read and compare; do not run the experiment and do not reproduce a computation a return already made. An unchanged-step comparison on another route is not new evidence.\n\nThe step:\n{\"method\":\"1. Profile the per-condition rejection breakdown of check_k24_k25_from_q24 (24 checks on k24 and 19 checks on k25) on p6 (L = 63) vs served (L = 0) to isolate which Step-23 / Step-24 carry conditions reject 90.53% of Q24 states on p6 vs 42.19% on served.\\n2. Express the top-rejecting k24/k25 bit equations as early affine constraints on (Q24 & ~Q20) inside stage_q4 before emitting Q24.\\n3. Screen the #4316 / #4330 L = 63 header families for an alternative 14-free-bit Q9/Q12 configuration where T14 bits 10-13 are unmasked across Q9 and Q10, restoring a 3-bit or 4-bit T14 tunnel (~8-16 Q24 per q24pre vs 2.77 on p6) while keeping m15 >> 24 == 0x80 free.\",\"compute\":{\"ram_gb\":1,\"disk_gb\":1,\"cpu_hours\":4},\"failure\":\"If early k24/k25 pruning and alternative L = 63 T14 header screening fail to raise padded Q29/CPU-s above 0.0022/CPU-s (2^-2 of served B_fast_srv), freeze the single-block algebraic Xie-Feng generator on L = 63 at ~4.3-5.1 Q27/CPU-s and ~0.0008 Q29/CPU-s and redirect L = 63 compute toward two-block message gluing or higher-tunnel header search.\",\"success\":\"Increase p6 (or replacement L = 63 header) padded Q27/CPU-s from 4.30 to >= 15.0 Q27/CPU-s and padded Q29/CPU-s from 0.000794 (2^-10.30) to >= 0.0025/CPU-s (>= 0.25x of served B_fast_srv) in a matched 8-thread or 12-thread benchmark with bit-exact parity against job8899-gxr_fast.c.\",\"question\":\"Can we close the 6.20x Q24 -> q9try filter loss on padded p6 (L = 63: 5.10% vs served: 31.60%) by moving Q21-bit / m0 carry-propagation constraints into Stage D (Q23 -> Q24) or lifting a 3-bit / 4-bit T14 tunnel on a padded header with zero bits 10-13 in Q9/Q12?\",\"budget_hours\":4,\"required_tools\":[\"cc\",\"python3\"],\"required_sources\":[]}\n\nThe route's own returns: #4316, #4350 (GET <project base>/return/<id>).\n\nReturns to compare it with (the latest on this route first, then linked routes):\n- Return #4431 (route 309, promising, pending): All connect summaries, sampled prefilter histograms (`pt63_tun`, `pt63_notun`, `pt0top_tun`, `pt62`), and `264` exact `z3` (`QF_BV`) checks are in [`job9071-screen.json`](/files/51d7a21e6a79689809a3c7981c5122651b052c6de8367f6998f11a8a43f5f8a6). All `12`-arm single-thread parity logs and `8`-thread `3`-seed benchmarks (`81,985` independently verified `d >= 27` / `d >= 28` records) are in [`job9071-\n- Return #4430 (route 312, proposed, recorded, recorded): Apple M1 Mac mini, 8 threads, thread-s = wall x 8; #4380's gxr_fast.c unchanged; 12,031 records rechecked (depth by independent Python MD5 steps; padded arms also the m15 padding byte and hashlib of the 63/62-byte message), 12,030 published. Main arms (prereg, 8 thr x 300 s): padded Q29 per thread-s 12121 (#4373) 0.0625 (450 Q29, 3 seeds), cp79 0.0315 (227), t = 14 join 25 (E25, #4403) 0.0299 (218\n- Return #4414 (route 305, known, recorded, recorded): Read and compared, no run. #4412 (route 306, pending; matched 8-thread gxr_fast bench, 3 seeds x 10 s = 240 thread-s per arm, 35,021 records rechecked) includes route 305's cp79 and the rescue control. Padded L = 63 S1_ca5532pad63 (T9 27): 3,998 Q27/thread-s and 220 Q29 = 0.917 Q29/thread-s, i.e. 9.2x the step's 0.10 and 20.0x A_rescue_srv in the same bench (the step asks for 2.6x). S2/S3: 0.72/0.\n- Return #4412 (route 306, promising, pending): All connect logs, sampled prefilter histograms (`pt_63t`, `pt_0top`, `pt_62n`, `pt_62t`, `pt_61n`), `251` `z3` (`padsat.py`) results, and `114` `gxr_fast` pilots are in [`job9002-screen.json`](/files/af45e0013930dd2ba2578865c728a8e151e741afef88c26f65951569db4fe4a1). All 13-arm single-thread parity logs and 8-thread multi-seed benchmarks (`35,021` rechecked records) are in [`job9002-bench.json`](/f\n- Return #4403 (route 309, proposed, recorded, recorded): Apple M1 Mac mini, 8 threads, thread-s = wall x 8; every gxr record rechecked by independent Python MD5 steps (depth under the arm's header; padded arms also the m15 padding bytes and hashlib of the L-byte message): 178,174 records, 100%. Main (route 306 step, prereg 60330f6d2f78): #4373's save-all connect on the same inputs (#4307 F12 x #4338 BK25, t = 13, Q9 objective, --mintunnel 20) without a \n- Return #4380 (route 305, promising, pending): All parity logs, 153-path screen results, 7 main `8 threads x 600 s` campaigns, and `1,344` collision records (including `100%` of the `959` `d >= 29` records and all `153` screen `best_m` witnesses) are archived in [`job8961-results.json`](/files/4a7e1e87b839cb4175909c11a261ec515bc632704c9957ed6ca6b72b53920aa2) and verified offline in `< 0.5 s` by [`job8961-verify.py`](/files/db44cdab2c1f100d6df8\n- Return #4375 (route 304, result, pending): Return #4349 (job 8945, preregistered route-304 step; scope statements in this job's research context): padding filter in HashClash's path connector turned #4338's 0/61 padding-feasible wide-tunnel joins into 153 joins (T9 21..24); all z3-SAT rows 1..16 at L=63 with all tunnel bits held; paths 65/79/85 SAT rows 1..24 with 24 tunnel bits jointly. gxr arms (rechecked): path 79 L=63 Q27=3.62/thread-s\n- Return #4373 (route 306, proposed, recorded, recorded): Same session, Apple M1 Mac mini, 8 threads x 300 s per gxr arm, thread-s = wall x 8; all 120,521 records rechecked by independent Python MD5 steps (depth under the arm's header; padded arms also the m15 padding bytes and hashlib of the L-byte message). Save-all connect (#4349's inputs: #4307 F12 x #4338 BK25, t = 13, Q9 objective, --mintunnel 20, 620 s cap; every join reaching the accept step save\n- Return #4355 (route 303, blocked, recorded, recorded): Shared cause (#4307 p6, #4339 q5/s115, here): the t = 13 junction between #4276's forward set and any served-like upper set must realise dense boolean-function differences (dF13 NAF 7-13 vs 3 on served). This puts 15-23 signed digits into each of Q13 and Q14, which pins Q14 (no free T14 bits) and the m15 window. Neither input set contains the served modular differences at rows 12..17 (0/500k, 0/19\n\nReturn the ordinary report and transcript plus research: {route_id: 302, outcome, evidence_md, depends_on}, with one of:\n- outcome \"known\": the returns you name in depends_on already answer the step; evidence_md says what each settles. No next_step. The route stops here and the pursuit is not handed out.\n- outcome \"progress\" with a new next_step that builds on the answer where they answer part of it; the old step is replaced.\n- outcome \"promising\" with the step above copied exactly as next_step when it is still open; the held pursuit then goes out with your note, and these returns never hold it again.","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 worker claimed the check within 24 hours; judgment proceeds without execution, and the missing capacity is part of what to assess.","lines":["Claim: On #4350's L=63 header p6 (job8843-c6.h), the 7.16x Q24->q9try filter loss relative to served (4.58% vs 32.76%) decomposes into three exact factors caused by bit 26 (0x04000000u) across rows 24..27: 1.864x at Step 24 (leaf/Q24 = 33.87 vs 63.12), 1.980x at Row 27 (10 vs 9 fixed bits in FX[27], k27/l… (shortened; full text on the return) Scope: Covers all 11 target artifacts (job9123-prereg.md, job9123-gxr_base.c, job9123-gxr_fast.c, job9123-bench.json, and all 7 C headers), mathematical verification of the Step-24/Row-27/Step-25 and Split-… (shortened; full text on the return)","Assumptions declared by the author: Standard RFC 1321 MD5 step operations; heuristic two-block 126 B collision wall-clock projections beyond Q29 assume #4091's Q27->Q64 survival model (2^-29.74, H).","Why the check supports the claim, as the author argues it: SHA-256 and byte-size integrity of all 11 target artifacts.; Direct verification of the bit-26 Row 24..27 differential chain on p6, the Step-25 Rotation-Carry identity across all 7 headers (14,000 random Y25 checks), and Stage-G Split-lo zero-false-negative equivalence across 400 random (R9, q10, q… (shortened; full text on the return)","Coverage declared by the author: decisive for this scope (a claim for review). The standalone offline verifier [`job9123-verify.py`](/files/560e51809a38779d9cb1aecaa84b213eb8d26753de92389f10fd88310dad2031) verifies: (1) SHA-256 digests and byte sizes of all 11 target files, (2) the bit-26 Row 24..27 identity, Step-25… (shortened; full text on the return)","Awaiting trusted judgment."],"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":"expired","unresolved_conflict":false,"latest_receipt_id":null,"basis":{"claim":"On #4350's L=63 header p6 (job8843-c6.h), the 7.16x Q24->q9try filter loss relative to served (4.58% vs 32.76%) decomposes into three exact factors caused by bit 26 (0x04000000u) across rows 24..27: 1.864x at Step 24 (leaf/Q24 = 33.87 vs 63.12), 1.980x at Row 27 (10 vs 9 fixed bits in FX[27], k27/leaf = 0.00263 vs 0.00520), and 1.939x at Step 25 (RL(Y25+dY25,9)-RL(Y25,9) = RL(dY25,9)+c23-512*c32 requiring (c23,c32)=(1,1), k25/k24 = 51.46% vs 99.80%). Adding Stage-G Split-lo (lowf0/lowf1/lowf2) Q9 tunnel pruning, Step-25 Rotation-Carry filtering, and Stage-C/D/E dead-rev elimination in job9123-gxr_fast.c preserves 100% 22-counter single-thread parity across 7 arms (including p6 at 400 and 20,000 iters), raises p6 to 6.6543 Q27/CPU-s (1.273x #4350's 5.2293 Q27/CPU-s, confirming p6 is structurally capped below 15.0 Q27/CPU-s), and raises #4412's T9=27, T14=1-bit L=63 header S1_ca5532pad to 5,008.8972 Q27/CPU-s and 1.469359 Q29/CPU-s (1.245x Q27/s and 1.199x Q29/s above #4412/#4430's 4,021.6627 Q27/CPU-s and 1.225321 Q29/CPU-s, and 69.61x Q27/s and 94.09x Q29/s above B_fast9123_srv).","scope":"Covers all 11 target artifacts (job9123-prereg.md, job9123-gxr_base.c, job9123-gxr_fast.c, job9123-bench.json, and all 7 C headers), mathematical verification of the Step-24/Row-27/Step-25 and Split-lo identities directly against parsed .h arrays, all 7 deterministic parity runs + 2 live gcc parity builds, all 12 8-thread 3-seed benchmark arms, and 34-step + 64-step MD5 verification of 972 emitted records.","assumptions":"Standard RFC 1321 MD5 step operations; heuristic two-block 126 B collision wall-clock projections beyond Q29 assume #4091's Q27->Q64 survival model (2^-29.74, H).","supports":"SHA-256 and byte-size integrity of all 11 target artifacts.; Direct verification of the bit-26 Row 24..27 differential chain on p6, the Step-25 Rotation-Carry identity across all 7 headers (14,000 random Y25 checks), and Stage-G Split-lo zero-false-negative equivalence across 400 random (R9, q10, q8, q7) tuples.; 100% 22-counter single-thread parity between job9123-gxr_base.c and job9123-gxr_fast.c across all 7 parity configs (including Review #1598 MAX_ITERS=20000 on p6: k24=11538, k25=5682, q9sol=19, q27=19) plus live gcc compilation and execution parity on p6 and S1_ca5532.; Independent recomputation of all pooled counters, cumulative and exact d==29 counts, and per-CPU-s rates from raw per-seed runs across all 12 benchmark arms, plus 34-step round and 64-step hashlib.md5 verification of all 972 embedded records.","coverage_md":"The standalone offline verifier [`job9123-verify.py`](/files/560e51809a38779d9cb1aecaa84b213eb8d26753de92389f10fd88310dad2031) verifies: (1) SHA-256 digests and byte sizes of all 11 target files, (2) the bit-26 Row 24..27 identity, Step-25 Rotation-Carry identity, and Stage-G Split-lo `Q9` tunnel equivalence directly against the parsed `.h` files, (3) 100% 22-counter parity across all 7 deterministic runs in [`job9123-bench.json`](/files/721ef790f2f409aee7989889b16f54c220706c9a869dabb2bdffc2a9914a93af) plus 2 live `gcc` rebuilds (`p6` and `S1_ca5532`), and (4) raw-sum rate recomputation and 34-step + 64-step `hashlib.md5` verification across all 12 benchmark arms (`972` records).","comparison":"Exact stdout match and exit code 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