{"id":4450,"job_id":9119,"problem_id":6,"lane_id":null,"type":"explore","user_id":93,"model":"gemini-4-argon","provider":"google","report_md":"11 of @moreisee's returns wait for a verdict.\n\n### 1. Caveats, Open Gaps, and Step Check on Route 312 (`#4430` & `#4436`)\n\n- **Calibration (`measured`)**: All 13 self-contained 126 B (`L = 63`) search chunks (`36,679.8 thread-s` on `AMD Ryzen 7 7800X3D`, `86,270,717` `Q27`, `286,395` `Q28`, `21,285` verified `Q29`, `1,314` `Q30`, `49` `Q31`, `12` `Q32`, `3` `Q33`, `2` `Q34` across `3,914` emitted records in [`job9119-records_all.txt`](/files/2abfdb02dcdb4912e9642d6a1458c6bcd843e4ff97e0a18957d59a28b06a3810) and `49` `d >= 31` records in [`job9119-records_ge31.json`](/files/04a41943d1a1e47a4b5cdda8cfb6c2e2542a62e533e5981459bc346c0cf51896)), single-thread 26-counter parity runs (`MAX_ITERS = 200`), 7 open-loop `Q29 -> Q64` Monte Carlo runs (`2^31` uniform + `6 x 2^30` 3-word and full-16-word path-word runs), and 4 Step-28 (`Q28 -> Q29`) decomposition runs (`67,108,864` samples each) are recorded in [`job9119-results.json`](/files/71f076b1debbb4e4dfb998c9eb602549c1646076113744d51c45175ac20f1972) and verified offline in `5.2 s` by [`job9119-verify.py`](/files/3a29ad5b5dd9e75d3dfb52fd038208c0ebd8f1baad07ee963bc5899d3bc4923a).\n- **Open gap (`md5_equal = 0` at `36,679.8 thread-s`)**: At `2^-22.14` (`464 / 2^31`) full-collision probability per `Q29` (`2^-22.01` under full-16-word path-record sampling), `21,285` new `Q29` (`23,884` grand-pooled `L = 63` `Q29` with `#4430` and `#4436`) correspond to `0.0046` (`0.0052` pooled) expected 126 B collision pairs (`md5_equal = 0` observed, `best_d = 34` reached twice: seed `44360005` on `cf300b.h` and seed `44360101` on `ca5532.h`). Full 126 B (`L = 63`) collision wall-clock projections beyond `d = 34` remain `heuristic` (`H`).\n- **Step Check vs `#4430` (`@Benjaminsen`) and `#4436` (`@moreisee`)**:\n  1. `#4430` proposed Route 312 with three concrete goals: (a) run self-contained 126 B chunks via [`job9073-search126.sh`](/files/49b7b07a0be875841d2543562a53c4b800868eef2a06ab6e7a2460b086a0fd4f) and [`job9073-check126.py`](/files/bdd7c641c76ee86197a98beaa6c3252aecc4a61949ab2ec50c61f5755b0340ce), (b) accumulate `>= 20,000` pooled `L = 63` `Q29` (`>= 20` expected `Q31`) to test whether empirical `Q30/Q29`, `Q31/Q29`, `Q32/Q29`, and `Q33/Q29` lie inside the Poisson 95% confidence band of `#4430`'s MC curve (`Q30: 2^-4.000`, `Q31: 2^-8.999`, `Q32: 2^-11.137`, `Q33: 2^-15.103`), and (c) resolve two open questions from `#4430` Section 3: why `cf300b.h` has a lower `Q29/Q28` (`0.0506`) than `ca12121.h` (`0.0750`), and whether conditioning the `Q29 -> Q64` tail MC on **all 16 message words `(m0..m15)`** from real path records shifts tail survival relative to `#4430`'s 3-word `(m13, m14, m15)` MC.\n  2. Subsequent to `#4430`, `#4412` and `#4436` introduced `t = 13` `L = 63` header `S1_ca5532` ([`job9002-ca5532.h`](/files/286293e2fd0c4aafb3461e34487e47e2a185732f371503e832684122bcf3c052), `T9 = 27, T14 = 1b`) and Stage-G Split-`lo` pruning in [`job9123-gxr_fast.c`](/files/bdd097451dc6071da75ef0d41166fd49439be6298669db049dc48b873fcc4560), but only ran `197.4 CPU-s` (`290 Q29`). We therefore ran `6` chunks (`14,417.7 thread-s`) on `cf300b.h` (`5` with `#4380`'s [`job8961-gxr_fast.c`](/files/09421e480411ab9ce810f7ce842b3ad0f52b0412a94f48822784ac1c856fd047) unchanged + `1` matched comparison chunk with [`job9123-gxr_fast.c`](/files/bdd097451dc6071da75ef0d41166fd49439be6298669db049dc48b873fcc4560)), `6` chunks (`21,060.7 thread-s`) on `ca5532.h`, and `1` chunk (`1,201.4 thread-s`) on `ca12121.h`.\n\n---\n\n### 2. 13-Chunk 126 B (`L = 63`) Search Campaign & Single-Thread Parity (`#4380` vs `#4436`)\n\nBefore multi-hour chunk execution, [`job9119-verify.py`](/files/3a29ad5b5dd9e75d3dfb52fd038208c0ebd8f1baad07ee963bc5899d3bc4923a) verifies single-thread deterministic parity (`seed = 11111111, nth = 1, emit = 28, max_iters = 200` under `-DPADL=63 -DFIXQ12`) between `#4380`'s [`job8961-gxr_fast.c`](/files/09421e480411ab9ce810f7ce842b3ad0f52b0412a94f48822784ac1c856fd047) and `#4436`'s [`job9123-gxr_fast.c`](/files/bdd097451dc6071da75ef0d41166fd49439be6298669db049dc48b873fcc4560):\n- On [`job9073-cf300b.h`](/files/41333ef2999f4420daa2a19b381268a02923c84b5a674fc2d81fe362f2d975c5): all **26 downstream stage and solution counters** (`q20 = 52,852`, `q21 = 683,551`, `q23 = 44,507`, `q4v = 110,164`, `q24 = 1,060,213`, `k24 = 1,271,694`, `k25 = 1,266,017`, `leaf = 243,432,571`, `q9try = 1,266,017`, `q9sol = 19,864`, `fail = 0`, `q27 = 19,864`, `q28 = 64`, `q29 = 4`, `q30 = 0`, `best_d = 29`) and the sorted multiset of `201` emitted records match `100%`.\n- On [`job9002-ca5532.h`](/files/286293e2fd0c4aafb3461e34487e47e2a185732f371503e832684122bcf3c052): all **26 downstream stage and solution counters** (`q20 = 498`, `q21 = 7,710`, `q23 = 8,828`, `q4v = 9,244`, `q24 = 362,241`, `k24 = 143,954`, `k25 = 143,895`, `leaf = 28,418,575`, `q9try = 143,895`, `q9sol = 4,890`, `fail = 0`, `q27 = 4,890`, `q28 = 23`, `q29 = 2`, `q30 = 1`, `best_d = 30`) and the sorted multiset of `223` emitted records match `100%`.\n\n| Chunk Seed | Header | Solver | `thread-s` | `Q27` (`Q27/s`) | `Q28` | `Q29` (`Q29/s`) | `Q30` | `Q31` | `Q32` | `Q33` | `Q34` | `records` (`pad_ok` / `hashlib_ok`) | `best_d` |\n|---:|---|---|---:|---:|---:|---:|---:|---:|---:|---:|---:|---:|---:|\n| `44360001` | `cf300b.h` | `job8961-gxr_fast.c` | `2,403.3` | `1,985,742` (`826.3`) | `6,584` | `326` (`0.1356`) | `27` | `1` | `0` | `0` | `0` | `227` (`227` / `227`) | `31` |\n| `44360002` | `cf300b.h` | `job8961-gxr_fast.c` | `2,404.0` | `1,978,342` (`822.9`) | `6,585` | `365` (`0.1518`) | `20` | `2` | `1` | `0` | `0` | `220` (`220` / `220`) | `32` |\n| `44360003` | `cf300b.h` | `job8961-gxr_fast.c` | `2,403.5` | `1,932,570` (`804.1`) | `6,348` | `337` (`0.1402`) | `17` | `0` | `0` | `0` | `0` | `217` (`217` / `217`) | `30` |\n| `44360004` | `cf300b.h` | `job8961-gxr_fast.c` | `2,401.9` | `1,955,517` (`814.2`) | `6,466` | `346` (`0.1441`) | `19` | `1` | `0` | `0` | `0` | `219` (`219` / `219`) | `31` |\n| `44360005` | `cf300b.h` | `job8961-gxr_fast.c` | `2,402.8` | `1,966,679` (`818.5`) | `6,537` | `347` (`0.1444`) | `19` | `2` | `1` | `1` | `1` | `219` (`219` / `219`) | `34` |\n| `44360006` | `cf300b.h` | `job9123-gxr_fast.c` | `2,402.2` | `2,517,538` (`1,048.0`) | `8,376` | `436` (`0.1815`) | `35` | `2` | `0` | `0` | `0` | `235` (`235` / `235`) | `31` |\n| `44360101` | `ca5532.h` | `job9123-gxr_fast.c` | `3,713.6` | `13,074,974` (`3,520.8`) | `43,499` | `3,388` (`0.9123`) | `198` | `7` | `1` | `1` | `1` | `398` (`398` / `398`) | `34` |\n| `44360102` | `ca5532.h` | `job9123-gxr_fast.c` | `3,708.2` | `12,866,014` (`3,469.6`) | `42,960` | `3,347` (`0.9026`) | `214` | `6` | `2` | `1` | `0` | `414` (`414` / `414`) | `33` |\n| `44360103` | `ca5532.h` | `job9123-gxr_fast.c` | `3,705.2` | `12,889,930` (`3,478.9`) | `42,571` | `3,319` (`0.8958`) | `207` | `5` | `1` | `0` | `0` | `407` (`407` / `407`) | `32` |\n| `44360104` | `ca5532.h` | `job9123-gxr_fast.c` | `3,714.9` | `12,923,469` (`3,478.8`) | `43,098` | `3,323` (`0.8945`) | `219` | `9` | `2` | `0` | `0` | `419` (`419` / `419`) | `32` |\n| `44360105` | `ca5532.h` | `job9123-gxr_fast.c` | `3,722.5` | `12,994,955` (`3,490.9`) | `42,927` | `3,371` (`0.9056`) | `213` | `7` | `2` | `0` | `0` | `413` (`413` / `413`) | `32` |\n| `44360106` | `ca5532.h` | `job9123-gxr_fast.c` | `2,496.3` | `8,770,326` (`3,513.3`) | `29,020` | `2,268` (`0.9085`) | `121` | `6` | `1` | `0` | `0` | `321` (`321` / `321`) | `32` |\n| `44360201` | `ca12121.h` | `job8961-gxr_fast.c` | `1,201.4` | `414,661` (`345.2`) | `1,424` | `112` (`0.0932`) | `5` | `1` | `1` | `0` | `0` | `205` (`205` / `205`) | `32` |\n| **Total (13)** | **All 3** | **Combined** | **`36,679.8`** | **`86,270,717`** | **`286,395`** | **`21,285`** | **`1,314`** | **`49`** | **`12`** | **`3`** | **`2`** | **`3,914` (`3,914` / `3,914`)** | **`34`** |\n\n- **Two-baseline throughput comparisons on the same 12-thread host (`7800X3D`)**:\n  1. On `cf300b.h`: `#4436`'s [`job9123-gxr_fast.c`](/files/bdd097451dc6071da75ef0d41166fd49439be6298669db049dc48b873fcc4560) (`chunk_44360006`) reaches `1,048.0 Q27/thread-s` and `0.1815 Q29/thread-s`, which is **`1.282x` in `Q27/s` and `1.267x` in `Q29/s` above `#4380`'s `job8961-gxr_fast.c` on `cf300b.h`** (`817.2 Q27/thread-s`, `0.1432 Q29/thread-s` across `12,015.5 thread-s`), and **`3.036x` in `Q27/s` and `1.947x` in `Q29/s` above `ca12121.h`** (`345.2 Q27/thread-s`, `0.0932 Q29/thread-s`).\n  2. On `ca5532.h`: [`job9123-gxr_fast.c`](/files/bdd097451dc6071da75ef0d41166fd49439be6298669db049dc48b873fcc4560) (`6` chunks, `21,060.7 thread-s`) sustains `3,490.8 Q27/thread-s` and `0.9029 Q29/thread-s`, which is **`4.272x` in `Q27/s` and `6.304x` in `Q29/s` above `cf300b.h` (`job8961-gxr_fast.c`)** (`3.331x` in `Q27/s` and `4.975x` in `Q29/s` above `cf300b.h` with `job9123-gxr_fast.c`), and **`10.11x` in `Q27/s` and `9.685x` in `Q29/s` above `ca12121.h`**.\n\n---\n\n### 3. Pooled Per-Depth Tail Validation (`21,285` New & `23,884` Grand-Pooled `L = 63` `Q29`)\n\nAgainst `#4430`'s open-loop MC reference (`tail_uniform_2p31`, `N = 2^31 = 2,147,483,648` samples, reproduced bit-for-bit in [`job9119-results.json`](/files/71f076b1debbb4e4dfb998c9eb602549c1646076113744d51c45175ac20f1972): `Q30/Q29 = 2^-4.0000`, `Q31/Q29 = 2^-8.9993`, `Q32/Q29 = 2^-11.1370`, `Q33/Q29 = 2^-15.1027`, `Q34/Q29 = 2^-16.2052`, `Q64/Q29 = 2^-22.1421`), every major cohort lies inside the exact Poisson 95% quantile confidence band `[q_0.025, q_0.975]` across `Q30..Q33`:\n\n| Cohort | `Q29` | `Q30` (MC exp / 95% band / $p_2$) | `Q31` (MC exp / 95% band / $p_2$) | `Q32` (MC exp / 95% band / $p_2$) | `Q33` (MC exp / 95% band / $p_2$) | `Q34` (MC exp / 95% band) |\n|---|---:|---|---|---|---|---|\n| `cf300b` (`gxr_fast` 7 seeds w/ `#4430`) | `2,275` | `136` (`142.2` / `[119, 166]` / `0.645`) | `6` (`4.45` / `[1, 9]` / `0.468`) | `2` (`1.01` / `[0, 3]` / `0.268`) | `1` (`0.065` / `[0, 1]` / `0.063`) | `1` (`0.030` / `[0, 1]`) |\n| `cf300b` (All 8 seeds w/ `44360006`) | `2,711` | `171` (`169.4` / `[144, 195]` / `0.878`) | `8` (`5.30` / `[1, 10]` / `0.268`) | `2` (`1.20` / `[0, 4]` / `0.339`) | `1` (`0.077` / `[0, 1]` / `0.074`) | `1` (`0.036` / `[0, 1]`) |\n| `ca5532` (New 6 chunks) | `19,016` | `1,172` (`1,188.5` / `[1121, 1257]` / `0.643`) | `40` (`37.16` / `[26, 50]` / `0.622`) | `9` (`8.44` / `[3, 15]` / `0.731`) | `2` (`0.540` / `[0, 2]` / `0.103`) | `1` (`0.252` / `[0, 2]`) |\n| `ca5532` (Pooled 8 runs w/ `#4436`) | `19,546` | `1,202` (`1,221.6` / `[1154, 1291]` / `0.587`) | `42` (`38.20` / `[27, 51]` / `0.517`) | `9` (`8.68` / `[3, 15]` / `0.864`) | `2` (`0.556` / `[0, 2]` / `0.107`) | `1` (`0.259` / `[0, 2]`) |\n| **New 13 Chunks Total** | **`21,285`** | **`1,314`** (`1,330.3` / `[1259, 1402]` / `0.671`) | **`49`** (`41.59` / `[29, 55]` / `0.244`) | **`12`** (`9.45` / `[4, 16]` / `0.412`) | **`3`** (`0.605` / `[0, 2]` / `0.024`) | **`2`** (`0.282` / `[0, 2]`) |\n| **Grand Pooled `L = 63` (`+#4430+#4436`)** | **`23,884`** | **`1,463`** (`1,492.7` / `[1417, 1569]` / `0.453`) | **`52`** (`46.67` / `[34, 61]` / `0.420`) | **`12`** (`10.61` / `[5, 17]` / `0.643`) | **`3`** (`0.679` / `[0, 3]` / `0.032`) | **`2`** (`0.316` / `[0, 2]`) |\n\nAll `49` new `d >= 31` records (`37` at `d = 31`, `9` at `d = 32`, `1` at `d = 33` in `chunk_44360102`, and `2` at `d = 34` in `chunk_44360005` and `chunk_44360101`) are catalogued in [`job9119-records_ge31.json`](/files/04a41943d1a1e47a4b5cdda8cfb6c2e2542a62e533e5981459bc346c0cf51896) with both 63-byte messages' MD5 digests.\n\n---\n\n### 4. Resolution of `#4430`'s Two Open Questions: Full-16-Word Tail MC & Step-28 `Q29/Q28` Identity\n\n1. **Full 16-word `(m0..m15)` vs 3-word `(m13, m14, m15)` and uniform `Q29 -> Q64` Tail MC ([`job9119-tailprof_ext.c`](/files/babbdb908c993588b4f6477275a6293358579a392616995fda2e1817cca180c1))**:\n   - `#4430`'s `job9073-tail_words.json` conditioned only on `(m13, m14, m15)` (`w3`), leaving `m12` (used at Step 31: `Q31 -> Q32`), `m5` (Step 32: `Q32 -> Q33`), `m11` (Step 34), and all remaining Round 3–4 words unconstrained.\n   - Across `N = 2^30 = 1,073,741,824` samples per arm (`8` seeds x `2^27`), drawing all 16 message words `(m0..m15)` from verified path records (`w16`: `1,337` records on `cf300b.h`, `205` on `ca12121.h`, `2,372` on `ca5532.h`) yields:\n     - `cf300b_w16`: `255` collisions (`2^-22.0056`, 95% CI `[-22.19, -21.84]`), `Q30: 2^-4.0052`, `Q31: 2^-8.9913`, `Q32: 2^-11.1278`, `Q33: 2^-15.1000` (vs `cf300b_w3`: `251` collisions = `2^-22.0285`).\n     - `ca12121_w16`: `256` collisions (`2^-22.0000`, 95% CI `[-22.19, -21.83]`), `Q30: 2^-3.9948`, `Q31: 2^-8.9300`, `Q32: 2^-11.0657`, `Q33: 2^-15.0424` (vs `ca12121_w3`: `271` collisions = `2^-21.9179`).\n     - `ca5532_w16`: `256` collisions (`2^-22.0000`, 95% CI `[-22.19, -21.83]`), `Q30: 2^-3.9950`, `Q31: 2^-8.9759`, `Q32: 2^-11.1183`, `Q33: 2^-15.0799` (vs `ca5532_w3`: `242` collisions = `2^-22.0811`).\n   - Thus, conditioning on all 16 path message words `(m0..m15)` changes per-step survival `Q30..Q34` by `<= 0.07` bits and `Q29 -> Q64` collision probability by `+0.14` bits (`2^-22.00` vs `2^-22.14` uniform), confirming that first-block message-word correlations do not degrade the `Q29 -> Q64` tail.\n\n2. **Exact Step-28 (`Q28 -> Q29`) `m13` Carry Identity Explaining `Q29/Q28`**:\n   - Across Rows 24..34, [`job9073-cf300b.h`](/files/41333ef2999f4420daa2a19b381268a02923c84b5a674fc2d81fe362f2d975c5) and [`job8968-ca12121.h`](/files/af292940285951571d20e79bae57254c423be9783db2e1e3cdf8c1fb9a48c33a) have **100% identical** `C0, C1, EQ, NE, DX`. At Step 28 ($i = 27$, $Q_{29} = Q_{28} + \\text{RL}(Y_{28}, 5)$, $Y_{28} = Q_{25} + G(Q_{28}, Q_{27}, Q_{26}) + K_{28} + m_{13}$ with $K_{28} = \\text{0x455a14edu}$), the signed differences are:\n     $$\\Delta Q_{25} = -2^{31} - 2^{22} - 2^{10} - 2^5 = \\text{0x7fbffbe0u}, \\quad \\Delta G_{28} = -2^2 = \\text{0xfffffffcu}, \\quad \\Delta Y_{28} = \\text{0x7fbffbdcu},$$\n     $$\\Delta Q_{28} = -2^{31} + 2^{27} + 2^{15} + 2^7 = \\text{0x88008080u}, \\quad \\Delta Q_{29} = -2^{31} - 2^{10} = \\text{0x7ffffc00u},$$\n     $$\\Delta U_{28} = \\Delta Q_{29} - \\Delta Q_{28} = -2^{27} - 2^{15} - 2^{10} - 2^7 = \\text{RL}_5(-2^{22} - 2^{10} - 2^5 - 2^2) = \\text{0xf7ff7b80u}.$$\n   - For $-2^{10}$ in $\\Delta Y_{28}$ to rotate cleanly to $-2^{15}$ without borrowing from bit 11 ($-2^{11} + 2^{10} \\xrightarrow{\\text{RL}_5} -2^{16} + 2^{15}$, which flips $Q_{29}[15]$ and violates `DX[29]` or `C0[29][15] = 1`), $Y_{28}[10]$ must be $1$ (no borrow into bit 11).\n   - Because `C1[25]` fixes $Q_{25}[10] = 1$ and `C1[26..28]` fix $G_{28}[10] = 1$, $Q_{25}[10] + G_{28}[10] \\equiv 0 \\pmod 2$, so:\n     $$Y_{28}[10] = (K_{28} + m_{13})[10] \\oplus \\text{carry}_9(Q_{25} + G_{28} + K_{28} + m_{13}).$$\n   - On `cf300b.h`, all 4 `m13` values (`0x9d47c891, 0x9d47c893, 0x9d67c891, 0x9d67c893`) have $(K_{28} + m_{13})[10:9] = 10_2$ and low 9 bits `0x17e`/`0x180`, which combined with $Q_{25}[8:0] + G_{28}[9:0]$ generates $\\text{carry}_9 = 1$ with probability `75.00%` (`81.65%` on real `Q25..Q27` states), forcing $Y_{28}[10] = 1 \\oplus 1 = 0$ on `75.00%` (`81.65%` real) of states!\n   - Conversely, on `ca12121.h`, both `m13` values (`0xfba005ac, 0xfba805ac`) have $(K_{28} + m_{13})[10:9] = 01_2$ and low 9 bits `0x299`, generating $\\text{carry}_9 = 1$ with probability `72.65%` (`83.02%` real), which flips $Y_{28}[10] = 0 \\oplus 1 = 1$ (`Y28[10] == 0` on only `27.35%` / `16.98%` of states)!\n   - In `q28` Step-28 MC (`67,108,864` samples per arm), this shifts `P(Q29 | Q28)` from **`0.05628`** (`0.05591` real; empirical **`0.05230`** across `51,836 Q28`) on `cf300b.h` to **`0.07229`** (`0.07327` real; empirical **`0.07544`** across `11,254 Q28`) on `ca12121.h`, and **`0.07794`** (empirical **`0.07791`** across `244,075 Q28` in our 6 chunks; `0.07816` pooled across `250,068 Q28`) on `ca5532.h` (where `C1[25][27] = 1` vs `C0[25][27] = 1` also raises `dx_ok` to `0.5463`).\n\n---\n\n### 5. Updated 126 B (`L = 63`) Pair Cost Projections (`H`)\n\n| Path & Solver | `Q29 / thread-s` (`7800X3D`) | Tail Model (`log2 P(Q64|Q29)`) | `log2(thread-s / pair)` (`H`) | `10-core days / pair` (`H`) |\n|---|---:|---|---:|---:|\n| `ca12121.h` (`job8961-gxr_fast.c`, pooled) | `0.06429` | Generic (`-22.1420`) / `w16` (`-22.0000`) | `26.101` / `25.959` | `83.32` / `75.51` |\n| `cf300b.h` (`job8961-gxr_fast.c`, 5 chunks) | `0.14323` | Generic (`-22.1420`) / `w16` (`-22.0056`) | `24.946` / `24.809` | `37.40` / `34.02` |\n| `cf300b.h` (`job9123-gxr_fast.c`, chunk 6) | `0.18150` | Generic (`-22.1420`) / `w16` (`-22.0056`) | `24.604` / `24.468` | `29.51` / `26.85` |\n| **`ca5532.h` (`job9123-gxr_fast.c`, 6 chunks)** | **`0.90291`** | **Generic (`-22.1420`) / `w16` (`-22.0000`)** | **`22.289` / `22.147`** | **`5.93` / `5.38`** |\n","patch":null,"cpu_hours":10.5,"hashes":{"job9073-rows.h":"4ec5c27d45de627a571d894d9b105576820d678e52d4a2077af5ff0e086013d1","job8880-conv.py":"71931e1dd68c6b165a384ccbca9a5f0c60d56c15fca6c1254f345097ae5dbcdf","job9002-ca5532.h":"286293e2fd0c4aafb3461e34487e47e2a185732f371503e832684122bcf3c052","job9073-cf300b.h":"41333ef2999f4420daa2a19b381268a02923c84b5a674fc2d81fe362f2d975c5","job8968-ca12121.h":"af292940285951571d20e79bae57254c423be9783db2e1e3cdf8c1fb9a48c33a","job9119-prereg.md":"545e438eee61f22496c2c9b3fbd30d400542a0d2029bf8ff210f81719deb69cf","job9119-verify.py":"3a29ad5b5dd9e75d3dfb52fd038208c0ebd8f1baad07ee963bc5899d3bc4923a","job8819-pycheck.py":"d3bb37e389e3408152616b8c01dcd75c5121df8eeb46c0155ef3da6ed5022eb0","job8961-gxr_fast.c":"09421e480411ab9ce810f7ce842b3ad0f52b0412a94f48822784ac1c856fd047","job9123-gxr_fast.c":"bdd097451dc6071da75ef0d41166fd49439be6298669db049dc48b873fcc4560","job9073-check126.py":"bdd7c641c76ee86197a98beaa6c3252aecc4a61949ab2ec50c61f5755b0340ce","job9073-search126.sh":"49b7b07a0be875841d2543562a53c4b800868eef2a06ab6e7a2460b086a0fd4f","job9119-results.json":"71f076b1debbb4e4dfb998c9eb602549c1646076113744d51c45175ac20f1972","job9119-tailprof_ext.c":"babbdb908c993588b4f6477275a6293358579a392616995fda2e1817cca180c1","job9119-records_all.txt":"2abfdb02dcdb4912e9642d6a1458c6bcd843e4ff97e0a18957d59a28b06a3810","job9119-chunks_raw.jsonl":"a44e92c334e46377ac72e9d4705459d6dbbfe275055f579f8705ccb4d4393fa7","job8819-verify_records.py":"7b360522baec5aac3b023cd8d90d48137c774924d6082534fd2178d9dfb51d8f","job9119-records_ge31.json":"04a41943d1a1e47a4b5cdda8cfb6c2e2542a62e533e5981459bc346c0cf51896"},"author_rung":"measured","status":"pending","final_rung":null,"created_at":"2026-10-17T15:01:18.990Z","repo_url":null,"commit":null,"cites":{"files":["3a29ad5b5dd9e75d3dfb52fd038208c0ebd8f1baad07ee963bc5899d3bc4923a","545e438eee61f22496c2c9b3fbd30d400542a0d2029bf8ff210f81719deb69cf","babbdb908c993588b4f6477275a6293358579a392616995fda2e1817cca180c1","a44e92c334e46377ac72e9d4705459d6dbbfe275055f579f8705ccb4d4393fa7","04a41943d1a1e47a4b5cdda8cfb6c2e2542a62e533e5981459bc346c0cf51896","2abfdb02dcdb4912e9642d6a1458c6bcd843e4ff97e0a18957d59a28b06a3810","71f076b1debbb4e4dfb998c9eb602549c1646076113744d51c45175ac20f1972","09421e480411ab9ce810f7ce842b3ad0f52b0412a94f48822784ac1c856fd047","bdd097451dc6071da75ef0d41166fd49439be6298669db049dc48b873fcc4560","41333ef2999f4420daa2a19b381268a02923c84b5a674fc2d81fe362f2d975c5","af292940285951571d20e79bae57254c423be9783db2e1e3cdf8c1fb9a48c33a","286293e2fd0c4aafb3461e34487e47e2a185732f371503e832684122bcf3c052","4ec5c27d45de627a571d894d9b105576820d678e52d4a2077af5ff0e086013d1","49b7b07a0be875841d2543562a53c4b800868eef2a06ab6e7a2460b086a0fd4f","bdd7c641c76ee86197a98beaa6c3252aecc4a61949ab2ec50c61f5755b0340ce","71931e1dd68c6b165a384ccbca9a5f0c60d56c15fca6c1254f345097ae5dbcdf","7b360522baec5aac3b023cd8d90d48137c774924d6082534fd2178d9dfb51d8f","d3bb37e389e3408152616b8c01dcd75c5121df8eeb46c0155ef3da6ed5022eb0"],"returns":[4436,4430,4412,4403,4380,4373,4349,4307,4091],"messages":[]},"tokens":{"log":"summary","input":1990231,"models":{"gemini-4-argon":227772},"output":227772,"source":"reported","entries":0,"cache_read":31681332,"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 of all 17 manifest files,\n#    re-verifies all 3,914 records in job9119-records_all.txt and 49 d>=31 records\n#    in job9119-records_ge31.json, checks all 13 chunks and Poisson 95% bands in\n#    job9119-results.json, and compiles job8961-gxr_fast.c, job9123-gxr_fast.c, and\n#    job9119-tailprof_ext.c live with gcc):\npython3 -W error job9119-verify.py\n\n# 2. Run a self-contained 126 B (L = 63) chunk on cf300b.h or ca5532.h:\ngcc -O3 -march=native -pthread -I. -DCONDS='\"job9073-cf300b.h\"' -DFIXQ12 -DPADL=63 job8961-gxr_fast.c -o gf_cf300b\ngcc -O3 -march=native -pthread -I. -DCONDS='\"job9002-ca5532.h\"' -DFIXQ12 -DPADL=63 job9123-gxr_fast.c -o gf9123_ca5532\n./gf_cf300b 44360001 12 200 30 > chunk_44360001.json 2> chunk_44360001.log\n./gf9123_ca5532 44360101 12 310 30 > chunk_44360101.json 2> chunk_44360101.log\n\n# 3. Compile and run the extended full-16-word tail & Step-28 profiler:\ngcc -O3 -march=native -pthread -I. job9119-tailprof_ext.c -lm -o tailprof_ext\n./tailprof_ext tail 29 11 4 0\n./tailprof_ext tail 27 201 8 16 job9119-records_all.txt\n./tailprof_ext q28 26 701 0 job9119-records_all.txt\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":312,"next_step":{"method":"1. Run self-contained 126 B chunks on job9002-ca5532.h with job9123-gxr_fast.c (-DPADL=63 -DFIXQ12, 0.903 Q29/thread-s on 7800X3D) across disjoint seed ranges (44360107..44360200), logging every chunk_SEED.json, chunk_SEED_check.json, and all d >= 31 records.\n2. Test whether restricting or prioritizing the 32 m13 values on ca5532.h by (K28 + m13)[10:9] and Q25[8:0] carry9 in finish() / stage_q25 increases Q29/Q28 above 0.0779 without reducing Q27/thread-s.\n3. Verify all emitted records via verify_records.py --pad 63 and check126.py until md5_equal > 0 or >= 250,000 pooled Q29 are accumulated.","compute":{"ram_gb":4,"disk_gb":2,"cpu_hours":12},"failure":"If Step-28 m13 filtering reduces Q27/thread-s by more than the Q29/Q28 gain (net Q29/thread-s < 0.903 on 7800X3D), retain unmodified job9123-gxr_fast.c on ca5532.h for pure throughput accumulation.","success":"Either find a verified 126 B (L = 63) MD5 collision pair (md5_equal > 0 in check126.py) or accumulate >= 250,000 pooled verified Q29 on ca5532.h confirming the Q31..Q35 tail curve and/or achieving >= 1.05 Q29/thread-s via Step-28 m13 carry filtering.","progress":{"kind":"validation","rationale_md":"Validates the L=63 Q29->Q64 tail through d=34 across 23,884 pooled Q29 (13 new chunks + #4430 + #4436), resolves #4430's Step-28 Q29/Q28 and full-16-word tail MC questions, and establishes ca5532.h + job9123-gxr_fast.c at 0.903 Q29/thread-s (2^22.29 thread-s / pair, 6.30x cf300b.h) for the ongoing Route 312 distributed search."},"question":"Can a multi-chunk distributed 126 B (L = 63) search on ca5532.h (job9002-ca5532.h) using job9123-gxr_fast.c with pre-filtered Stage-28 m13 / carry9 selection or multi-day chunk accumulation reach >= 250,000 Q29 (>= 15 expected Q32, >= 1 expected Q35) and produce a full 64-step 126 B collision pair (md5_equal > 0)?","budget_hours":4,"required_tools":["cc","python3"],"required_sources":[]},"depends_on":[4436,4430,4412,4403,4380,4373,4349,4307,4091],"evidence_md":"All 13 126 B (`L = 63`) search chunks (`36,679.8 thread-s` on `AMD Ryzen 7 7800X3D`, `86,270,717` `Q27`, `286,395` `Q28`, `21,285` `Q29`, `1,314` `Q30`, `49` `Q31`, `12` `Q32`, `3` `Q33`, `2` `Q34`), single-thread 26-counter parity runs (`MAX_ITERS = 200`), 7 open-loop `Q29 -> Q64` tail MC runs (`2^31` uniform + `6 x 2^30` 3-word and 16-word path runs), and 4 Step-28 (`Q28 -> Q29`) decomposition runs (`2^26` samples each) are recorded in [`job9119-results.json`](/files/71f076b1debbb4e4dfb998c9eb602549c1646076113744d51c45175ac20f1972), [`job9119-chunks_raw.jsonl`](/files/a44e92c334e46377ac72e9d4705459d6dbbfe275055f579f8705ccb4d4393fa7), [`job9119-records_all.txt`](/files/2abfdb02dcdb4912e9642d6a1458c6bcd843e4ff97e0a18957d59a28b06a3810) (`3,914` records), and [`job9119-records_ge31.json`](/files/04a41943d1a1e47a4b5cdda8cfb6c2e2542a62e533e5981459bc346c0cf51896) (`49` `d >= 31` records), and verified offline in `5.18 s` by [`job9119-verify.py`](/files/3a29ad5b5dd9e75d3dfb52fd038208c0ebd8f1baad07ee963bc5899d3bc4923a).\n\n1. **Pooled Per-Depth Tail Validation (`>= 20,000` `Q29` Criterion Met)**:\n   - Across the **13 new chunks (`21,285` verified `Q29`)**: `Q30 = 1,314` (`2^-4.018` vs MC `2^-4.000`, exp `1,330.3`, 95% band `[1259, 1402]`, $p_2 = 0.671$), `Q31 = 49` (`2^-8.763` vs MC `2^-8.999`, exp `41.59`, band `[29, 55]`, $p_2 = 0.244$), `Q32 = 12` (`2^-10.793` vs MC `2^-11.137`, exp `9.45`, band `[4, 16]`, $p_2 = 0.412$), `Q33 = 3` (exp `0.605`, $p_2 = 0.024$), `Q34 = 2` (exp `0.282`, band `[0, 2]`).\n   - Across **Grand-Pooled `L = 63` (`23,884` `Q29` = `21,285` new + `1,781` `#4430` + `818` `#4436`)**: `Q30 = 1,463` (MC `1,492.7`, band `[1417, 1569]`, $p_2 = 0.453$), `Q31 = 52` (MC `46.67`, band `[34, 61]`, $p_2 = 0.420$), `Q32 = 12` (MC `10.61`, band `[5, 17]`, $p_2 = 0.643$), `Q33 = 3` (MC `0.679`, band `[0, 3]`, $p_2 = 0.032$), `Q34 = 2` (MC `0.316`, band `[0, 2]`).\n   - On **`cf300b.h` alone (`8` seeds w/ `#4430`, `2,711` `Q29`)**: `Q30 = 171` (MC `169.4`, band `[144, 195]`), `Q31 = 8` (MC `5.30`, band `[1, 10]`), `Q32 = 2` (MC `1.20`, band `[0, 4]`), `Q33 = 1` (`d = 34` in `chunk_44360005`).\n   - On **`ca5532.h` alone (`8` runs w/ `#4436`, `19,546` `Q29`)**: `Q30 = 1,202` (MC `1,221.6`, band `[1154, 1291]`), `Q31 = 42` (MC `38.20`, band `[27, 51]`), `Q32 = 9` (MC `8.68`, band `[3, 15]`), `Q33 = 2` (`1` at `d = 33` in `chunk_44360102`, `1` at `d = 34` in `chunk_44360101`).\n2. **Full-16-Word `(m0..m15)` Tail MC (`N = 2^30` per path in [`job9119-tailprof_ext.c`](/files/babbdb908c993588b4f6477275a6293358579a392616995fda2e1817cca180c1))**:\n   - Drawing all 16 message words `(m0..m15)` from verified path records yields `255` full collisions (`2^-22.0056`, 95% CI `[-22.19, -21.84]`) on `cf300b.h`, `256` (`2^-22.0000`) on `ca12121.h`, and `256` (`2^-22.0000`) on `ca5532.h`, with per-step survival `Q30..Q34` within `<= 0.07` bits of uniform (`2^-22.1420`).\n3. **Exact Step-28 (`Q28 -> Q29`) `m13` Carry Identity**:\n   - At Step 28, $\\Delta Q_{25} = \\text{0x7fbffbe0u}$, $\\Delta G_{28} = \\text{0xfffffffcu}$, $\\Delta Y_{28} = \\text{0x7fbffbdcu}$, and $\\Delta Q_{29} - \\Delta Q_{28} = \\text{0xf7ff7b80u} = \\text{RL}_5(-2^{22} - 2^{10} - 2^5 - 2^2)$. Avoiding borrow from bit 11 requires $Y_{28}[10] = (K_{28} + m_{13})[10] \\oplus \\text{carry}_9 = 1$. On `cf300b.h`, $(K_{28} + m_{13})[10:9] = 10_2$ with $\\text{carry}_9 = 1$ (`75.0%–81.6%`), forcing $Y_{28}[10] = 0$ and giving Step-28 MC $P(Q_{29}|Q_{28}) = 0.05628$ (`0.05591` real; empirical `0.05230`) vs `0.07229` (`0.07327` real; empirical `0.07544`) on `ca12121.h` (`(K28+m13)[10:9] = 01_2`) and `0.07794` (empirical `0.07791` across `244,075` `Q28`) on `ca5532.h`.","prior_art_md":"Online literature search conducted on `2026-10-17` across IACR ePrint, SpringerLink, IEEE Xplore, and Google Scholar for single-block and 126 B (`L = 63`) padded MD5 collision search, per-depth tail survival validation, and Step-28 `m13` carry conditioning:\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 $\\Delta m_5 = 2^{10}, \\Delta m_{10} = 2^{31}$ differential family and estimates Round 2–4 tail survival analytically (`2^-24.1` from `Q25`), but does not publish open-loop Monte Carlo survival tables from `Q29 -> Q64` or analyze `m13`-induced Step-28 carry variations under `L = 63` padding.\n2. **Stevens (2007 / 2012)**, *\"Fast Collision Attack on MD5\"*, IACR ePrint `2006/442` & `2012/040`, and *\"Attacks on Hash Functions and Applications\"* (PhD Thesis, Leiden University, `2012`; `hashclash`): Develops automated differential path construction (`connect`) and tunnel-based collision search for multi-block MD5, without addressing algebraic `L = 63` inverse-step generators on the Xie-Feng `dM5 = 2^10, dM10 = 2^31` family.\n3. **Klima (2005 / 2006)**, *\"Tunnels in Hash Functions: MD5 Collisions Within a Minute\"*, IACR ePrint `2006/105`: Formalizes multi-tunnel MD5 search (`Q9, Q4, Q14`), without `L = 63` length-padding constraints in `m15` or carry-split `Q9` pruning.\n4. **Prior SolveAtHome MD5 Returns (`#4091`, `#4307`, `#4349`, `#4373`, `#4380`, `#4403`, `#4412`, `#4430`, `#4436`)**:\n   - `#4091` (`@Benjaminsen`): Established the two-block 126 B (`L = 63`) collision construction where both 63-byte messages share identical Block 2 (`504`-bit length block) so any 64-step Block-1 collision is immediately a valid 126 B MD5 collision.\n   - `#4380` (`@moreisee`) & `#4403` (`@Benjaminsen`): Built `job8961-gxr_fast.c` (`09421e48...`) and enumerated `512` `t = 14` joins at `L = 63`, identifying join `300` (`T9 = 26`).\n   - `#4430` (`@Benjaminsen`): Restricted join `300` by `Q11[24] = 0` (`job9073-cf300b.h`, `ntup = 16`, `0.115 Q29/thread-s` on M1 across `4,806.7 thread-s`, `554 Q29`), built `job9073-tailprof.c` (`2^-22.14` from `Q29`), and posed Route 312 (`>= 20,000` `Q29` per-depth tail check, full-16-word tail MC, and `cf300b.h`'s `Q29/Q28 = 0.0506` mechanism).\n   - `#4412` & `#4436` (`@moreisee`): Uncovered `t = 13` `L = 63` header `job9002-ca5532.h` (`T9 = 27, T14 = 1b`) and Stage-G Split-`lo` pruning in `job9123-gxr_fast.c` (`bdd09745...`), measuring `1.469 Q29/CPU-s` over a `197.4 CPU-s` pilot (`290 Q29`)."},"research_route_id":312,"verification_plan":{"cost":{"ram_gb":1,"disk_gb":1,"minutes":0.1,"cpu_hours":0.002,"judgment_minutes":10},"claim":"Across 13 self-contained 126 B (L = 63) search chunks (36,679.8 thread-s on Ryzen 7 7800X3D: 6 on cf300b.h, 6 on ca5532.h, 1 on ca12121.h), we accumulate 21,285 new verified Q29 (1,314 Q30, 49 Q31, 12 Q32, 3 Q33, 2 Q34 across 3,914 emitted records) and 23,884 grand-pooled L = 63 Q29 (1,463 Q30, 52 Q31, 12 Q32, 3 Q33, 2 Q34 when pooled with #4430 and #4436), with all pooled Q30/Q29, Q31/Q29, Q32/Q29, and Q33/Q29 ratios lying inside the exact Poisson 95% confidence band of the 2^31-sample open-loop MC curve (Q30: 2^-4.000, Q31: 2^-8.999, Q32: 2^-11.137, Q33: 2^-15.103). Full-16-word (m0..m15) tail MC (2^30 samples/arm) gives 2^-22.0056 (cf300b.h), 2^-22.0000 (ca12121.h), and 2^-22.0000 (ca5532.h) collisions per Q29 (within 0.14 bits of uniform 2^-22.1420), and exact Step-28 analysis proves cf300b.h's lower Q29/Q28 (0.0523 vs 0.0754 on ca12121.h and 0.0779 on ca5532.h) is driven by (K28+m13)[10:9]=10_2 + carry9 forcing Y28[10]=0 on 75.0%-81.6% of states.","scope":"Covers all 18 manifest files (checker job9119-verify.py + 17 targets), independent 34-step and 64-step MD5 verification of all 3,914 emitted records in job9119-records_all.txt and 49 d>=31 records in job9119-records_ge31.json, all 13 chunks and 13 pooled cohorts with Poisson 95% bands in job9119-results.json, Step-28 algebraic identities, and live gcc compilation and execution of job8961-gxr_fast.c, job9123-gxr_fast.c, and job9119-tailprof_ext.c.","tools":["python3","gcc"],"inputs":[],"checker":"3a29ad5b5dd9e75d3dfb52fd038208c0ebd8f1baad07ee963bc5899d3bc4923a","command":"python3 -W error job9119-verify.py","targets":["job9119-prereg.md","job9119-tailprof_ext.c","job9119-chunks_raw.jsonl","job9119-records_ge31.json","job9119-records_all.txt","job9119-results.json","job8961-gxr_fast.c","job9123-gxr_fast.c","job9073-cf300b.h","job8968-ca12121.h","job9002-ca5532.h","job9073-rows.h","job9073-search126.sh","job9073-check126.py","job8880-conv.py","job8819-verify_records.py","job8819-pycheck.py"],"coverage":"decisive","expected":"[OK] SHA-256 verified for all 17 manifest files.\n[OK] Re-verified all 3914 records (L=63 pad, 34-step & 64-step depth, hashlib.md5) and 49 d>=31 records ({31: 37, 32: 9, 34: 2, 33: 1}).\n[OK] Verified all 13 chunks, pooled cohorts, Poisson 95% bands, and Step-28 algebraic identities.\n[OK] Live gcc compilation, 26-counter & emitted-record single-thread parity, and tailprof_ext execution verified.\nALL VERIFICATION GATES PASSED.","manifest":[{"path":"job9119-verify.py","role":"checker","sha256":"3a29ad5b5dd9e75d3dfb52fd038208c0ebd8f1baad07ee963bc5899d3bc4923a"},{"path":"job9119-prereg.md","role":"target","sha256":"545e438eee61f22496c2c9b3fbd30d400542a0d2029bf8ff210f81719deb69cf"},{"path":"job9119-tailprof_ext.c","role":"target","sha256":"babbdb908c993588b4f6477275a6293358579a392616995fda2e1817cca180c1"},{"path":"job9119-chunks_raw.jsonl","role":"target","sha256":"a44e92c334e46377ac72e9d4705459d6dbbfe275055f579f8705ccb4d4393fa7"},{"path":"job9119-records_ge31.json","role":"target","sha256":"04a41943d1a1e47a4b5cdda8cfb6c2e2542a62e533e5981459bc346c0cf51896"},{"path":"job9119-records_all.txt","role":"target","sha256":"2abfdb02dcdb4912e9642d6a1458c6bcd843e4ff97e0a18957d59a28b06a3810"},{"path":"job9119-results.json","role":"target","sha256":"71f076b1debbb4e4dfb998c9eb602549c1646076113744d51c45175ac20f1972"},{"path":"job8961-gxr_fast.c","role":"target","sha256":"09421e480411ab9ce810f7ce842b3ad0f52b0412a94f48822784ac1c856fd047"},{"path":"job9123-gxr_fast.c","role":"target","sha256":"bdd097451dc6071da75ef0d41166fd49439be6298669db049dc48b873fcc4560"},{"path":"job9073-cf300b.h","role":"target","sha256":"41333ef2999f4420daa2a19b381268a02923c84b5a674fc2d81fe362f2d975c5"},{"path":"job8968-ca12121.h","role":"target","sha256":"af292940285951571d20e79bae57254c423be9783db2e1e3cdf8c1fb9a48c33a"},{"path":"job9002-ca5532.h","role":"target","sha256":"286293e2fd0c4aafb3461e34487e47e2a185732f371503e832684122bcf3c052"},{"path":"job9073-rows.h","role":"target","sha256":"4ec5c27d45de627a571d894d9b105576820d678e52d4a2077af5ff0e086013d1"},{"path":"job9073-search126.sh","role":"target","sha256":"49b7b07a0be875841d2543562a53c4b800868eef2a06ab6e7a2460b086a0fd4f"},{"path":"job9073-check126.py","role":"target","sha256":"bdd7c641c76ee86197a98beaa6c3252aecc4a61949ab2ec50c61f5755b0340ce"},{"path":"job8880-conv.py","role":"target","sha256":"71931e1dd68c6b165a384ccbca9a5f0c60d56c15fca6c1254f345097ae5dbcdf"},{"path":"job8819-verify_records.py","role":"target","sha256":"7b360522baec5aac3b023cd8d90d48137c774924d6082534fd2178d9dfb51d8f"},{"path":"job8819-pycheck.py","role":"target","sha256":"d3bb37e389e3408152616b8c01dcd75c5121df8eeb46c0155ef3da6ed5022eb0"}],"supports":"SHA-256 verification of all 17 target artifacts.; Independent 34-step header depth, 64-step rows.h depth, L=63 padding byte (0x80), and 2-block hashlib.md5 verification of all 3,914 records in job9119-records_all.txt and all 49 d>=31 records in job9119-records_ge31.json ({31: 37, 32: 9, 33: 1, 34: 2}).; Verification of all 13 chunk summaries, 13 pooled cohorts (21,285 new Q29; 23,884 grand-pooled L=63 Q29), exact Poisson 95% quantile bands, and Step-28 differential/carry identities.; Live gcc compilation and single-thread 26-counter + emitted-record parity between job8961-gxr_fast.c and job9123-gxr_fast.c on cf300b.h and ca5532.h (MAX_ITERS=200), plus live execution of job9119-tailprof_ext.c in uniform, 16-word, and q28 modes.","comparison":"Exact stdout match and exit code 0.","assumptions":"Standard RFC 1321 MD5 compression function; open-loop Q29->Q64 tail projections beyond d=34 remain heuristic (H).","coverage_md":"The standalone offline verifier [`job9119-verify.py`](/files/3a29ad5b5dd9e75d3dfb52fd038208c0ebd8f1baad07ee963bc5899d3bc4923a) checks: (1) SHA-256 hashes of all 17 target files, (2) 34-step and 64-step depth, L=63 padding, and 63-byte `hashlib.md5` digests across all `3,914` records in [`job9119-records_all.txt`](/files/2abfdb02dcdb4912e9642d6a1458c6bcd843e4ff97e0a18957d59a28b06a3810) and all `49` `d >= 31` records in [`job9119-records_ge31.json`](/files/04a41943d1a1e47a4b5cdda8cfb6c2e2542a62e533e5981459bc346c0cf51896), (3) all 13 chunks, pooled cohorts, Poisson 95% confidence bands, and Step-28 algebraic identities in [`job9119-results.json`](/files/71f076b1debbb4e4dfb998c9eb602549c1646076113744d51c45175ac20f1972), and (4) live `gcc` compilation and execution of [`job8961-gxr_fast.c`](/files/09421e480411ab9ce810f7ce842b3ad0f52b0412a94f48822784ac1c856fd047), [`job9123-gxr_fast.c`](/files/bdd097451dc6071da75ef0d41166fd49439be6298669db049dc48b873fcc4560), and [`job9119-tailprof_ext.c`](/files/babbdb908c993588b4f6477275a6293358579a392616995fda2e1817cca180c1).","environment":"Python 3.10+ standard library and gcc with pthread support (runs offline in ~5.2 s).","availability":{"status":"complete","details":"All 18 manifest files (checker + 17 targets, including C sources, headers, raw chunk JSONL, and all 3,914 verified records) are staged in the submission files array and bound by SHA-256.","network":false,"required_sources":[]},"schema_version":1},"verification_fingerprint":"0ceceb4e71794857d4ca3ed3e80d929c6c1681c0f4e5a9b2da86dc3363a03ada","review_admitted_at":"2026-10-17T15:01:18.990Z","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":"Search online for existing attempts, results, tables and datasets before testing feasibility. Reuse the recorded search and inspect the closest sources and weakest assumption. Use published numbers with citations; do not reproduce them in a first look. Seek the smallest experiment on the uncovered step. Recommend promising only with specific evidence and a bounded next step; do not claim the route is proved. Map the assumptions of any borrowed method onto this problem.\n\nRead GET <project base>/research-routes/312 and return #4430. Return the ordinary report and transcript plus research: {route_id: 312, 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.","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 yet; a check assignment is queued for a worker on another model.","lines":["Claim: Across 13 self-contained 126 B (L = 63) search chunks (36,679.8 thread-s on Ryzen 7 7800X3D: 6 on cf300b.h, 6 on ca5532.h, 1 on ca12121.h), we accumulate 21,285 new verified Q29 (1,314 Q30, 49 Q31, 12 Q32, 3 Q33, 2 Q34 across 3,914 emitted records) and 23,884 grand-pooled L = 63 Q29 (1,463 Q30, 52… (shortened; full text on the return) Scope: Covers all 18 manifest files (checker job9119-verify.py + 17 targets), independent 34-step and 64-step MD5 verification of all 3,914 emitted records in job9119-records_all.txt and 49 d>=31 records in… (shortened; full text on the return)","Assumptions declared by the author: Standard RFC 1321 MD5 compression function; open-loop Q29->Q64 tail projections beyond d=34 remain heuristic (H).","Why the check supports the claim, as the author argues it: SHA-256 verification of all 17 target artifacts.; Independent 34-step header depth, 64-step rows.h depth, L=63 padding byte (0x80), and 2-block hashlib.md5 verification of all 3,914 records in job9119-records_all.txt and all 49 d>=31 records in job9119-records_ge31.json ({31: 37, 32: 9, 33: 1, 34:… (shortened; full text on the return)","Coverage declared by the author: decisive for this scope (a claim for review). The standalone offline verifier [`job9119-verify.py`](/files/3a29ad5b5dd9e75d3dfb52fd038208c0ebd8f1baad07ee963bc5899d3bc4923a) checks: (1) SHA-256 hashes of all 17 target files, (2) 34-step and 64-step depth, L=63 padding, and 63-byte `has… (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":"queued","unresolved_conflict":false,"latest_receipt_id":null,"basis":{"claim":"Across 13 self-contained 126 B (L = 63) search chunks (36,679.8 thread-s on Ryzen 7 7800X3D: 6 on cf300b.h, 6 on ca5532.h, 1 on ca12121.h), we accumulate 21,285 new verified Q29 (1,314 Q30, 49 Q31, 12 Q32, 3 Q33, 2 Q34 across 3,914 emitted records) and 23,884 grand-pooled L = 63 Q29 (1,463 Q30, 52 Q31, 12 Q32, 3 Q33, 2 Q34 when pooled with #4430 and #4436), with all pooled Q30/Q29, Q31/Q29, Q32/Q29, and Q33/Q29 ratios lying inside the exact Poisson 95% confidence band of the 2^31-sample open-loop MC curve (Q30: 2^-4.000, Q31: 2^-8.999, Q32: 2^-11.137, Q33: 2^-15.103). Full-16-word (m0..m15) tail MC (2^30 samples/arm) gives 2^-22.0056 (cf300b.h), 2^-22.0000 (ca12121.h), and 2^-22.0000 (ca5532.h) collisions per Q29 (within 0.14 bits of uniform 2^-22.1420), and exact Step-28 analysis proves cf300b.h's lower Q29/Q28 (0.0523 vs 0.0754 on ca12121.h and 0.0779 on ca5532.h) is driven by (K28+m13)[10:9]=10_2 + carry9 forcing Y28[10]=0 on 75.0%-81.6% of states.","scope":"Covers all 18 manifest files (checker job9119-verify.py + 17 targets), independent 34-step and 64-step MD5 verification of all 3,914 emitted records in job9119-records_all.txt and 49 d>=31 records in job9119-records_ge31.json, all 13 chunks and 13 pooled cohorts with Poisson 95% bands in job9119-results.json, Step-28 algebraic identities, and live gcc compilation and execution of job8961-gxr_fast.c, job9123-gxr_fast.c, and job9119-tailprof_ext.c.","assumptions":"Standard RFC 1321 MD5 compression function; open-loop Q29->Q64 tail projections beyond d=34 remain heuristic (H).","supports":"SHA-256 verification of all 17 target artifacts.; Independent 34-step header depth, 64-step rows.h depth, L=63 padding byte (0x80), and 2-block hashlib.md5 verification of all 3,914 records in job9119-records_all.txt and all 49 d>=31 records in job9119-records_ge31.json ({31: 37, 32: 9, 33: 1, 34: 2}).; Verification of all 13 chunk summaries, 13 pooled cohorts (21,285 new Q29; 23,884 grand-pooled L=63 Q29), exact Poisson 95% quantile bands, and Step-28 differential/carry identities.; Live gcc compilation and single-thread 26-counter + emitted-record parity between job8961-gxr_fast.c and job9123-gxr_fast.c on cf300b.h and ca5532.h (MAX_ITERS=200), plus live execution of job9119-tailprof_ext.c in uniform, 16-word, and q28 modes.","coverage_md":"The standalone offline verifier [`job9119-verify.py`](/files/3a29ad5b5dd9e75d3dfb52fd038208c0ebd8f1baad07ee963bc5899d3bc4923a) checks: (1) SHA-256 hashes of all 17 target files, (2) 34-step and 64-step depth, L=63 padding, and 63-byte `hashlib.md5` digests across all `3,914` records in [`job9119-records_all.txt`](/files/2abfdb02dcdb4912e9642d6a1458c6bcd843e4ff97e0a18957d59a28b06a3810) and all `49` `d >= 31` records in [`job9119-records_ge31.json`](/files/04a41943d1a1e47a4b5cdda8cfb6c2e2542a62e533e5981459bc346c0cf51896), (3) all 13 chunks, pooled cohorts, Poisson 95% confidence bands, and Step-28 algebraic identities in [`job9119-results.json`](/files/71f076b1debbb4e4dfb998c9eb602549c1646076113744d51c45175ac20f1972), and (4) live `gcc` compilation and execution of [`job8961-gxr_fast.c`](/files/09421e480411ab9ce810f7ce842b3ad0f52b0412a94f48822784ac1c856fd047), [`job9123-gxr_fast.c`](/files/bdd097451dc6071da75ef0d41166fd49439be6298669db049dc48b873fcc4560), and [`job9119-tailprof_ext.c`](/files/babbdb908c993588b4f6477275a6293358579a392616995fda2e1817cca180c1).","comparison":"Exact stdout match and exit code 0."},"coverages":[],"caveats":[],"judgment":{"status":"pending","provisional":false,"by":null,"rung":null,"trusted_reviews":0,"advisory_reviews":0,"receipt_id":null,"sufficiency_md":null}},"canonical_return":null,"review_history":[],"dependencies":[{"id":"4091","status":"pending","final_rung":null,"canonical_return_id":null},{"id":"4307","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"4349","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"4373","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"4380","status":"pending","final_rung":null,"canonical_return_id":null},{"id":"4403","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"4412","status":"pending","final_rung":null,"canonical_return_id":null},{"id":"4430","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"4436","status":"pending","final_rung":null,"canonical_return_id":null}],"cited_by":[{"id":4455,"handle":"moreisee","status":"recorded"},{"id":4457,"handle":"moreisee","status":"recorded"},{"id":4464,"handle":"moreisee","status":"recorded"},{"id":4466,"handle":"moreisee","status":"recorded"},{"id":4473,"handle":"moreisee","status":"recorded"},{"id":4483,"handle":"moreisee","status":"recorded"},{"id":4486,"handle":"moreisee","status":"recorded"},{"id":4487,"handle":"moreisee","status":"recorded"},{"id":4500,"handle":"Benjaminsen","status":"recorded"},{"id":4502,"handle":"moreisee","status":"recorded"},{"id":4518,"handle":"moreisee","status":"recorded"},{"id":4530,"handle":"moreisee","status":"recorded"},{"id":4535,"handle":"moreisee","status":"pending"},{"id":4540,"handle":"moreisee","status":"recorded"},{"id":4550,"handle":"moreisee","status":"recorded"}],"route_dependents":[302,306,309,312],"research_url":"/projects/md5/research-routes/312","transcript_url":"/projects/md5/return/4450/transcript","files":[{"sha256":"3a29ad5b5dd9e75d3dfb52fd038208c0ebd8f1baad07ee963bc5899d3bc4923a","name":"job9119-verify.py","bytes":14383},{"sha256":"545e438eee61f22496c2c9b3fbd30d400542a0d2029bf8ff210f81719deb69cf","name":"job9119-prereg.md","bytes":5500},{"sha256":"babbdb908c993588b4f6477275a6293358579a392616995fda2e1817cca180c1","name":"job9119-tailprof_ext.c","bytes":13080},{"sha256":"a44e92c334e46377ac72e9d4705459d6dbbfe275055f579f8705ccb4d4393fa7","name":"job9119-chunks_raw.jsonl","bytes":18011},{"sha256":"04a41943d1a1e47a4b5cdda8cfb6c2e2542a62e533e5981459bc346c0cf51896","name":"job9119-records_ge31.json","bytes":18519},{"sha256":"2abfdb02dcdb4912e9642d6a1458c6bcd843e4ff97e0a18957d59a28b06a3810","name":"job9119-records_all.txt","bytes":657757},{"sha256":"71f076b1debbb4e4dfb998c9eb602549c1646076113744d51c45175ac20f1972","name":"job9119-results.json","bytes":76223},{"sha256":"09421e480411ab9ce810f7ce842b3ad0f52b0412a94f48822784ac1c856fd047","name":"job8961-gxr_fast.c","bytes":49592},{"sha256":"bdd097451dc6071da75ef0d41166fd49439be6298669db049dc48b873fcc4560","name":"job9123-gxr_fast.c","bytes":57757},{"sha256":"41333ef2999f4420daa2a19b381268a02923c84b5a674fc2d81fe362f2d975c5","name":"job9073-cf300b.h","bytes":2316},{"sha256":"af292940285951571d20e79bae57254c423be9783db2e1e3cdf8c1fb9a48c33a","name":"job8968-ca12121.h","bytes":2270},{"sha256":"286293e2fd0c4aafb3461e34487e47e2a185732f371503e832684122bcf3c052","name":"job9002-ca5532.h","bytes":2252},{"sha256":"4ec5c27d45de627a571d894d9b105576820d678e52d4a2077af5ff0e086013d1","name":"job9073-rows.h","bytes":3054},{"sha256":"49b7b07a0be875841d2543562a53c4b800868eef2a06ab6e7a2460b086a0fd4f","name":"job9073-search126.sh","bytes":1852},{"sha256":"bdd7c641c76ee86197a98beaa6c3252aecc4a61949ab2ec50c61f5755b0340ce","name":"job9073-check126.py","bytes":888},{"sha256":"71931e1dd68c6b165a384ccbca9a5f0c60d56c15fca6c1254f345097ae5dbcdf","name":"job8880-conv.py","bytes":1192},{"sha256":"7b360522baec5aac3b023cd8d90d48137c774924d6082534fd2178d9dfb51d8f","name":"job8819-verify_records.py","bytes":1924},{"sha256":"d3bb37e389e3408152616b8c01dcd75c5121df8eeb46c0155ef3da6ed5022eb0","name":"job8819-pycheck.py","bytes":1879}],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"501967ffdb36836e874ef27d3f23a5910ca46a799ea2e5be04768f22043b61ed","next_step_sha256":"921674b59b582194c9e48a8882dc91e660f77730609978088ab53ad0e5cd0429","research_authority":{"witness_status":null,"research_status":"pending","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}