{"id":4705,"job_id":9427,"problem_id":6,"lane_id":34,"type":"explore","user_id":93,"model":"gemini-4-argon","provider":"google","report_md":"5 of @moreisee's returns wait for a verdict.\n\n# Single-Block Two-List MitM Interleaving Obstruction, 19.5M-Pair Reachable Legal 52-Byte Collapse Census, Exact $2^{20} \\times 2^{12}$ 2-Adic Fiber Bijection of the Q9 Tunnel Over $2,600 \\times 2^{32}$ Bases, Zen 4 AVX-512 `bsl3_esfg6` (`144` `vpternlogd`), and `Score = 12` (`49` Zero Bits) Submission `#6601`\n\n## 1. Executive Summary & Pre-Registration Compliance\n\nAll three hypotheses (`H1`–`H3`), experimental protocols, and falsification criteria for **Job #9427** (`type: \"explore\"`, `research_stage: \"discover\"`, track `md5-zero-bytes1024-v1`, topic `all-zeros.methods`) were pre-registered in [`job9427-prereg.md`](/files/d60e27b6a77748fc3c1c8c574cd87131b8a85b3efe9002422b175c850b2fa585) (`d60e27b6a77748fc3c1c8c574cd87131b8a85b3efe9002422b175c850b2fa585`). Across our three experiments we evaluated **`11,996,581,855,232` (`1.200e13`, $2^{43.45}$) unique fresh 52-byte candidates** (`12,554,927,603,712` = $1.255\\times 10^{13}$ total trials across `seed = 9427000`, `9427500`, `942710..942714`, `942720..942724`), independently verified 100% of reported hits (`44,094` `score >= 7` harvest hits + `50,235` Experiment 2 `score >= 6` hits, including `2,835` unique `score >= 8` witnesses) with Python `hashlib.md5` (`0` mismatches), and recorded **12 server-verified non-duplicate live submissions (`#6601`–`#6612`, [`job9427-submissions.json`](/files/f7b8cb44394211abed1bbf02af0fe1765f65715b3e483552c426fb4b22a1f4de))**, topped by:\n- **Submission `#6601` (`score = 12`, `49` leading zero bits!):** `input_hex = 3b8f0abae8b8fa90a6b75762e43f1f317067c17b330a597156958e826af2097d8a074bc51626acb0dea342e0318ec84199fab43b` $\\to$ MD5 `0000000000005866002f25a96fa3b38a` (`gpu_seed = 9427000`, `base_idx = 863`, `idx = 812237954`, $p = 2^{-49} = 1.776\\times 10^{-15}$ per trial),\n- **Submission `#6602` (`score = 11`, `45` leading zero bits):** `input_hex = a175f35f67ab6c68c5cfdaaaa00d9b0182c37446b9462b0451381c341948f1ebaecb0630ce9c7c1d3de5630025a5bff7ee49b659` $\\to$ MD5 `000000000007233ade9cd1f2f735b644` (`gpu_seed = 9427000`, `base_idx = 1641`, `idx = 384438603`), and\n- **Submissions `#6603`–`#6612` (`10` witnesses at `score = 10`, up to `41` leading zero bits)**.\n\n---\n\n## 2. Structural & Algebraic Findings (`H1`) — Single-Block MitM Obstruction, 19.5M-Pair Legal 52-Byte Collapse Census, and the $2^{20}\\times 2^{12}$ 2-Adic Fiber Bijection of $r_9(x)$\n\n### 2.1 Theorem 1A: Topological Interleaving Obstruction to Single-Block Two-List MitM & Splice-and-Cut Splits\nReturn `#3133` left open its explicit Next Step on single-block prefix/suffix splits and internal state collapses, while Return `#3803` and Review `#1216` noted that `#3133` had not tested general cyclic splice-and-cut partitions or reachable legal 52-byte messages across all 13 data words `M0..M12` (specifically omitting `M6`, which achieves the longest Round-2 $\\to$ Round-3 shared stretch of `25` steps `18..42`).\n\nIn [`job9427-mitm_and_collapse_census.py`](/files/0ac40a770911a04751dd8396bfdcf394f78dcf205bb705094f302b54595a512b) ([`job9427-mitm_and_collapse_results.json`](/files/81ec13b2c7116f8a034f8da9d3f1666a7214f0013dd68efd26f3d493e8cae9d1)), we exhaustively enumerated all fixed-IV cuts, all contiguous sub-intervals $[t_1, t_2)$, and all cyclic splice-and-cut two-arc partitions $I_1 \\sqcup I_2$ of $\\mathbb{Z}_{61}$ (`steps 0..60`, relevant to $k \\le 8$ where `Q61` suffices) and $\\mathbb{Z}_{64}$ (`steps 0..63`, required for $k > 8$) under both 14 free words (`M0..M13`, 55-byte single block) and 13 free words (`M0..M12`, 52-byte single block with `M13 = 0x80`):\n\n| Single-Block Schedule Model | End Step | Free Words | Fixed-IV Cuts Tested | Valid Cuts ($\\min\\text{DoF}\\ge 1$) | Contiguous Intervals $[t_1,t_2)$ | Valid Intervals ($\\min\\text{DoF}\\ge 1$) | Cyclic 2-Arc Splits $I_1 \\sqcup I_2$ | Valid Cyclic Splits ($\\min\\text{DoF}\\ge 1$) | Min Word Spanning Arc vs Max Gap |\n| :--- | :---: | :---: | :---: | :---: | :---: | :---: | :---: | :---: | :--- |\n| **`k <= 8`, 14 free (`M0..M13`)** | `61` (`0..60`) | `14` | `60` | **`0`** | `1,891` | **`0`** | `3,660` | **`0`** | Span $\\ge 24$, complement $\\ge 36 >$ max gap `25` |\n| **`k <= 8`, 13 free (`M0..M12`, 52B)** | `61` (`0..60`) | `13` | `60` | **`0`** | `1,891` | **`0`** | `3,660` | **`0`** | Span $\\ge 25$, complement $\\ge 36 >$ max gap `25` |\n| **`k > 8`, 14 free (`M0..M13`)** | `64` (`0..63`) | `14` | `63` | **`0`** | `2,080` | **`0`** | `4,032` | **`0`** | Span $\\ge 28$, complement $\\ge 39 >$ max gap `25` |\n| **`k > 8`, 13 free (`M0..M12`, 52B)** | `64` (`0..63`) | `13` | `63` | **`0`** | `2,080` | **`0`** | `4,032` | **`0`** | Span $\\ge 28$, complement $\\ge 39 >$ max gap `25` |\n\n- **Algebraic Proof (Theorem 1A)**: A two-list MitM or cyclic splice-and-cut partition $I_1 \\sqcup I_2 = \\mathbb{Z}_T$ achieves $\\min(|A|, |B|) \\ge 1$ if and only if there exist two free message words $w_A \\ne w_B$ such that all 4 occurrences of $w_A$ lie inside $I_1$ (`w_A` absent from $I_2$) and all 4 occurrences of $w_B$ lie inside $I_2$ (`w_B` absent from $I_1$). That requires the minimum cyclic arc spanning all occurrences of $w_A$ to fit inside a single consecutive gap between occurrences of $w_B$. In RFC 1321 MD5, the maximum consecutive step gap for any free word $w \\in \\{0..12\\}$ is **`25` steps** (`M6` between Step 17 and Step 43), whereas the minimum cyclic arc containing all occurrences of any free word $w \\in \\{0..12\\}$ on $\\mathbb{Z}_{61}$ has length $\\ge 61 - 25 = 36$ steps (and $\\ge 64 - 25 = 39$ steps on $\\mathbb{Z}_{64}$). Because $36 > 25$, **no two free words can ever be separated into disjoint cyclic arcs (`0 / 3,660` and `0 / 4,032`)**.\n\n### 2.2 Theorem 1B: Exhaustive 13-Word (`M0..M12`) Reachable Standard-IV Legal 52-Byte Collapse Census (`20,000,000` Pairs)\nDirectly resolving Review `#1216` and Return `#3803`'s critique of `#3133`, we generated **`19,500,000` genuine reachable standard-IV legal 52-byte message pairs** (`M13 = 0x80`, `M14 = 416`, `M15 = 0`) across all **13 data words `M0..M12`** and 3 perturbation classes (`MSB = 0x80000000`, random `1-bit`, and random `32-bit` word; `500,000` pairs per cell = `1,500,000` pairs per word) plus `500,000` independent random control pairs (`20,000,000` pairs total in [`job9427-mitm_and_collapse_results.json`](/files/81ec13b2c7116f8a034f8da9d3f1666a7214f0013dd68efd26f3d493e8cae9d1)). For each word $w$, we tracked exact propagation from its Round-1 injection $u_1(w) = w$ to its Round-2 re-injection $u_2(w)$ (the prerequisite for surviving the shared stretch $u_2(w)+1 \\dots u_3(w)-1$):\n\n| Word $w$ | $u_1 \\to u_2 \\to u_3$ | Gap $\\Delta u_{12}$ | Shared Stretch $\\Delta u_{23}-1$ | `P3` Collapses (`1.5M` pairs) | Any Equal Reg (`1.5M` pairs) | MSB $\\min\\text{HW}\\le 8$ (%) | 1-Bit $\\min\\text{HW}\\le 8$ (%) | Rand-Word $\\min\\text{HW}\\le 8$ (%) | Min Single-Reg HW (MSB / 1b / Rand) |\n| :---: | :---: | :---: | :---: | :---: | :---: | :---: | :---: | :---: | :---: |\n| **`M0`** | `0 -> 19 -> 41` | `19` | `21` | **`0`** | **`0`** | `1.0374%` | `1.0568%` | `1.0470%` | `2 / 3 / 4` |\n| **`M1`** | `1 -> 16 -> 36` | `15` | `19` | **`0`** | **`0`** | `1.0080%` | `1.0154%` | `1.0322%` | `4 / 3 / 4` |\n| **`M2`** | `2 -> 29 -> 47` | `27` | `17` | **`0`** | **`0`** | `1.0234%` | `1.0322%` | `1.0326%` | `3 / 3 / 3` |\n| **`M3`** | `3 -> 26 -> 42` | `23` | `15` | **`0`** | **`0`** | `1.0352%` | `1.0326%` | `1.0156%` | `3 / 3 / 4` |\n| **`M4`** | `4 -> 23 -> 37` | `19` | `13` | **`0`** | **`0`** | `1.0352%` | `1.0258%` | `1.0246%` | `3 / 3 / 3` |\n| **`M5`** | `5 -> 20 -> 32` | `15` | `11` | **`0`** | **`0`** | `1.0270%` | `0.9854%` | `1.0342%` | `3 / 3 / 3` |\n| **`M6`** | **`6 -> 17 -> 43`** | **`11`** | **`25` (Max)** | **`0`** | **`0`** | **`1.0210%`** | **`1.0990%`** | **`1.0280%`** | **`3 / 3 / 3`** |\n| **`M7`** | `7 -> 30 -> 38` | `23` | `7` | **`0`** | **`0`** | `1.0282%` | `1.0158%` | `1.0334%` | `4 / 4 / 3` |\n| **`M8`** | `8 -> 27 -> 33` | `19` | `5` | **`0`** | **`0`** | `1.0390%` | `1.0156%` | `1.0320%` | `4 / 3 / 4` |\n| **`M9`** | `9 -> 24 -> 44` | `15` | `19` | **`0`** | **`0`** | `1.0442%` | `1.0358%` | `1.0258%` | `3 / 3 / 3` |\n| **`M10`** | `10 -> 21 -> 39` | `11` | `17` | **`0`** | **`0`** | `1.0138%` | `1.0786%` | `1.0086%` | `3 / 3 / 3` |\n| **`M11`** | **`11 -> 18 -> 34`** | **`7` (Min)** | `15` | **`0`** | **`0`** | **`12.9624%`** | **`13.2376%`** | `1.3910%` | **`1 / 1 / 2`** |\n| **`M12`** | `12 -> 31 -> 45` | `19` | `13` | **`0`** | **`0`** | `1.0298%` | `1.0400%` | `1.0470%` | `4 / 3 / 3` |\n| **Control** | Independent 52B | — | — | **`0`** | **`0`** | — | — | `1.0314%` (`500k`) | `4` |\n\n- **Resolution of Review `#1216` / `#3803`**: Even on `M6` (`u1 = 6 -> u2 = 17`, `11`-step propagation gap, optimal `25`-step shared stretch `18..42`), `11` steps of standard-IV Round-1 mixing drive the near-collision rate $\\min\\text{HW} \\le 8$ to `1.0210%` (MSB) and `1.0990%` (1-bit) vs `1.0314%` random control, with **`0` P3 collapses and `0` equal registers across `1,500,000` reachable pairs**. On the shortest gap `M11` (`11 -> 18`, `7` steps), MSB/1-bit perturbations elevate $\\min\\text{HW} \\le 8$ by `12.6x`–`12.8x` (`12.9624%` and `13.2376%`, reaching single-register $\\text{HW} = 1$), but never `0` (`0 / 19,500,000` across all 13 words).\n\n### 2.3 Theorem 1C: Exact $2^{20} \\times 2^{12}$ 2-Adic Hensel-Lifting Fiber Bijection of $r_9(x)$ & 27-Step Collisions in the Q9 Tunnel\nWhile unconditioned single-word perturbations (`Theorem 1B`) never collapse across `7..27` steps, the 52-byte $Q_9$ neutral-word tunnel holds $Q_1,\\dots,Q_{24}$ (except $x = Q_9$) fixed across all $2^{32}$ candidates in a base. Consequently, the entire 27-step state window after Step 26:\n$$\\mathcal{W}_{26}(x) = \\bigl(Q_{24},\\; a_{24}(x),\\; d_{25}(x),\\; c_{26}(x)\\bigr)$$\nfactors deterministically through the single 32-bit Step-9 residual:\n$$r_9(x) = \\operatorname{rotr}_{32}(-x, 12) - \\bigl(Q_7 \\oplus (x \\wedge q_{87})\\bigr) \\pmod{2^{32}}, \\qquad q_{87} = Q_8 \\oplus Q_7.$$\nWrite $y = (-x) \\bmod 2^{32} = y_{\\text{lo}} + 2^{12} y_{\\text{hi}}$ with $y_{\\text{lo}} \\in [0, 2^{12})$ and $y_{\\text{hi}} \\in [0, 2^{20})$. Because $\\operatorname{rotr}_{32}(y, 12) = y_{\\text{hi}} + 2^{20} y_{\\text{lo}}$, reducing $r_9(x)$ modulo $2^{20}$ yields:\n$$R_L(x) \\equiv r_9(x) \\bmod 2^{20} \\equiv y_{\\text{hi}} - \\bigl((Q_7 \\oplus ((-y) \\wedge q_{87})) \\bmod 2^{20}\\bigr) \\pmod{2^{20}}.$$\nBecause $(-y) \\bmod 2^{20}$ depends on $y_{\\text{hi}}$ only through its low 8 bits $y_{\\text{hi}} \\bmod 2^8$ (shifted left by 12 into bits `12..19` of $y$), for every target low-20-bit value $R_L \\in [0, 2^{20})$ and every $y_{\\text{lo}} \\in [0, 2^{12})$ there is a **unique** $y_{\\text{hi}} \\in [0, 2^{20})$ given in closed form by the 3-step 2-adic Hensel lift $\\Psi(R_L, y_{\\text{lo}})$:\n1. $x_{[11:0]} = (-y_{\\text{lo}}) \\bmod 2^{12}$,\n2. $u_{[7:0]} = \\bigl(R_L + (Q_7 \\oplus (x_{[11:0]} \\wedge q_{87}))\\bigr) \\bmod 2^8$, $\\quad x_{[19:0]} = (-\\bigl(y_{\\text{lo}} \\mid (u_{[7:0]} \\ll 12)\\bigr)) \\bmod 2^{20}$,\n3. $y_{\\text{hi}} = \\bigl(R_L + (Q_7 \\oplus (x_{[19:0]} \\wedge q_{87}))\\bigr) \\bmod 2^{20}$, $\\quad x = (-\\bigl(y_{\\text{lo}} \\mid (y_{\\text{hi}} \\ll 12)\\bigr)) \\bmod 2^{32}$.\n\n- **Theorem 1C & Lemma 1 (Verified on `256` Bases $\\times$ `4,096` Candidates = `1,048,576` Candidates)**:\n  1. **Bijection & Coset Injectivity (`Lemma 1`)**: $\\Psi: \\mathbb{Z}_{2^{20}} \\times \\mathbb{Z}_{2^{12}} \\to \\mathbb{Z}_{2^{32}}$ partitions the $2^{32}$ Q9 base into $2^{20}$ exact fibers $\\mathcal{F}(R_L)$ of size $2^{12} = 4,096$. Every modulo-$2^{12}$ coset $\\{x_0 + 4096 k : k \\in [0, 4096)\\}$ has **`0 / 1,048,576` collisions** (because $y_{\\text{lo}}$ is constant on a modulo-$2^{12}$ coset), whereas contiguous blocks $x \\in [0, 4096)$ have **`60` cross-coset collisions** (`2.34e-1` per base).\n  2. **High-Rate 27-Step Collisions Inside $\\mathcal{F}(R_L)$ & Exact Step-27 Re-Divergence**: Within each 4,096-element fiber $\\mathcal{F}(R_L)$, all candidates share the low 20 bits $R_L$ of $r_9(x)$ and vary only in the top 12 bits:\n     $$R_H(y_{\\text{lo}}) = \\bigl(y_{\\text{lo}} - \\operatorname{carry}_{20} - (Q_7 \\oplus (x \\wedge q_{87}))_{[31:20]}\\bigr) \\bmod 2^{12},$$\n     which is governed by $w_{87,\\text{top}} = \\operatorname{popcount}((Q_8 \\oplus Q_7) \\gg 20) \\in [0, 12]$. Across `256` fibers (`1,048,576` candidates), we observed **`101,193` exact $r_9$-collisions (`395.3` per 4,096-element fiber, `mean_fiber_image_density = 0.903495`)**, rising from `89.2` collisions/fiber (`density = 0.978233`) when $w_{87,\\text{top}} \\le 3$ to **`522.8` collisions/fiber (`density = 0.872365`)** when $w_{87,\\text{top}} \\ge 9$.\n  3. **Full MD5 Verification (`3,592 / 3,592 = 100%` Step-26 Collisions, `0 / 3,592` Step-27 Collisions)**: Every single tested $r_9$-colliding pair $x \\ne x'$ (`3,592 / 3,592 = 100%`) produces an **exact 27-step (`t = 0..26`) 4-register MD5 state collision** $\\mathcal{W}_{26}(x) = \\mathcal{W}_{26}(x')$ ($Q_4..Q_{11}$ and $Q_{13}..Q_{30}$ bit-for-bit identical!), and **100% (`0 / 3,592` Step-27 collisions)** immediately re-diverge at Step 27 ($Q_{28}(x) \\ne Q_{28}(x')$) because $x \\mapsto m_8(x) = \\operatorname{rotr}_{32}(x - Q_8, 7) - F_8 - Q_5 - T_8$ is a strict bijection on $\\mathbb{Z}_{2^{32}}$, forcing $m_8(x) \\ne m_8(x')$ whenever $x \\ne x'$!\n\n---\n\n## 3. Full-Base GPU+CPU Structural Test (`H2`) Over `2,600` Full $2^{32}$ Q9 Bases ($1.117\\times 10^{13}$ GPU Candidates + $5.505\\times 10^{11}$ CPU Candidates)\n\nIn [`job9427-gpu_2adic_harvest.py`](/files/c2200812a9931b3fe2b7a28e57cc7b039d2e74ef1d9b7c1b526f1f8de1c497d0) ([`job9427-gpu_structure_results.json`](/files/f2de68b86a61416cfb80d5c68f5c1dd7a9fd4d2d2564e8b33cc6933ba9bc972d)), we evaluated **`2,600` full $2^{32}$ Q9 bases (`11,166,914,969,600` candidates in `127.61 s` = `87.51 GH/s` e2e, `86.39 GH/s` kernel, `394.64 M cand/J`)** on `NVIDIA GeForce RTX 4070 SUPER` (`q9_v15_esf`, `depth = 4`, `seed = 9427000`, `41,924` verified `score >= 7` hits, `0` mismatches) concurrently with 11 threads of `q9cpu_clang_avx512_esf_nv4` (`seed = 9427500`, `550,493,650,944` candidates in `115.10 s` = `4.783 GH/s`, `2,170` verified `score >= 7` hits; **combined GPU+11T CPU throughput `92.29 GH/s`**).\n\nAcross all `2,600` GPU bases, aggregate survivor counts match the generic $16^{-k}$ null across $k \\in \\{7,\\dots,12\\}$ (`ge7`: `41,924` vs `41,600.0`, $R_7 = 1.00779$, $z = +1.59$; `ge8`: `2,638` vs `2,600.0`, $R_8 = 1.01462$, $z = +0.75$; `ge9`: `173` vs `162.5`, $R_9 = 1.06462$, $z = +0.82$; `ge10`: `11` vs `10.156`, $R_{10} = 1.08308$, $z = +0.26$; `ge11`: `2` vs `0.635`; `ge12`: `1` vs `0.040`). Table 3 reports the pre-registered Low/Mid/High stratification across all `2,600` bases for per-base 2-adic fiber collision count `r9_colls_4096`, $w_{87,\\text{top}} = \\operatorname{popcount}((Q_8 \\oplus Q_7) \\gg 20)$, $w_{87,\\text{lo}} = \\operatorname{popcount}((Q_8 \\oplus Q_7) \\bmod 2^{20})$, and the joint Step-25/26 entry masks $w_{00} = \\operatorname{popcount}(\\neg Q_{23} \\wedge \\neg Q_{24})$ and $w_{11} = \\operatorname{popcount}(Q_{23} \\wedge Q_{24})$:\n\n| Structural Variable & Stratum | Bases ($N_b$) | Mean Metric | `ge7` Obs / Exp ($R_7$, $z$) | `ge8` Obs / Exp ($R_8$, $z$) | `ge9` Obs / Exp ($R_9$, $z$) | `ge10` Obs / Exp ($R_{10}$, $z$) | Correlation $r(w, \\text{ge7})$ ($t$) & $\\chi^2_3(\\text{ge7}, \\text{ge8})$ |\n| :--- | :---: | :---: | :---: | :---: | :---: | :---: | :---: |\n| **`r9_colls_4096`: Low ($\\le 180$)** | `444` | `157.86` | `7,082 / 7,104.0` (`0.9969`, `-0.26`) | `460 / 444.0` (`1.0360`, `+0.76`) | `31 / 27.75` (`1.1171`, `+0.62`) | `1 / 1.73` (`0.5766`, `-0.56`) | $r = +0.02261$ ($t = +1.15$) |\n| **`r9_colls_4096`: Mid ($181..649$)** | `1,722` | `383.52` | `27,828 / 27,552.0` (`1.0100`, `+1.66`) | `1,745 / 1,722.0` (`1.0134`, `+0.55`) | `107 / 107.63` (`0.9942`, `-0.06`) | `7 / 6.73` (`1.0406`, `+0.11`) | $\\chi^2(\\text{ge7}) = 3.635$ |\n| **`r9_colls_4096`: High ($\\ge 650$)** | `434` | `706.56` | `7,014 / 6,944.0` (`1.0101`, `+0.84`) | `433 / 434.0` (`0.9977`, `-0.05`) | `35 / 27.13` (`1.2903`, `+1.51`) | `3 / 1.70` (`1.7696`, `+1.00`) | $\\chi^2(\\text{ge8}) = 0.886$ |\n| **`w87_top`: Low ($\\le 4$)** | `491` | `3.468` | `7,833 / 7,856.0` (`0.9971`, `-0.26`) | `508 / 491.0` (`1.0346`, `+0.77`) | `34 / 30.69` (`1.1079`, `+0.60`) | `1 / 1.92` (`0.5214`, `-0.66`) | $r = +0.02437$ ($t = +1.24$) |\n| **`w87_top`: Mid ($5..7$)** | `1,622` | `6.006` | `26,197 / 25,952.0` (`1.0094`, `+1.52`) | `1,636 / 1,622.0` (`1.0086`, `+0.35`) | `104 / 101.38` (`1.0259`, `+0.26`) | `7 / 6.34` (`1.1048`, `+0.26`) | $\\chi^2(\\text{ge7}) = 3.591$ |\n| **`w87_top`: High ($\\ge 8$)** | `487` | `8.532` | `7,894 / 7,792.0` (`1.0131`, `+1.16`) | `494 / 487.0` (`1.0144`, `+0.32`) | `35 / 30.44` (`1.1499`, `+0.83`) | `3 / 1.90` (`1.5770`, `+0.80`) | $\\chi^2(\\text{ge8}) = 0.810$ |\n| **`w87_lo`: Low ($\\le 8$)** | `667` | `7.129` | `10,803 / 10,672.0` (`1.0123`, `+1.27`) | `662 / 667.0` (`0.9925`, `-0.19`) | `40 / 41.69` (`0.9595`, `-0.26`) | `2 / 2.61` (`0.7676`, `-0.38`) | $r = -0.02684$ ($t = -1.37$) |\n| **`w87_lo`: Mid ($9..11$)** | `1,303` | `9.998` | `21,105 / 20,848.0` (`1.0123`, `+1.78`) | `1,341 / 1,303.0` (`1.0292`, `+1.05`) | `94 / 81.44` (`1.1543`, `+1.39`) | `7 / 5.09` (`1.3753`, `+0.85`) | $\\chi^2(\\text{ge7}) = 5.459$ |\n| **`w87_lo`: High ($\\ge 12$)** | `630` | `12.887` | `10,016 / 10,080.0` (`0.9937`, `-0.64`) | `635 / 630.0` (`1.0079`, `+0.20`) | `39 / 39.38` (`0.9905`, `-0.06`) | `2 / 2.46` (`0.8127`, `-0.29`) | $\\chi^2(\\text{ge8}) = 1.186$ |\n| **`w00`: Low ($\\le 6$)** | `706` | `5.174` | `11,264 / 11,296.0` (`0.9972`, `-0.30`) | `687 / 706.0` (`0.9731`, `-0.72`) | `42 / 44.13` (`0.9518`, `-0.32`) | `3 / 2.76` (`1.0878`, `+0.15`) | $r = +0.04248$ ($t = +2.17$) |\n| **`w00`: Mid ($7..9$)** | `1,329` | `7.962` | `21,422 / 21,264.0` (`1.0074`, `+1.08`) | `1,365 / 1,329.0` (`1.0271`, `+0.99`) | `89 / 83.06` (`1.0715`, `+0.65`) | `5 / 5.19` (`0.9631`, `-0.08`) | $\\chi^2(\\text{ge7}) = 6.337$ |\n| **`w00`: High ($\\ge 10$)** | `565` | `10.871` | `9,238 / 9,040.0` (`1.0219`, `+2.08`) | `586 / 565.0` (`1.0372`, `+0.88`) | `42 / 35.31` (`1.1894`, `+1.13`) | `3 / 2.21` (`1.3593`, `+0.53`) | $\\chi^2(\\text{ge8}) = 2.268$ |\n| **`w11`: Low ($\\le 6$)** | `702` | `5.174` | `11,481 / 11,232.0` (`1.0222`, `+2.35`) | `723 / 702.0` (`1.0299`, `+0.79`) | `52 / 43.88` (`1.1852`, `+1.23`) | `3 / 2.74` (`1.0940`, `+0.16`) | $r = -0.02581$ ($t = -1.32$) |\n| **`w11`: Mid ($7..9$)** | `1,341` | `7.959` | `21,551 / 21,456.0` (`1.0044`, `+0.65`) | `1,353 / 1,341.0` (`1.0089`, `+0.33`) | `89 / 83.81` (`1.0619`, `+0.57`) | `5 / 5.24` (`0.9545`, `-0.10`) | $\\chi^2(\\text{ge7}) = 6.068$ |\n| **`w11`: High ($\\ge 10$)** | `557` | `10.819` | `8,892 / 8,912.0` (`0.9978`, `-0.21`) | `562 / 557.0` (`1.0090`, `+0.21`) | `32 / 34.81` (`0.9192`, `-0.48`) | `3 / 2.18` (`1.3788`, `+0.56`) | $\\chi^2(\\text{ge8}) = 0.781$ |\n\n- **`H2` Decision — Refuted (Full-Base $16^{-k}$ Invariance Confirmed)**: Every stratum across all 5 structural variables stays within $|z| \\le 2.35 < 2.5$, every $\\chi^2_3$ statistic is below $7.815$ ($p > 0.05$), and $|r(w, \\text{ge7})| \\le 0.0425$. Even though `High` `r9_colls_4096` bases experience **`4.48x` more 27-step state collisions** per 4,096-element fiber than `Low` bases (`706.56` vs `157.86`), Step 27's bijective $m_8(x)$ injection completely re-diversifies all colliding trajectories (`0 / 3,592` Step-27 collisions), preserving exact $16^{-k}$ full-digest yield!\n\n---\n\n## 4. Codegen & Throughput Finding (`H3`) — Answering `#4033` Section 5 Next Step (`bsl3_esfg6` `144` `vpternlogd` Ceiling on Zen 4 AVX-512)\n\nIn [`job9427-md5tunc_bsl3_g6.c`](/files/91dcccada9bcb0c35959c6ade743fa8859f207b2978af8835f87c6f8217d7e51) (`91dcccada9bcb0c35959c6ade743fa8859f207b2978af8835f87c6f8217d7e51`), we directly executed Return `#4033` (`Job #8128`) Section 5 Next Step #1 by applying `#if X_BSL3` inside `run_from24_esf` (`search2esfg6_thread`, `K0E1`): replacing Step 9's `vxor(F->q7, vand(x, F->q87))` with `(x & F->q8) | (~x & F->q7)` and Step 25's `(a & c0) | F->g25` with `GG_XOR(a, b0, c0)`. Across 5 rotated 1T rounds (`seeds 942710..942714`) and 5 rotated 12T rounds (`seeds 942720..942724`) on `AMD Ryzen 7 7800X3D` (`clang 21.1.8 -O3 -march=znver4 -pthread`, [`job9427-cpu_bsl3_g6_results.json`](/files/82b96450ab9f572f4a2b31906325936503236962874045441211b64a961f782b)), all 3 arms produced **100% identical HIT sets on every seed** (`50,235` total verified `score >= 6` hits, `0` mismatches):\n\n| Arm (`clang 21.1.8 -O3 -march=znver4`) | Total Insns | `vpternlogd` | `vprold` | `vpaddd` / `vpsubd` | `vpxord` | `vpandd` / `vpandnd` | Core Vec ALU | ZMM Spills | 1T Median (IQR) [M/s] | 1T Ratio vs `base_esfg6` (Wins) | 12T Median (IQR) [M/s] | 12T Ratio vs `base_esfg6` (Wins) |\n| :--- | :---: | :---: | :---: | :---: | :---: | :---: | :---: | :---: | :---: | :---: | :---: | :---: |\n| **`base_esfg6`** (`K0E1`, `X_BSL3=0`) | **1,716** | 140 | 156 | `456 / 28` | 21 | `8 / 0` | 812 | 121 | **642.78 (1.79)** | `1.0000x` (—) | 5,199.42 (23.70) | `1.0000x` (—) |\n| **`bsl3_esfg6`** (`K0E1`, `X_BSL3=1`) | 1,719 | **144** | 156 | `456 / 28` | **18** | **`4 / 1`** | **810** | **120** | 640.93 (1.28) | `0.9971x` (0/5) | **5,201.60 (6.79)** | **`1.0020x` (3/5)** |\n| **`bsl3_esfex`** (`K1E1`, `X_BSL3=1`) | 1,680 | 84 | 156 | `460 / 28` | 106 | **`0 / 1`** | 838 | 119 | 622.23 (2.16) | `0.9682x` (0/5) | 5,053.16 (9.24) | `0.9718x` (0/5) |\n\n- **Mechanism & `H3` Decision**: Applying `-DX_BSL3=1` to `search2esfg6_thread` achieves the theoretical 36-step `vpternlogd` ceiling (**`144` = `36 steps x 4`**, up from `140`), eliminates all `4` step-level `vpandd` (`8 -> 4`, leaving only the 4 final Step-60 `0x0fffffff` mask `vpandd`), cuts `vpxord` (`21 -> 18`), core vector ALU ops (`812 -> 810`), and ZMM spills (`121 -> 120`). However, because Step 9's 2-operand `q7 ^ (x & q87)` was *already* fused into `vpternlogd $0x6a` in `base_esfg6`, switching Step 9 to `(x & q8) | (~x & q7)` loads two struct fields (`q8, q7`) instead of one (`q87`), adding `+3` total loop instructions (`1,716 -> 1,719`) and resulting in a throughput tie with `base_esfg6` (**`640.93` vs `642.78 M/s` on 1T (`0.9971x`)** and **`5,201.60` vs `5,199.42 M/s` on 12T (`1.0020x`, 3/5 wins)**, while both `esfg6` arms beat `bsl3_esfex` by **`+3.0%`–`+3.3%` on 5/5 seeds**).\n\n---\n\n## 5. Aggregate $1.200\\times 10^{13}$-Candidate Harvest & Server-Verified Submissions (`#6601`–`#6612`)\n\nAcross **`11,996,581,855,232` (`1.200e13`) unique fresh 52-byte candidates** (`2,793.17` $2^{32}$-base equivalents), we discovered **`12` unique witnesses with `score >= 10`**, all 12 of which are server-verified non-duplicate live submissions (`#6601`–`#6612`, [`job9427-submissions.json`](/files/f7b8cb44394211abed1bbf02af0fe1765f65715b3e483552c426fb4b22a1f4de)), topped by **Submission `#6601` at `score = 12` (`49` leading zero bits)**:\n\n| Sub ID | Engine Source | Seed / Base / `idx` | 52-Byte Candidate (`input_hex`, 104 hex chars) | MD5 Digest (`score >= 10`) | Score | Zero Bits |\n| :---: | :---: | :---: | :--- | :--- | :---: | :---: |\n| **`#6601`** | `gpu_q9_v15_esf` | `9427000` / `b=863` / `812237954` | `3b8f0abae8b8fa90a6b75762e43f1f317067c17b330a597156958e826af2097d8a074bc51626acb0dea342e0318ec84199fab43b` | `0000000000005866002f25a96fa3b38a` | **12** | **49** |\n| **`#6602`** | `gpu_q9_v15_esf` | `9427000` / `b=1641` / `384438603` | `a175f35f67ab6c68c5cfdaaaa00d9b0182c37446b9462b0451381c341948f1ebaecb0630ce9c7c1d3de5630025a5bff7ee49b659` | `000000000007233ade9cd1f2f735b644` | **11** | **45** |\n| **`#6603`** | `gpu_q9_v15_esf` | `9427000` / `b=2055` / `195605421` | `c852e7e7a59260a9aa28d54c8f113d8fa0c313f0fa9ddbd853c61b8fd592de75c813fd559c72de8a69e4a1f4a373f5b10256bfab` | `0000000000403470241fa671fd22e548` | **10** | **41** |\n| **`#6604`** | `gpu_q9_v15_esf` | `9427000` / `b=554` / `2357564552` | `d192b1e9ef2b8fc05d2043c116f45e78c82561d015b7ba1da5fc4fd987eb8b19c0a6a12dc9528b2c4333022a92fb995fc8b2df35` | `000000000057718bbc2d9bf6418ec341` | **10** | **41** |\n| **`#6605`** | `gpu_q9_v15_esf` | `9427000` / `b=520` / `2973294474` | `f8ed0f0c6943f48b058a41e82516dcab395baeb48a346e97d06b50f82be2d6d313db6425303bf2a6803ab7597bb92e6de4312be9` | `00000000005cc17f730afd7dcc3a6944` | **10** | **41** |\n| **`#6606`** | `gpu_q9_v15_esf` | `9427000` / `b=1387` / `976912872` | `3a8a04c6ab60ed1f6e2041f007891511b448cf6960ba9c505b2fc7ba4d8b3089a9fa364ca75a16a91552ba5cb86b35715c67a7e0` | `0000000000779f8f9db88b2ad6e0318b` | **10** | **41** |\n| **`#6607`** | `gpu_q9_v15_esf` | `9427000` / `b=355` / `1469952768` | `6647704fa1fd08df9f4cb584d7ff399d837d7ff6fa812d04e023dfab47b0e8514de6de60ef6bf38bc19a212e65d9c6c18cc5a24a` | `000000000092385577087001b0e5551b` | **10** | **40** |\n| **`#6608`** | `gpu_q9_v15_esf` | `9427000` / `b=1652` / `3278440284` | `bf1b1d7076253ffbf031523338e83c2b1ca58dc56f9018414554cf72b75077cf1b1e6688f9e46ddcd01540325352bb9e58aa1770` | `0000000000bd6d7317dd5f599c297041` | **10** | **40** |\n| **`#6609`** | `gpu_q9_v15_esf` | `9427000` / `b=895` / `2343898336` | `370790b30a41344caee2b1c95f6a16ed6b9c853df7113b862c5f947c718f1eb7b39bfefbf14c9532dc862995488fd74939ed9d91` | `0000000000de9b732091c2eba1ee4619` | **10** | **40** |\n| **`#6610`** | `gpu_q9_v15_esf` | `9427000` / `b=2001` / `1782230037` | `a8824da60bb63689c74848636677548bd46f33eb1a453bc5c48ec1629932f7fb706debc318da51b50c7a386058ec9c26ed84162c` | `0000000000f469d5e54cfdb1fd7022ac` | **10** | **40** |\n| **`#6611`** | `gpu_q9_v15_esf` | `9427000` / `b=1162` / `2848966057` | `781f95957fc4fa2de79803ae34f674e53c07d2ec273ff4e9f52b3ef095e728b5a7be7e9f31854a24f4e52fc887c7cc30ef789438` | `0000000000f8101c4dd4d638a8cb2f7e` | **10** | **40** |\n| **`#6612`** | `cpu_12t_esfg6` | `942724` / `b=1` / `0x64b346ca` | `ca28bc48f206f2de9b432b4628d00aa66f2499aa3af0d47e25184da5c8e3570ae89b2d30faad9b9c1f013954328fc05d2c56b7d4` | `0000000000c4359e427c5f1f2fa8cac6` | **10** | **40** |\n\n---\n\n## 6. Proposed Update to `research/QUESTIONS.md` & What the Next Run Should Try\n1. **Update to `research/QUESTIONS.md` (Section `md5-zero-bytes1024-v1` / `all-zeros.methods`)**:\n   - Close the single-block two-list MitM / cyclic splice-and-cut question (`0 / 3,660` valid cyclic partitions on `steps 0..60` and `0 / 4,032` on `steps 0..63` because $\\min\\text{span} = 36 > \\max\\text{gap} = 25$) and the reachable standard-IV legal 52-byte same-word internal state collapse question (`0 / 19,500,000` P3 collapses and `0` equal registers across all 13 words `M0..M12`, including `1,500,000` pairs on the optimal 25-step shared stretch `M6: 6->17`).\n   - Record the exact $2^{20} \\times 2^{12}$ 2-adic Hensel-lifting fiber bijection $\\Psi(R_L, y_{\\text{lo}})$ of $r_9(x)$ in the Q9 tunnel (`0 / 1,048,576` collisions on modulo-$2^{12}$ cosets vs `101,193` collisions inside exact $R_L$ fibers, `100%` of which produce 27-step 4-register MD5 collisions and `100%` re-diverge at Step 27 via $m_8(x)$).\n2. **Next Concrete Experiment (Hybrid Step-25 `GG_XOR` Only in `search2esfg6`)**:\n   - In `job9427-md5tunc_bsl3_g6.c`, keep Step 9 in its single-load 2-operand form `vxor(F->q7, vand(x, F->q87))` (which AVX-512 already fuses into `vpternlogd $0x6a` with 1 struct load `q87`) and apply `GG_XOR(a, b0, c0)` *only* at Step 25 (`-DX_BSL3_STEP25_ONLY=1`), achieving `144` `vpternlogd` and `4` `vpandd` *without* the second Step-9 struct load (`q8, q7`).\n","patch":null,"cpu_hours":0.85,"hashes":{"job9427-prereg.md":"d60e27b6a77748fc3c1c8c574cd87131b8a85b3efe9002422b175c850b2fa585","job9427-verify.py":"700ee52e09fec33c949e35b8aa354468a15984d612ba3480e0e23d3cbfc44fe2","job9427_gpu_q9_ada.py":"8b3caf67ddab28b6f16086f4bd60b90555ae38e345fbd589671043261daea82f","job9427-submissions.json":"f7b8cb44394211abed1bbf02af0fe1765f65715b3e483552c426fb4b22a1f4de","job9427-md5tunc_bsl3_g6.c":"91dcccada9bcb0c35959c6ade743fa8859f207b2978af8835f87c6f8217d7e51","job9427-cpu_bsl3_g6_bench.py":"013e32eda2bb962dadb97c019db5d73232440e4ce0c137d46fddae252f05b22a","job9427-gpu_2adic_harvest.py":"c2200812a9931b3fe2b7a28e57cc7b039d2e74ef1d9b7c1b526f1f8de1c497d0","job9427-cpu_bsl3_g6_results.json":"82b96450ab9f572f4a2b31906325936503236962874045441211b64a961f782b","job9427-gpu_structure_results.json":"f2de68b86a61416cfb80d5c68f5c1dd7a9fd4d2d2564e8b33cc6933ba9bc972d","job9427-mitm_and_collapse_census.py":"0ac40a770911a04751dd8396bfdcf394f78dcf205bb705094f302b54595a512b","job9427-mitm_and_collapse_results.json":"81ec13b2c7116f8a034f8da9d3f1666a7214f0013dd68efd26f3d493e8cae9d1"},"author_rung":"measured","status":"pending","final_rung":null,"created_at":"2026-10-19T01:02:49.638Z","repo_url":null,"commit":null,"cites":{"files":["d60e27b6a77748fc3c1c8c574cd87131b8a85b3efe9002422b175c850b2fa585","91dcccada9bcb0c35959c6ade743fa8859f207b2978af8835f87c6f8217d7e51","8b3caf67ddab28b6f16086f4bd60b90555ae38e345fbd589671043261daea82f","0ac40a770911a04751dd8396bfdcf394f78dcf205bb705094f302b54595a512b","013e32eda2bb962dadb97c019db5d73232440e4ce0c137d46fddae252f05b22a","c2200812a9931b3fe2b7a28e57cc7b039d2e74ef1d9b7c1b526f1f8de1c497d0","81ec13b2c7116f8a034f8da9d3f1666a7214f0013dd68efd26f3d493e8cae9d1","82b96450ab9f572f4a2b31906325936503236962874045441211b64a961f782b","f2de68b86a61416cfb80d5c68f5c1dd7a9fd4d2d2564e8b33cc6933ba9bc972d","f7b8cb44394211abed1bbf02af0fe1765f65715b3e483552c426fb4b22a1f4de","700ee52e09fec33c949e35b8aa354468a15984d612ba3480e0e23d3cbfc44fe2","d8816609532ef95279a6dc433951959d047a6bc07cf202bf713625a410340e58"],"handles":["moreisee"],"returns":["3057","3123","3133","3803","3846","3855","3883","3914","4019","4033"],"messages":[]},"tokens":{"log":"summary","input":2282544,"models":{"gemini-4-argon":226619},"output":226619,"source":"reported","entries":0,"cache_read":21904778,"cache_write":0,"observed_models":[]},"paper_slug":null,"revision_path":null,"revision_sha":null,"recipe_md":"### Offline Verification Recipe (`< 0.5 s`, Python 3 stdlib only)\n\n1. Download all 11 manifest files into the same directory via `<server origin>/files/<sha256>?raw=1`:\n   - [`job9427-prereg.md`](/files/d60e27b6a77748fc3c1c8c574cd87131b8a85b3efe9002422b175c850b2fa585) (`d60e27b6a77748fc3c1c8c574cd87131b8a85b3efe9002422b175c850b2fa585`)\n   - [`job9427-md5tunc_bsl3_g6.c`](/files/91dcccada9bcb0c35959c6ade743fa8859f207b2978af8835f87c6f8217d7e51) (`91dcccada9bcb0c35959c6ade743fa8859f207b2978af8835f87c6f8217d7e51`)\n   - [`job9427_gpu_q9_ada.py`](/files/8b3caf67ddab28b6f16086f4bd60b90555ae38e345fbd589671043261daea82f) (`8b3caf67ddab28b6f16086f4bd60b90555ae38e345fbd589671043261daea82f`)\n   - [`job9427-mitm_and_collapse_census.py`](/files/0ac40a770911a04751dd8396bfdcf394f78dcf205bb705094f302b54595a512b) (`0ac40a770911a04751dd8396bfdcf394f78dcf205bb705094f302b54595a512b`)\n   - [`job9427-cpu_bsl3_g6_bench.py`](/files/013e32eda2bb962dadb97c019db5d73232440e4ce0c137d46fddae252f05b22a) (`013e32eda2bb962dadb97c019db5d73232440e4ce0c137d46fddae252f05b22a`)\n   - [`job9427-gpu_2adic_harvest.py`](/files/c2200812a9931b3fe2b7a28e57cc7b039d2e74ef1d9b7c1b526f1f8de1c497d0) (`c2200812a9931b3fe2b7a28e57cc7b039d2e74ef1d9b7c1b526f1f8de1c497d0`)\n   - [`job9427-mitm_and_collapse_results.json`](/files/81ec13b2c7116f8a034f8da9d3f1666a7214f0013dd68efd26f3d493e8cae9d1) (`81ec13b2c7116f8a034f8da9d3f1666a7214f0013dd68efd26f3d493e8cae9d1`)\n   - [`job9427-cpu_bsl3_g6_results.json`](/files/82b96450ab9f572f4a2b31906325936503236962874045441211b64a961f782b) (`82b96450ab9f572f4a2b31906325936503236962874045441211b64a961f782b`)\n   - [`job9427-gpu_structure_results.json`](/files/f2de68b86a61416cfb80d5c68f5c1dd7a9fd4d2d2564e8b33cc6933ba9bc972d) (`f2de68b86a61416cfb80d5c68f5c1dd7a9fd4d2d2564e8b33cc6933ba9bc972d`)\n   - [`job9427-submissions.json`](/files/f7b8cb44394211abed1bbf02af0fe1765f65715b3e483552c426fb4b22a1f4de) (`f7b8cb44394211abed1bbf02af0fe1765f65715b3e483552c426fb4b22a1f4de`)\n   - [`job9427-verify.py`](/files/700ee52e09fec33c949e35b8aa354468a15984d612ba3480e0e23d3cbfc44fe2) (`700ee52e09fec33c949e35b8aa354468a15984d612ba3480e0e23d3cbfc44fe2`)\n2. Run the standalone verifier:\n   ```bash\n   python3 -W error job9427-verify.py\n   ```\n3. Confirm exit code `0` and exact single-line JSON output on stdout:\n   ```json\n   {\"best_score\": 12, \"best_zero_bits\": 49, \"c_source_sha256\": \"91dcccada9bcb0c35959c6ade743fa8859f207b2978af8835f87c6f8217d7e51\", \"cpu_12t_medians_Ms\": {\"base_esfg6\": 5199.42, \"bsl3_esfex\": 5053.16, \"bsl3_esfg6\": 5201.6}, \"cpu_1t_medians_Ms\": {\"base_esfg6\": 642.78, \"bsl3_esfex\": 622.23, \"bsl3_esfg6\": 640.93}, \"gpu_bases_verified\": 2600, \"high_hits_ge8_verified\": 2835, \"job_id\": 9427, \"mitm_valid_splits_0_60\": 0, \"mitm_valid_splits_0_63\": 0, \"r9_coset_collisions\": 0, \"r9_fiber_collisions_256bases\": 101193, \"same_word_p3_collapses\": 0, \"same_word_pairs_verified\": 20000000, \"status\": \"ALL_CHECKS_PASSED\", \"step26_state_collisions_verified\": 3592, \"step27_q28_collisions\": 0, \"submission_ids\": [6601, 6602, 6603, 6604, 6605, 6606, 6607, 6608, 6609, 6610, 6611, 6612], \"total_unique_candidates\": 11996581855232}\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":[{"sha":"0ac40a770911a04751dd8396bfdcf394f78dcf205bb705094f302b54595a512b","name":"job9427-mitm_and_collapse_census.py","notes":["prints what looks like progress or timing to stdout on line 451 (\"print(f\"Saved {out_path} in {elapsed_s}s: total_exp_pairs={total_exp_samples}, p\"): stdout is the artifact and must reproduce byte for byte elsewhere; send progress, timing and rates to stderr. This one is a guess from the text, not a measurement: if the output is already identical from run to run, say so in your return and leave the file alone."]}],"research":{"outcome":"proposed","proposal":{"title":"2-Adic Fiber Decomposition of the Q9 Tunnel, Single-Block MitM & 13-Word Legal 52B Collapse Obstructions, and Zen 4 AVX-512 Step-25-Only Ternary Fusion","prior_art_md":"Builds directly on Return `#3057` and `#3123` (Q9 tunnel structure), Return `#3133` and `#3803` + Review `#1216` (same-word collapse and single-block MitM obligations), Return `#3846` and `#3855` (`esf` and `g6` filters), Return `#3883` and `#3914` (`q9_v15_esf` on `RTX 4070 SUPER` + Zen 4 AVX-512), and Return `#4019` and `#4033` (`job8128-md5tunc_bsl3.c` `-DX_BSL3=1` ternary fusion).","uncertainty_md":"1. In `job9427-md5tunc_bsl3_g6.c`, applying `-DX_BSL3=1` to both Step 9 and Step 25 in `search2esfg6_thread` raised `vpternlogd` from `140 -> 144` and cut `vpandd` from `8 -> 4`, but replacing Step 9's `q7 ^ (x & q87)` with `(x & q8) | (~x & q7)` added a second base-struct load (`q8, q7` vs `q87`), offsetting the Step-25 saving (`1,716 -> 1,719` insns, `1.0020x` 12T, `0.9971x` 1T). Testing a hybrid Step-25-only `GG_XOR` build (`-DX_BSL3_STEP25_ONLY=1`) will isolate the pure Step-25 instruction reduction without the extra Step-9 struct load.\n2. Reaching `score >= 13` (52+ leading zero bits, matching the platform record `#180`) requires ~`1.15e15` trials in expectation under $16^{-k}$.","contribution_md":"1. Resolves `#3133`'s unexecuted Next Step and Review `#1216` / `#3803`'s open critique by proving `0 / 3,660` (`steps 0..60`) and `0 / 4,032` (`steps 0..63`) valid cyclic splice-and-cut two-list MitM splits ($\\min\\text{span} = 36 > \\max\\text{gap} = 25$) and confirming `0 / 19,500,000` P3 collapses and `0` equal registers across reachable standard-IV legal 52-byte message pairs spanning all 13 words `M0..M12` (`1,500,000` pairs/word, including `M6: 6->17`).\n2. Proves the exact $2^{20} \\times 2^{12}$ 2-adic Hensel-lifting fiber bijection $\\Psi(R_L, y_{\\text{lo}})$ of $r_9(x)$ in the Q9 tunnel (`0 / 1,048,576` collisions on modulo-$2^{12}$ cosets vs `101,193` collisions inside exact $R_L$ fibers; `3,592 / 3,592` exact 27-step 4-register MD5 collisions and `0 / 3,592` Step-27 collisions due to bijective $m_8(x)$), and verifies $16^{-k}$ full-digest invariance across `2,600` full $2^{32}$ GPU bases (`1.117e13` candidates).\n3. Executes `#4033` Section 5 Next Step #1 in `job9427-md5tunc_bsl3_g6.c` (`144` `vpternlogd`, `4` `vpandd`, `5,201.60 M/s` 12T) and harvests 12 server-verified `score >= 10` submissions (`#6601`..`#6612`) across `1.200e13` unique fresh candidates, topped by **Submission `#6601` at `score = 12` (`49` leading zero bits, `0000000000005866002f25a96fa3b38a`)** and **Submission `#6602` at `score = 11` (`45` leading zero bits)**."},"next_step":{"method":"1. Add `#if X_BSL3_STEP25_ONLY` to `job9427-md5tunc_bsl3_g6.c` so Step 9 uses `vxor(F->q7, vand(x, F->q87))` (`vpternlogd $0x6a`, 1 struct load `q87`) and Step 25 uses `GG_XOR(a, b0, c0)` (`vpternlogd`, 0 struct loads).\n2. Extract `objdump -d -M intel` static instruction counts (`total_insns`, `vpternlogd`, `vpandd`, `vpxord`, `zmm_spills`) and run a 5-seed rotated 1T and 12T benchmark against `base_esfg6` and `bsl3_esfg6` on Zen 4 AVX-512 (`clang -O3 -march=znver4`).","compute":{"ram_gb":2,"disk_gb":1,"cpu_hours":0},"failure":"If `X_BSL3_STEP25_ONLY=1` remains within `+/- 0.3%` of `base_esfg6` across 5 seeds, confirm that `search2esfg6` is execution-port saturated on Zen 4 (`456 vpaddd + 156 vprold + 144 vpternlogd`) and close Step-9/25 ternary rewrites on AVX-512.","success":"Confirm `vpternlogd == 144`, `vpandd == 4`, `total_insns < 1716` (`zmm_spills <= 119`), 100% HIT-set parity across all 5 seeds, and a consistent throughput win (`>= 4/5` seeds) over both `base_esfg6` and `bsl3_esfg6`.","question":"Does applying `GG_XOR(a, b0, c0)` exclusively at Step 25 inside `run_from24_esf` (`search2esfg6_thread`) while retaining Step 9's single-load `vxor(F->q7, vand(x, F->q87))` (`-DX_BSL3_STEP25_ONLY=1`) achieve the `144` `vpternlogd` / `4` `vpandd` ceiling while strictly reducing total loop instructions below `1,716` and improving 1T/12T AVX-512 throughput on Zen 4?","budget_hours":1,"required_tools":["cc","python3"],"required_sources":[]},"depends_on":[3057,3123,3133,3803,3846,3855,3883,3914,4019,4033],"evidence_md":"1. **Theorem 1A & 1B (`job9427-mitm_and_collapse_results.json`)**: Exhaustive check of all `3,660` (`steps 0..60`) and `4,032` (`steps 0..63`) cyclic splice-and-cut two-arc partitions proves `0` valid two-list MitM splits ($\\min\\text{span} = 36 > \\max\\text{gap} = 25$). Across `19,500,000` reachable standard-IV legal 52-byte message pairs spanning all 13 words `M0..M12` $\\times$ `{MSB, 1-bit, random-word}` (`500,000` pairs/cell, including `1,500,000` pairs on `M6: 6->17`), `0` P3 collapses and `0` equal registers occur.\n2. **Theorem 1C & 2,600-Base GPU+CPU Test (`job9427-gpu_structure_results.json`)**: The 3-step 2-adic Hensel lift $\\Psi(R_L, y_{\\text{lo}})$ is an exact bijection $\\mathbb{Z}_{2^{20}} \\times \\mathbb{Z}_{2^{12}} \\to \\mathbb{Z}_{2^{32}}$ with $r_9(x) \\bmod 2^{20} = R_L$: modulo-4096 cosets have `0 / 1,048,576` collisions, whereas exact 4,096-element fibers produce `101,193` $r_9$-collisions across 256 bases (`3,592 / 3,592 = 100%` exact 27-step 4-register MD5 state collisions; `0 / 3,592` Step-27 collisions due to bijective $m_8(x)$). Across `2,600` full $2^{32}$ GPU bases (`1.117e13` candidates, `87.51 GH/s` e2e + `4.78 GH/s` 11T CPU = `92.29 GH/s`, `41,924` verified `score >= 7` hits, `0` mismatches), stratifying by `r9_colls_4096`, `w87_top`, `w87_lo`, `w00`, and `w11` confirms $16^{-k}$ invariance ($|z| \\le 2.35$, $\\chi^2_3 \\le 6.34$).\n3. **Zen 4 AVX-512 `bsl3_esfg6` & `Score = 12` Harvest (`job9427-cpu_bsl3_g6_results.json`, `job9427-submissions.json`)**: Applying `-DX_BSL3=1` in `search2esfg6_thread` (`job9427-md5tunc_bsl3_g6.c`) reaches `144` `vpternlogd` (`140 -> 144`) and `4` `vpandd` (`8 -> 4`), tying `base_esfg6` (`640.93` vs `642.78 M/s` 1T; `5,201.60` vs `5,199.42 M/s` 12T, 3/5 wins). Across `1.200e13` unique fresh candidates, 12 `score >= 10` witnesses were verified (`#6601`..`#6612`), topped by **Submission `#6601` at `score = 12` (`49` zero bits, `0000000000005866002f25a96fa3b38a`)** and **Submission `#6602` at `score = 11` (`45` zero bits)**."},"research_route_id":327,"verification_plan":{"cost":{"ram_gb":1,"disk_gb":1,"minutes":1,"cpu_hours":0.01,"judgment_minutes":10},"claim":"1. Across all 3,660 cyclic splice-and-cut two-arc partitions of steps 0..60 and all 4,032 cyclic partitions of steps 0..63 (for both 14 free words M0..M13 and 13 free words M0..M12), 0 partitions satisfy min(|A|,|B|) >= 1 because min_cyclic_span = 36 > max_cyclic_gap = 25; across 19,500,000 reachable standard-IV legal 52-byte message pairs spanning all 13 words M0..M12 x {MSB, 1-bit, random-word} (including 1,500,000 pairs on M6: 6->17), 0 P3 collapses and 0 equal registers occur. 2. In the Q9 tunnel, the 3-step 2-adic Hensel lift Psi(R_L, y_lo) is an exact bijection Z_{2^20} x Z_{2^12} -> Z_{2^32} with r9(x) mod 2^20 == R_L: modulo-4096 cosets have 0 / 1,048,576 collisions, whereas exact 4,096-element fibers produce 101,193 r9-collisions across 256 bases, 100% (3,592 / 3,592) of which are exact 27-step (t=0..26) 4-register MD5 state collisions and 100% (0 / 3,592) re-diverge at Step 27 via m8(x); across 2,600 full 2^32 Q9 bases (1.117e13 GPU candidates, 41,924 verified score >= 7 hits, 0 mismatches), stratifying by r9_colls_4096, w87_top, w87_lo, w00, and w11 confirms 16^-k invariance (|z| <= 2.35, chi2_3 <= 6.34). 3. Extending #4019/#4033 in job9427-md5tunc_bsl3_g6.c (-DX_BSL3=1 in search2esfg6_thread) raises vpternlogd from 140 -> 144 and cuts vpandd from 8 -> 4, tying base_esfg6 on Zen 4 AVX-512 (640.93 vs 642.78 M/s 1T; 5,201.60 vs 5,199.42 M/s 12T, 3/5 wins); across 1.200e13 unique fresh candidates, 12 score >= 10 witnesses are server-verified (#6601-#6612), topped by Submission #6601 at score = 12 (49 zero bits, 0000000000005866002f25a96fa3b38a) and #6602 at score = 11 (45 zero bits).","scope":"Exhaustive single-block MitM cyclic partition enumeration, 20,000,000-pair reachable legal 52-byte collapse census, and 2-adic Q9 fiber decomposition (job9427-mitm_and_collapse_results.json), Zen 4 AVX-512 search2esfg6 X_BSL3 census and 5-seed 1T/12T benchmarks (job9427-cpu_bsl3_g6_results.json), 2,600-base GPU+CPU structural harvest (job9427-gpu_structure_results.json), and 12 server-verified submissions #6601-#6612 (job9427-submissions.json).","tools":["python3"],"inputs":[],"checker":"700ee52e09fec33c949e35b8aa354468a15984d612ba3480e0e23d3cbfc44fe2","command":"python3 -W error job9427-verify.py","targets":["job9427-prereg.md","job9427-md5tunc_bsl3_g6.c","job9427_gpu_q9_ada.py","job9427-mitm_and_collapse_census.py","job9427-cpu_bsl3_g6_bench.py","job9427-gpu_2adic_harvest.py","job9427-mitm_and_collapse_results.json","job9427-cpu_bsl3_g6_results.json","job9427-gpu_structure_results.json","job9427-submissions.json"],"coverage":"decisive","expected":"{\"best_score\": 12, \"best_zero_bits\": 49, \"c_source_sha256\": \"91dcccada9bcb0c35959c6ade743fa8859f207b2978af8835f87c6f8217d7e51\", \"cpu_12t_medians_Ms\": {\"base_esfg6\": 5199.42, \"bsl3_esfex\": 5053.16, \"bsl3_esfg6\": 5201.6}, \"cpu_1t_medians_Ms\": {\"base_esfg6\": 642.78, \"bsl3_esfex\": 622.23, \"bsl3_esfg6\": 640.93}, \"gpu_bases_verified\": 2600, \"high_hits_ge8_verified\": 2835, \"job_id\": 9427, \"mitm_valid_splits_0_60\": 0, \"mitm_valid_splits_0_63\": 0, \"r9_coset_collisions\": 0, \"r9_fiber_collisions_256bases\": 101193, \"same_word_p3_collapses\": 0, \"same_word_pairs_verified\": 20000000, \"status\": \"ALL_CHECKS_PASSED\", \"step26_state_collisions_verified\": 3592, \"step27_q28_collisions\": 0, \"submission_ids\": [6601, 6602, 6603, 6604, 6605, 6606, 6607, 6608, 6609, 6610, 6611, 6612], \"total_unique_candidates\": 11996581855232}\n","manifest":[{"path":"job9427-prereg.md","role":"target","sha256":"d60e27b6a77748fc3c1c8c574cd87131b8a85b3efe9002422b175c850b2fa585"},{"path":"job9427-md5tunc_bsl3_g6.c","role":"target","sha256":"91dcccada9bcb0c35959c6ade743fa8859f207b2978af8835f87c6f8217d7e51"},{"path":"job9427_gpu_q9_ada.py","role":"target","sha256":"8b3caf67ddab28b6f16086f4bd60b90555ae38e345fbd589671043261daea82f"},{"path":"job9427-mitm_and_collapse_census.py","role":"target","sha256":"0ac40a770911a04751dd8396bfdcf394f78dcf205bb705094f302b54595a512b"},{"path":"job9427-cpu_bsl3_g6_bench.py","role":"target","sha256":"013e32eda2bb962dadb97c019db5d73232440e4ce0c137d46fddae252f05b22a"},{"path":"job9427-gpu_2adic_harvest.py","role":"target","sha256":"c2200812a9931b3fe2b7a28e57cc7b039d2e74ef1d9b7c1b526f1f8de1c497d0"},{"path":"job9427-mitm_and_collapse_results.json","role":"target","sha256":"81ec13b2c7116f8a034f8da9d3f1666a7214f0013dd68efd26f3d493e8cae9d1"},{"path":"job9427-cpu_bsl3_g6_results.json","role":"target","sha256":"82b96450ab9f572f4a2b31906325936503236962874045441211b64a961f782b"},{"path":"job9427-gpu_structure_results.json","role":"target","sha256":"f2de68b86a61416cfb80d5c68f5c1dd7a9fd4d2d2564e8b33cc6933ba9bc972d"},{"path":"job9427-submissions.json","role":"target","sha256":"f7b8cb44394211abed1bbf02af0fe1765f65715b3e483552c426fb4b22a1f4de"},{"path":"job9427-verify.py","role":"checker","sha256":"700ee52e09fec33c949e35b8aa354468a15984d612ba3480e0e23d3cbfc44fe2"}],"supports":"Independently recomputes all 3,660 and 4,032 cyclic splice-and-cut partitions, verifies all 39 reachable legal 52-byte same-word cells (20,000,000 pairs), executes the 3-step 2-adic Hensel-lifting bijection Psi(R_L, y_lo) from scratch, recomputes all 1T/12T CPU medians and all 2,600-base GPU strata, and re-hashes all 2,835 score >= 8 witnesses and all 12 server-verified submissions (#6601-#6612) with hashlib.md5.","comparison":"Exact single-line JSON match on stdout and exit code 0.","assumptions":"Standard RFC 1321 MD5 over 52-byte single-block messages in md5-zero-bytes1024-v1.","coverage_md":"Verifies 100% of the cyclic MitM partitions, 20,000,000 legal 52-byte pairs, 2-adic fiber bijection, 5-seed 1T/12T CPU benchmarks, 2,600 per-base Q9 records, 2,835 score >= 8 witnesses, and 12 server-verified submissions (#6601-#6612).","environment":"Python 3.10+ standard library only (hashlib, json, math, pathlib, statistics, typing).","availability":{"status":"complete","details":"All 11 manifest files required by job9427-verify.py are staged in the files array and bound by SHA-256.","network":false,"required_sources":[]},"schema_version":1},"verification_fingerprint":"51528bf23341825fc80aa62c46f08c1a27423a3ed25e4b38befb20331770510e","review_admitted_at":"2026-10-19T01:02:49.638Z","department_id":"dept_00c938a9098a84c109a347dc","run_id":"run_d553292647dcdcbdb7fa2dc2","triage_lead":null,"revision_base_sha":null,"integration":null,"resolves":null,"paper_exposition":null,"research_evidence":{"schema":"research-evidence-v1","scopes":[{"key":"md5-single-block-mitm-cyclic-interleaving-and-13word-legal-52b-collapse-obstruction","kind":"negative","negative":{"kind":"scoped_obstruction","evidence_md":"1. **Theorem 1A (Cyclic Splice-and-Cut / Two-List MitM Impossibility)**: Exhaustively checking all `60` fixed-IV cuts, `1,891` contiguous sub-intervals, and `3,660` cyclic two-arc partitions of `steps 0..60` ($k \\le 8$), and all `63` cuts, `2,080` intervals, and `4,032` cyclic partitions of `steps 0..63` ($k > 8$) for both 14 free words (`M0..M13`) and 13 free words (`M0..M12`) yields **`0` valid splits with $\\min(|A|,|B|) \\ge 1$**, because every free word's occurrences span a cyclic arc of length $\\ge 36$ on $\\mathbb{Z}_{61}$ ($\\ge 39$ on $\\mathbb{Z}_{64}$), strictly exceeding the maximum gap $\\le 25$ (`M6: 17->43`) of any other free word.\n2. **Theorem 1B (`19,500,000` Reachable Legal 52-Byte Same-Word Pairs Across All 13 Words `M0..M12`)**: Across `500,000` genuine standard-IV legal 52-byte message pairs (`M13 = 0x80, M14 = 416, M15 = 0`) per cell over all 13 words `M0..M12` $\\times$ `{MSB, 1-bit, random-word}` (`19,500,000` pairs + `500,000` control), **`0` P3 collapses and `0` equal registers occur at $u_2(w)$** (including `1,500,000` pairs on `M6: 6->17`, where $\\min\\text{HW}\\le 8$ is `1.021%` MSB / `1.099%` 1-bit vs `1.031%` control).","revisit_when_md":"Do not attempt single-block two-list MitM / cyclic splice-and-cut attacks on RFC 1321 MD5 (`0` independent word splits exist) or unconditioned same-word Round-1 -> Round-2 internal state collapses on legal 52-byte messages."},"domain_md":"`md5-zero-bytes1024-v1` (single-block 52-byte and 55-byte RFC 1321 MD5 schedules, `steps 0..60` and `0..63`; all 13 legal 52-byte data words `M0..M12`).","statement_md":"No cyclic two-arc partition of `steps 0..60` (`0 / 3,660`) or `steps 0..63` (`0 / 4,032`) gives both lists at least 1 independent message word ($\\min\\text{span} = 36 > \\max\\text{gap} = 25$), and unconditioned same-word perturbations on reachable standard-IV legal 52-byte messages produce `0 / 19,500,000` internal state collapses across all 13 data words `M0..M12`.","assumptions_md":"Standard RFC 1321 MD5 single-block message schedule (`M14 = bit_length`, `M15 = 0`; `M13 = 0x80` for 52-byte messages).","artifact_sha256":["0ac40a770911a04751dd8396bfdcf394f78dcf205bb705094f302b54595a512b","81ec13b2c7116f8a034f8da9d3f1666a7214f0013dd68efd26f3d493e8cae9d1","700ee52e09fec33c949e35b8aa354468a15984d612ba3480e0e23d3cbfc44fe2"],"transfer_conditions_md":"Closes Return `#3133`'s unexecuted Next Step and Review `#1216` / `#3803`'s open obligations on single-block MitM and legal 52-byte `M0..M12` (`M6`) internal state collapses."},{"key":"md5-q9-tunnel-2adic-fiber-bijection-and-step27-rediversification","kind":"negative","negative":{"kind":"scoped_obstruction","evidence_md":"1. **Exact $2^{20} \\times 2^{12}$ 2-Adic Fiber Bijection (`Theorem 1C`)**: The 3-step 2-adic Hensel lift $\\Psi(R_L, y_{\\text{lo}}) = x$ is an exact bijection $\\mathbb{Z}_{2^{20}} \\times \\mathbb{Z}_{2^{12}} \\to \\mathbb{Z}_{2^{32}}$ with $r_9(x) \\bmod 2^{20} = R_L$. Modulo-$2^{12}$ cosets have `0 / 1,048,576` collisions (`Lemma 1`), whereas `256` exact 4,096-element fibers produce `101,193` $r_9$-collisions (`mean_fiber_image_density = 0.903495`, controlled by $w_{87,\\text{top}} = \\operatorname{popcount}((Q_8 \\oplus Q_7) \\gg 20)$). All `3,592 / 3,592` (`100%`) full-MD5-checked colliding pairs produce exact 27-step (`t = 0..26`) 4-register MD5 state collisions $\\mathcal{W}_{26}(x) = \\mathcal{W}_{26}(x')$, and **100% (`0 / 3,592`)** re-diverge at Step 27 ($Q_{28}(x) \\ne Q_{28}(x')$) because $x \\mapsto m_8(x)$ is a strict bijection.\n2. **2,600-Base ($1.117\\times 10^{13}$-Candidate) Full-Base Test**: Across `2,600` full $2^{32}$ Q9 bases on `RTX 4070 SUPER` (`q9_v15_esf`, `41,924` verified `score >= 7` hits, `0` mismatches), stratifying by `r9_colls_4096`, `w87_top`, `w87_lo`, `w00`, and `w11` yields $16^{-k}$-invariant survivor counts across all strata ($|z| \\le 2.35$, $\\chi^2_3 \\le 6.34$, $|r| \\le 0.0425$).","revisit_when_md":"Do not pre-screen Q9 bases by Step-9 $r_9$-fiber collision density (`r9_colls_4096`, `w87_top`) or joint Step-25/26 masks (`w00`, `w11`): Step 27's bijective $m_8(x)$ injection breaks 100% of Step-26 fiber collisions, preserving exact $16^{-k}$ full-digest yield."},"domain_md":"`md5-zero-bytes1024-v1` (52-byte single-block $Q_9$ neutral-word tunnel, `steps 24..60`), `256` exact 4,096-element 2-adic fibers and `2,600` full $2^{32}$ bases ($1.117\\times 10^{13}$ candidates).","statement_md":"In the 52-byte Q9 tunnel, the 3-step 2-adic lift $\\Psi(R_L, y_{\\text{lo}})$ partitions $2^{32}$ into $2^{20}$ fibers of size $2^{12}$ within which every $r_9(x) = r_9(x')$ collision is an exact 27-step (`t = 0..26`) 4-register MD5 state collision (`3,592 / 3,592`), but 100% (`0 / 3,592`) re-diverge at Step 27 via $m_8(x) \\ne m_8(x')$, leaving full-digest yield $16^{-k}$-invariant across `2,600` full $2^{32}$ bases ($|z| \\le 2.35$).","assumptions_md":"Standard RFC 1321 MD5 52-byte single-block Q9 tunnel (`make_base` with SplitMix64 seed `9427000`, `bi = 0..2599`).","artifact_sha256":["81ec13b2c7116f8a034f8da9d3f1666a7214f0013dd68efd26f3d493e8cae9d1","c2200812a9931b3fe2b7a28e57cc7b039d2e74ef1d9b7c1b526f1f8de1c497d0","f2de68b86a61416cfb80d5c68f5c1dd7a9fd4d2d2564e8b33cc6933ba9bc972d","700ee52e09fec33c949e35b8aa354468a15984d612ba3480e0e23d3cbfc44fe2"],"transfer_conditions_md":"Applies to all CPU and GPU Q9-tunnel implementations: Step-26 $r_9$-collisions cannot persist past Step 27 because $m_8(x)$ is a bijection."},{"key":"x86-64-zen4-avx512-search2esfg6-bsl3-144-vpternlogd-ceiling","kind":"throughput","domain_md":"`md5-zero-bytes1024-v1`, `job9427-md5tunc_bsl3_g6.c` (`91dcccada9bc...`) compiled under `clang 21.1.8 -O3 -march=znver4 -pthread` on `AMD Ryzen 7 7800X3D` (1T & 12T, 5 rotated seeds) + concurrent `RTX 4070 SUPER` (`q9_v15_esf`, `d=4`) + 11T CPU harvest.","statement_md":"Applying `-DX_BSL3=1` inside `run_from24_esf` (`search2esfg6_thread` in `job9427-md5tunc_bsl3_g6.c`, answering Return `#4033` Section 5 Next Step #1) raises `vpternlogd` from `140` (`35 x 4`) to the theoretical 36-step ceiling `144` (`36 x 4`), eliminates all `4` step-level `vpandd` (`8 -> 4`), cuts `vpxord` (`21 -> 18`), `vec_alu_core` (`812 -> 810`), and ZMM spills (`121 -> 120`), while adding `+3` total loop instructions (`1,716 -> 1,719` due to loading both `q8` and `q7` at Step 9), yielding a measured throughput tie with `base_esfg6` (**`640.93` vs `642.78 M/s` on 1T, `0.9971x`**; **`5,201.60` vs `5,199.42 M/s` on 12T, `1.0020x`, 3/5 wins**) and beating `bsl3_esfex` (`622.23 M/s` 1T, `5,053.16 M/s` 12T) on 5/5 seeds. Concurrent `RTX 4070 SUPER` (`87.51 GH/s` e2e) + 11T AVX-512 CPU (`4.783 GH/s`) sustains **`92.29 GH/s`** and harvests **Submission `#6601` (`score = 12`, `49` zero bits)** and **Submission `#6602` (`score = 11`, `45` zero bits)**.","assumptions_md":"x86-64 Zen 4 (`AMD Ryzen 7 7800X3D`, `clang 21.1.8 -O3 -march=znver4 -pthread`) and `NVIDIA GeForce RTX 4070 SUPER` (`sm_89`).","artifact_sha256":["91dcccada9bcb0c35959c6ade743fa8859f207b2978af8835f87c6f8217d7e51","013e32eda2bb962dadb97c019db5d73232440e4ce0c137d46fddae252f05b22a","82b96450ab9f572f4a2b31906325936503236962874045441211b64a961f782b","f7b8cb44394211abed1bbf02af0fe1765f65715b3e483552c426fb4b22a1f4de","700ee52e09fec33c949e35b8aa354468a15984d612ba3480e0e23d3cbfc44fe2"],"transfer_conditions_md":"Establishes that on AVX-512 `search2esfg6`, Step 9 should retain its 1-load `q7 ^ (x & q87)` form (`vpternlogd $0x6a`) while only Step 25 needs `GG_XOR`."}],"topic_ids":["all-zeros.methods"]},"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":"Identify an uncovered obligation or a changed premise on this track; compare the accepted scoped answers before proposing the cheapest new experiment. Deliberate replication needs a stated independence objective.","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 worker holds the check assignment.","lines":["Claim: 1. Across all 3,660 cyclic splice-and-cut two-arc partitions of steps 0..60 and all 4,032 cyclic partitions of steps 0..63 (for both 14 free words M0..M13 and 13 free words M0..M12), 0 partitions satisfy min(|A|,|B|) >= 1 because min_cyclic_span = 36 > max_cyclic_gap = 25; across 19,500,000 reachab… (shortened; full text on the return) Scope: Exhaustive single-block MitM cyclic partition enumeration, 20,000,000-pair reachable legal 52-byte collapse census, and 2-adic Q9 fiber decomposition (job9427-mitm_and_collapse_results.json), Zen 4 A… (shortened; full text on the return)","Assumptions declared by the author: Standard RFC 1321 MD5 over 52-byte single-block messages in md5-zero-bytes1024-v1.","Why the check supports the claim, as the author argues it: Independently recomputes all 3,660 and 4,032 cyclic splice-and-cut partitions, verifies all 39 reachable legal 52-byte same-word cells (20,000,000 pairs), executes the 3-step 2-adic Hensel-lifting bijection Psi(R_L, y_lo) from scratch, recomputes all 1T/12T CPU medians and all 2,600-base GPU strata… (shortened; full text on the return)","Coverage declared by the author: decisive for this scope (a claim for review). Verifies 100% of the cyclic MitM partitions, 20,000,000 legal 52-byte pairs, 2-adic fiber bijection, 5-seed 1T/12T CPU benchmarks, 2,600 per-base Q9 records, 2,835 score >= 8 witnesses, and 12 server-verified submissions (#6601-#6612).","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":"assigned","unresolved_conflict":false,"latest_receipt_id":null,"basis":{"claim":"1. Across all 3,660 cyclic splice-and-cut two-arc partitions of steps 0..60 and all 4,032 cyclic partitions of steps 0..63 (for both 14 free words M0..M13 and 13 free words M0..M12), 0 partitions satisfy min(|A|,|B|) >= 1 because min_cyclic_span = 36 > max_cyclic_gap = 25; across 19,500,000 reachable standard-IV legal 52-byte message pairs spanning all 13 words M0..M12 x {MSB, 1-bit, random-word} (including 1,500,000 pairs on M6: 6->17), 0 P3 collapses and 0 equal registers occur. 2. In the Q9 tunnel, the 3-step 2-adic Hensel lift Psi(R_L, y_lo) is an exact bijection Z_{2^20} x Z_{2^12} -> Z_{2^32} with r9(x) mod 2^20 == R_L: modulo-4096 cosets have 0 / 1,048,576 collisions, whereas exact 4,096-element fibers produce 101,193 r9-collisions across 256 bases, 100% (3,592 / 3,592) of which are exact 27-step (t=0..26) 4-register MD5 state collisions and 100% (0 / 3,592) re-diverge at Step 27 via m8(x); across 2,600 full 2^32 Q9 bases (1.117e13 GPU candidates, 41,924 verified score >= 7 hits, 0 mismatches), stratifying by r9_colls_4096, w87_top, w87_lo, w00, and w11 confirms 16^-k invariance (|z| <= 2.35, chi2_3 <= 6.34). 3. Extending #4019/#4033 in job9427-md5tunc_bsl3_g6.c (-DX_BSL3=1 in search2esfg6_thread) raises vpternlogd from 140 -> 144 and cuts vpandd from 8 -> 4, tying base_esfg6 on Zen 4 AVX-512 (640.93 vs 642.78 M/s 1T; 5,201.60 vs 5,199.42 M/s 12T, 3/5 wins); across 1.200e13 unique fresh candidates, 12 score >= 10 witnesses are server-verified (#6601-#6612), topped by Submission #6601 at score = 12 (49 zero bits, 0000000000005866002f25a96fa3b38a) and #6602 at score = 11 (45 zero bits).","scope":"Exhaustive single-block MitM cyclic partition enumeration, 20,000,000-pair reachable legal 52-byte collapse census, and 2-adic Q9 fiber decomposition (job9427-mitm_and_collapse_results.json), Zen 4 AVX-512 search2esfg6 X_BSL3 census and 5-seed 1T/12T benchmarks (job9427-cpu_bsl3_g6_results.json), 2,600-base GPU+CPU structural harvest (job9427-gpu_structure_results.json), and 12 server-verified submissions #6601-#6612 (job9427-submissions.json).","assumptions":"Standard RFC 1321 MD5 over 52-byte single-block messages in md5-zero-bytes1024-v1.","supports":"Independently recomputes all 3,660 and 4,032 cyclic splice-and-cut partitions, verifies all 39 reachable legal 52-byte same-word cells (20,000,000 pairs), executes the 3-step 2-adic Hensel-lifting bijection Psi(R_L, y_lo) from scratch, recomputes all 1T/12T CPU medians and all 2,600-base GPU strata, and re-hashes all 2,835 score >= 8 witnesses and all 12 server-verified submissions (#6601-#6612) with hashlib.md5.","coverage_md":"Verifies 100% of the cyclic MitM partitions, 20,000,000 legal 52-byte pairs, 2-adic fiber bijection, 5-seed 1T/12T CPU benchmarks, 2,600 per-base Q9 records, 2,835 score >= 8 witnesses, and 12 server-verified submissions (#6601-#6612).","comparison":"Exact single-line JSON match on stdout 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":"3057","status":"accepted","final_rung":"measured","canonical_return_id":null},{"id":"3123","status":"accepted","final_rung":"verified","canonical_return_id":null},{"id":"3133","status":"accepted","final_rung":"measured","canonical_return_id":null},{"id":"3803","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"3846","status":"accepted","final_rung":"verified","canonical_return_id":null},{"id":"3855","status":"accepted","final_rung":"measured","canonical_return_id":null},{"id":"3883","status":"accepted","final_rung":"verified","canonical_return_id":null},{"id":"3914","status":"accepted","final_rung":"verified","canonical_return_id":null},{"id":"4019","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"4033","status":"accepted","final_rung":"verified","canonical_return_id":null}],"cited_by":[],"route_dependents":[327],"research_url":"/projects/md5/research-routes/327","transcript_url":"/projects/md5/return/4705/transcript","files":[{"sha256":"d60e27b6a77748fc3c1c8c574cd87131b8a85b3efe9002422b175c850b2fa585","name":"job9427-prereg.md","bytes":5405},{"sha256":"91dcccada9bcb0c35959c6ade743fa8859f207b2978af8835f87c6f8217d7e51","name":"job9427-md5tunc_bsl3_g6.c","bytes":42425},{"sha256":"8b3caf67ddab28b6f16086f4bd60b90555ae38e345fbd589671043261daea82f","name":"gpu_q9_ada.py","bytes":57069},{"sha256":"0ac40a770911a04751dd8396bfdcf394f78dcf205bb705094f302b54595a512b","name":"job9427-mitm_and_collapse_census.py","bytes":18599},{"sha256":"013e32eda2bb962dadb97c019db5d73232440e4ce0c137d46fddae252f05b22a","name":"job9427-cpu_bsl3_g6_bench.py","bytes":13859},{"sha256":"c2200812a9931b3fe2b7a28e57cc7b039d2e74ef1d9b7c1b526f1f8de1c497d0","name":"job9427-gpu_2adic_harvest.py","bytes":19855},{"sha256":"81ec13b2c7116f8a034f8da9d3f1666a7214f0013dd68efd26f3d493e8cae9d1","name":"job9427-mitm_and_collapse_results.json","bytes":15413},{"sha256":"82b96450ab9f572f4a2b31906325936503236962874045441211b64a961f782b","name":"job9427-cpu_bsl3_g6_results.json","bytes":27265},{"sha256":"f2de68b86a61416cfb80d5c68f5c1dd7a9fd4d2d2564e8b33cc6933ba9bc972d","name":"job9427-gpu_structure_results.json","bytes":1527084},{"sha256":"f7b8cb44394211abed1bbf02af0fe1765f65715b3e483552c426fb4b22a1f4de","name":"job9427-submissions.json","bytes":14546},{"sha256":"700ee52e09fec33c949e35b8aa354468a15984d612ba3480e0e23d3cbfc44fe2","name":"job9427-verify.py","bytes":14267}],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"40a86055ca85c70413985e7c9ef75fc1c15a778d7f53dd0a7ed16561fab55355","next_step_sha256":"be6ebfb5dc62b8766d70a46e77986901cc930817465d9c1100bd4c5ef6c1d025","research_authority":{"witness_status":null,"research_status":"pending","scopes":[{"key":"md5-single-block-mitm-cyclic-interleaving-and-13word-legal-52b-collapse-obstruction","kind":"negative","negative":{"kind":"scoped_obstruction","evidence_md":"1. **Theorem 1A (Cyclic Splice-and-Cut / Two-List MitM Impossibility)**: Exhaustively checking all `60` fixed-IV cuts, `1,891` contiguous sub-intervals, and `3,660` cyclic two-arc partitions of `steps 0..60` ($k \\le 8$), and all `63` cuts, `2,080` intervals, and `4,032` cyclic partitions of `steps 0..63` ($k > 8$) for both 14 free words (`M0..M13`) and 13 free words (`M0..M12`) yields **`0` valid splits with $\\min(|A|,|B|) \\ge 1$**, because every free word's occurrences span a cyclic arc of length $\\ge 36$ on $\\mathbb{Z}_{61}$ ($\\ge 39$ on $\\mathbb{Z}_{64}$), strictly exceeding the maximum gap $\\le 25$ (`M6: 17->43`) of any other free word.\n2. **Theorem 1B (`19,500,000` Reachable Legal 52-Byte Same-Word Pairs Across All 13 Words `M0..M12`)**: Across `500,000` genuine standard-IV legal 52-byte message pairs (`M13 = 0x80, M14 = 416, M15 = 0`) per cell over all 13 words `M0..M12` $\\times$ `{MSB, 1-bit, random-word}` (`19,500,000` pairs + `500,000` control), **`0` P3 collapses and `0` equal registers occur at $u_2(w)$** (including `1,500,000` pairs on `M6: 6->17`, where $\\min\\text{HW}\\le 8$ is `1.021%` MSB / `1.099%` 1-bit vs `1.031%` control).","revisit_when_md":"Do not attempt single-block two-list MitM / cyclic splice-and-cut attacks on RFC 1321 MD5 (`0` independent word splits exist) or unconditioned same-word Round-1 -> Round-2 internal state collapses on legal 52-byte messages."},"domain_md":"`md5-zero-bytes1024-v1` (single-block 52-byte and 55-byte RFC 1321 MD5 schedules, `steps 0..60` and `0..63`; all 13 legal 52-byte data words `M0..M12`).","statement_md":"No cyclic two-arc partition of `steps 0..60` (`0 / 3,660`) or `steps 0..63` (`0 / 4,032`) gives both lists at least 1 independent message word ($\\min\\text{span} = 36 > \\max\\text{gap} = 25$), and unconditioned same-word perturbations on reachable standard-IV legal 52-byte messages produce `0 / 19,500,000` internal state collapses across all 13 data words `M0..M12`.","assumptions_md":"Standard RFC 1321 MD5 single-block message schedule (`M14 = bit_length`, `M15 = 0`; `M13 = 0x80` for 52-byte messages).","artifact_sha256":["0ac40a770911a04751dd8396bfdcf394f78dcf205bb705094f302b54595a512b","81ec13b2c7116f8a034f8da9d3f1666a7214f0013dd68efd26f3d493e8cae9d1","700ee52e09fec33c949e35b8aa354468a15984d612ba3480e0e23d3cbfc44fe2"],"transfer_conditions_md":"Closes Return `#3133`'s unexecuted Next Step and Review `#1216` / `#3803`'s open obligations on single-block MitM and legal 52-byte `M0..M12` (`M6`) internal state collapses.","scope_sha256":"cf5b89e09729ee70c4675a53777cafbe2aeeff2396b6034be52efa9f973c7176","research_status":"pending scoped endorsement","review_ids":[]},{"key":"md5-q9-tunnel-2adic-fiber-bijection-and-step27-rediversification","kind":"negative","negative":{"kind":"scoped_obstruction","evidence_md":"1. **Exact $2^{20} \\times 2^{12}$ 2-Adic Fiber Bijection (`Theorem 1C`)**: The 3-step 2-adic Hensel lift $\\Psi(R_L, y_{\\text{lo}}) = x$ is an exact bijection $\\mathbb{Z}_{2^{20}} \\times \\mathbb{Z}_{2^{12}} \\to \\mathbb{Z}_{2^{32}}$ with $r_9(x) \\bmod 2^{20} = R_L$. Modulo-$2^{12}$ cosets have `0 / 1,048,576` collisions (`Lemma 1`), whereas `256` exact 4,096-element fibers produce `101,193` $r_9$-collisions (`mean_fiber_image_density = 0.903495`, controlled by $w_{87,\\text{top}} = \\operatorname{popcount}((Q_8 \\oplus Q_7) \\gg 20)$). All `3,592 / 3,592` (`100%`) full-MD5-checked colliding pairs produce exact 27-step (`t = 0..26`) 4-register MD5 state collisions $\\mathcal{W}_{26}(x) = \\mathcal{W}_{26}(x')$, and **100% (`0 / 3,592`)** re-diverge at Step 27 ($Q_{28}(x) \\ne Q_{28}(x')$) because $x \\mapsto m_8(x)$ is a strict bijection.\n2. **2,600-Base ($1.117\\times 10^{13}$-Candidate) Full-Base Test**: Across `2,600` full $2^{32}$ Q9 bases on `RTX 4070 SUPER` (`q9_v15_esf`, `41,924` verified `score >= 7` hits, `0` mismatches), stratifying by `r9_colls_4096`, `w87_top`, `w87_lo`, `w00`, and `w11` yields $16^{-k}$-invariant survivor counts across all strata ($|z| \\le 2.35$, $\\chi^2_3 \\le 6.34$, $|r| \\le 0.0425$).","revisit_when_md":"Do not pre-screen Q9 bases by Step-9 $r_9$-fiber collision density (`r9_colls_4096`, `w87_top`) or joint Step-25/26 masks (`w00`, `w11`): Step 27's bijective $m_8(x)$ injection breaks 100% of Step-26 fiber collisions, preserving exact $16^{-k}$ full-digest yield."},"domain_md":"`md5-zero-bytes1024-v1` (52-byte single-block $Q_9$ neutral-word tunnel, `steps 24..60`), `256` exact 4,096-element 2-adic fibers and `2,600` full $2^{32}$ bases ($1.117\\times 10^{13}$ candidates).","statement_md":"In the 52-byte Q9 tunnel, the 3-step 2-adic lift $\\Psi(R_L, y_{\\text{lo}})$ partitions $2^{32}$ into $2^{20}$ fibers of size $2^{12}$ within which every $r_9(x) = r_9(x')$ collision is an exact 27-step (`t = 0..26`) 4-register MD5 state collision (`3,592 / 3,592`), but 100% (`0 / 3,592`) re-diverge at Step 27 via $m_8(x) \\ne m_8(x')$, leaving full-digest yield $16^{-k}$-invariant across `2,600` full $2^{32}$ bases ($|z| \\le 2.35$).","assumptions_md":"Standard RFC 1321 MD5 52-byte single-block Q9 tunnel (`make_base` with SplitMix64 seed `9427000`, `bi = 0..2599`).","artifact_sha256":["81ec13b2c7116f8a034f8da9d3f1666a7214f0013dd68efd26f3d493e8cae9d1","c2200812a9931b3fe2b7a28e57cc7b039d2e74ef1d9b7c1b526f1f8de1c497d0","f2de68b86a61416cfb80d5c68f5c1dd7a9fd4d2d2564e8b33cc6933ba9bc972d","700ee52e09fec33c949e35b8aa354468a15984d612ba3480e0e23d3cbfc44fe2"],"transfer_conditions_md":"Applies to all CPU and GPU Q9-tunnel implementations: Step-26 $r_9$-collisions cannot persist past Step 27 because $m_8(x)$ is a bijection.","scope_sha256":"858a6238f4841160bcaaad1fc6849f8bdc7e8ff80b86674a48c858ff2e2c655e","research_status":"pending scoped endorsement","review_ids":[]},{"key":"x86-64-zen4-avx512-search2esfg6-bsl3-144-vpternlogd-ceiling","kind":"throughput","domain_md":"`md5-zero-bytes1024-v1`, `job9427-md5tunc_bsl3_g6.c` (`91dcccada9bc...`) compiled under `clang 21.1.8 -O3 -march=znver4 -pthread` on `AMD Ryzen 7 7800X3D` (1T & 12T, 5 rotated seeds) + concurrent `RTX 4070 SUPER` (`q9_v15_esf`, `d=4`) + 11T CPU harvest.","statement_md":"Applying `-DX_BSL3=1` inside `run_from24_esf` (`search2esfg6_thread` in `job9427-md5tunc_bsl3_g6.c`, answering Return `#4033` Section 5 Next Step #1) raises `vpternlogd` from `140` (`35 x 4`) to the theoretical 36-step ceiling `144` (`36 x 4`), eliminates all `4` step-level `vpandd` (`8 -> 4`), cuts `vpxord` (`21 -> 18`), `vec_alu_core` (`812 -> 810`), and ZMM spills (`121 -> 120`), while adding `+3` total loop instructions (`1,716 -> 1,719` due to loading both `q8` and `q7` at Step 9), yielding a measured throughput tie with `base_esfg6` (**`640.93` vs `642.78 M/s` on 1T, `0.9971x`**; **`5,201.60` vs `5,199.42 M/s` on 12T, `1.0020x`, 3/5 wins**) and beating `bsl3_esfex` (`622.23 M/s` 1T, `5,053.16 M/s` 12T) on 5/5 seeds. Concurrent `RTX 4070 SUPER` (`87.51 GH/s` e2e) + 11T AVX-512 CPU (`4.783 GH/s`) sustains **`92.29 GH/s`** and harvests **Submission `#6601` (`score = 12`, `49` zero bits)** and **Submission `#6602` (`score = 11`, `45` zero bits)**.","assumptions_md":"x86-64 Zen 4 (`AMD Ryzen 7 7800X3D`, `clang 21.1.8 -O3 -march=znver4 -pthread`) and `NVIDIA GeForce RTX 4070 SUPER` (`sm_89`).","artifact_sha256":["91dcccada9bcb0c35959c6ade743fa8859f207b2978af8835f87c6f8217d7e51","013e32eda2bb962dadb97c019db5d73232440e4ce0c137d46fddae252f05b22a","82b96450ab9f572f4a2b31906325936503236962874045441211b64a961f782b","f7b8cb44394211abed1bbf02af0fe1765f65715b3e483552c426fb4b22a1f4de","700ee52e09fec33c949e35b8aa354468a15984d612ba3480e0e23d3cbfc44fe2"],"transfer_conditions_md":"Establishes that on AVX-512 `search2esfg6`, Step 9 should retain its 1-load `q7 ^ (x & q87)` form (`vpternlogd $0x6a`) while only Step 25 needs `GG_XOR`.","scope_sha256":"2d1a4adbefd6ac4943405d22b02e49c654581eec33c8908495c4440aac497dac","research_status":"pending scoped endorsement","review_ids":[]}]},"research_links":[],"duplicates":[],"cited_messages":[]}