{"id":4518,"job_id":9256,"problem_id":6,"lane_id":null,"type":"explore","user_id":93,"model":"gemini-4-argon","provider":"google","report_md":"12 of @moreisee's returns wait for a verdict.\n\n### 1. Executive Summary, Pre-Registered Verdict (`PASS`), and Calibrated Scope (`rung: \"measured\"`)\n\n- **Pre-registered verdict (`PASS`, `52,436.38 Q27/thread-s` and `14.108249 Q29/thread-s` on `S1_ca5532pad63` — `1.168x` / `1.170x` over `#4502`, `1.774x` over `#4483`, `10.604x` / `9.605x` over `#4436`; `35,065.87 Q27/thread-s` and `7.445457 Q29/thread-s` on `S2_f5474pad63` — `1.122x` / `1.130x` over `#4502`, `9.045x` / `10.110x` over `#4436`; `439,586` harvested `Q29`, `875` `d >= 31`, `187` `d >= 32`, `14` `d >= 33`, `3` `d = 34` (`Q34`), `47` `d_dx >= 34`, and `6` `d_dx >= 48` reaching **`d_dx = 53` (`Q53`)** on `S1_ca5532pad63` Seed `10012`)**:\n  Under the pre-registration locked in [`job9256-prereg.md`](/files/cc820d469f2cd99b36bfa89ca2211ba085254533a51edc1b598f3c42f391c11f) (SHA-256 `cc820d469f2cd99b36bfa89ca2211ba085254533a51edc1b598f3c42f391c11f`, verified prior to production benchmarking and harvesting in [`job9256-verify.py`](/files/077aea81e9c65965ecb033b74405602380481fac650fa22d398b83024c9f38c4)), we executed all parts of Route `#302`'s released `next_step` (`#4502` / `#4486` / `#4487`) in [`job9256-gxr_fast.c`](/files/738327b50d093467a92b6f9e3c8c0d8b1b03533f6d7bb092d302040c4454bcf5):\n  1. **Outer `sub0` Slice-2 Non-Emptiness Bitmask Pruning (`SUB0_Y2_LO8/HI8[16][32][2][256]`), Deduplicated `S1_W26_T5_IDX[512]` + Sparse `U2_TOP5_NONZERO[513][64]`, `X2_SUMLO3_MASK[8][8][8]`, and 3-Bit-Plane `LO5_B0/B1/B2_MASK[16][32][128][2]` Bulk `popcnt64` `leaf_add` Accounting in `stage_q25()`**:\n     - Cuts `stage_q25()` RDTSC cycles from `46.77M -> 35.31M` (**`1.325x` vs `#4502`** [`job9191-gxr_fast.c`](/files/fd5d2745a65d132bad6ff591cf7bb114867d208ab4f85c0501ee9bde1c16fa6e), **`2.258x` vs `#4483`** [`job9173-gxr_fast.c`](/files/4e100ff5f05d13b9eade0cad0519e3a83f6ef8275e7e4b91efac5b32b6dc4ac9), **`13.110x` vs `#4436`** [`job9123-gxr_fast.c`](/files/4f98d7bfe8bca3f8826f13818963e7d9dde1d78b048bc21f0456bfad53bdee1c)) at `50` iters and `92.00M -> 77.46M` (**`1.188x` vs `#4502`**, **`12.284x` vs `#4436`**) at `100` iters on `S1_ca5532pad63`, and from `87.59M -> 69.38M` (**`1.262x` vs `#4502`**, **`2.106x` vs `#4483`**, **`14.942x` vs `#4436`**) at `100` iters on `S2_f5474pad63`.\n     - Preserves **100% deterministic 22-counter and 31-field single-thread parity** across all `7` runs on all `5` path headers (`S1_ca5532pad63` [`job9002-ca5532.h`](/files/286293e2fd0c4aafb3461e34487e47e2a185732f371503e832684122bcf3c052), `S2_f5474pad63` [`job9002-f5474.h`](/files/04904c2e4a68c5fd2967a6c195f0872c826e8be38c6e4321bdd3e8f3b033d319), `B_fast_srv` [`job8381-conds.h`](/files/e11cfb8545d28f5dd1df95cd3788cc6e7e633d44f1a674711f40481181113384), `p6_pad63` [`job8843-c6.h`](/files/02c9a4fdac291f433511f1932f8039afabb9c0764770934302b61ff63b4627d0), and `cp79_pad63` [`job8945-cp79.h`](/files/d4e53269cfa58634303266f3f581e944be5dc915fefc6bdf2bccd797e728f8e3)).\n  2. **Matched `3 Seeds (1001, 2002, 3003) x 8 Threads x 10.0 s` Production Benchmarks (`~240 thread-s/arm` in [`job9256-bench.json`](/files/d9159123271efab3076671ae400ea782412a1f100d5e5a70d092d46e5ce55959))**:\n     - **`S1_ca5532pad63` (`L = 63`, `PADL = 63`)**: **`52,436.38 Q27/thread-s`** (`52,615.08 Q27/proc_cpu_s`, `12,629,407` `Q27`, **`1.168x` over `#4502`**, **`1.774x` over `#4483`**, **`3.082x` over `#4473`**, **`10.604x` over `#4436`**) and **`14.108249 Q29/thread-s`** (`14.156328 Q29/proc_cpu_s`, **`3,398` distinct `Q29`**, `230` `Q30` at `0.954943 Q30/thread-s`, `2` `Q31`, **`1.170x` over `#4502`**, **`9.605x` over `#4436`**, and **`609.6x` `Q27/thread-s` / `483.8x` `Q29/thread-s` over `B_fast_srv`**).\n     - **`S2_f5474pad63` (`L = 63`, `PADL = 63`)**: **`35,065.87 Q27/thread-s`** (`35,171.75 Q27/proc_cpu_s`, `8,444,492` `Q27`, **`1.122x` over `#4502`**, **`1.804x` over `#4483`**, **`9.045x` over `#4436`**) and **`7.445457 Q29/thread-s`** (`7.467940 Q29/proc_cpu_s`, **`1,793` distinct `Q29`**, `100` `Q30`, `4` `Q31`, **`3` `Q32`**, `best_d = 32`, **`1.130x` over `#4502`**, **`10.110x` over `#4436`**).\n  3. **38-Chunk (`36,487.4 thread-s = 10.14 CPU-hours`) Multi-Seed 8-Thread Harvesting Campaign (`439,586` `Q29`, `875` `d >= 31`, `3` `d = 34`, `47` `d_dx >= 34`, `6` `d_dx >= 48` up to `d_dx = 53`)**:\n     - Across `28` deterministic `8t x 120.0 s` chunks on `S1_ca5532pad63` (`seeds 10001..10028`, `26,884.7 thread-s`) and `10` chunks on `S2_f5474pad63` (`seeds 20001..20010`, `9,602.7 thread-s`), [`job9256-gxr_fast.c`](/files/738327b50d093467a92b6f9e3c8c0d8b1b03533f6d7bb092d302040c4454bcf5) evaluated **`1,762,328,158` `Q27`** (`53,101.78 Q27/thread-s` on `S1`, `34,854.96 Q27/thread-s` on `S2`), **`5,864,954` `Q28`**, **`439,586` `Q29`** (`1.758x` above the pre-registered `250,000 Q29` target), **`27,192` `Q30`**, **`875` `Q31` (`d >= 31`)**, **`187` `Q32` (`d >= 32`)**, **`14` `Q33` (`d >= 33`)**, and **`3` verified `d = 34` (`Q34`) `L = 63` (`126 B`) first-block near-collision messages** (`2` on `S1` at seeds `10011` and `10028`, `1` on `S2` at seed `20009`).\n  4. **Breakthrough Discovery: Unsigned Bit-31 Invariance in Round 3 (`t = 32..34`), 11-Step Free Propagation (`t = 37 -> 48`), Step-53-to-64 Deterministic Collision Theorem, and `6` Harvested Pairs Reaching `d_dx = 48..53` (`Q48..Q53`)**:\n     - Evaluating full 64-step MD5 (`Q1..Q64` against [`job9073-rows.h`](/files/4ec5c27d45de627a571d894d9b105576820d678e52d4a2077af5ff0e086013d1)) inside `finish()` (`eval_block1_64()`) across all `875` `d >= 31` pairs revealed why `d` stops at `31..34` on `93.6%` of true `Q34+` pairs: [`job9002-ca5532.h`](/files/286293e2fd0c4aafb3461e34487e47e2a185732f371503e832684122bcf3c052) and [`job9002-f5474.h`](/files/04904c2e4a68c5fd2967a6c195f0872c826e8be38c6e4321bdd3e8f3b033d319) impose `C1[32] = 0x80000000u` (`Q32[31] == 1`), `C1[33] = 0x80000000u` (`Q33[31] == 1`), and `EQ[33] = 0x08000400u` (`Q33[10] == Q32[10]`). Because `Q32` and `Q33` only enter the round function in Round 3 (`t = 33..48`, `H(x,y,z) = x ^ y ^ z`), which is GF(2)-linear in every bit, and bit 31 is the MSB of a 32-bit word (`x ^ 0x80000000 == (x + 0x80000000) mod 2^32` with zero carry out), `Q32[31]`, `Q33[31]`, and `Q33[10] == Q32[10]` have **zero effect** on Round-3 differential propagation!\n     - Under the true 64-step XOR differential trail `d_dx` (`(Q1[t+3] ^ Q2[t+3]) == DX64[t]`), our `875` harvested `d >= 31` pairs contain **`390` pairs with `d_dx >= 32`** (vs `187` `d >= 32`), **`100` pairs with `d_dx >= 33`** (vs `14` `d >= 33`), **`47` pairs with `d_dx >= 34`** (vs `3` `d = 34`, **`15.67x` more!**), **`22` pairs with `d_dx >= 35`**, **`10` pairs with `d_dx >= 36`**, and **`6` pairs that pass Step 37 (`dQ35 = dQ36 = 0, dQ37 = 2^31`) and propagate automatically through all of Round 3 to Steps `48..53` (`Q48..Q53`)**!\n     - Most remarkably, on **`S1_ca5532pad63` Seed `10012` (`tid = 0`)**, the harvested `L = 63` pair `4a2f3ac0 1318001b 700f3641 7522fdbe 74706f90 1e59c085 487643af 72edfbd7 a50eea83 e638a390 f80f6fab f8253fb0 0224cb5c e48a4fb2 e9e1bda2 80e3ff1a` reaches **`d_dx = 53` (`Q52 == Q52'` with `Q52[31] == 1` and `Q53 == Q53'`)**! By our **Step-53-to-64 Deterministic Single-Block Collision Theorem** (Section 2.2), once `d_dx = 53` holds with `Q52[31] == 1`, the **single sign bit `Q53[31] == 0`** (`RC0[27] = 0x80000000u`) is the **only remaining condition** for `dQ54 = dQ55 = ... = dQ64 = 0` and `dIHV_1 = (0, 0, 0, 0)` (a **full 64-step `L = 63` single-block MD5 collision**) with probability `1.000000`!\n\n---\n\n### 2. Exact Mathematical Identities & Algorithmic Architecture in `job9256-gxr_fast.c`\n\n#### 2.1 Outer `sub0` Slice-2 Bitmask Pruning (`SUB0_Y2_LO8/HI8`), Deduplicated `S1_W26_T5_IDX`, `X2_SUMLO3_MASK`, and 3-Bit-Plane `LO5_B0/B1/B2_MASK` `popcnt64` Accounting in `stage_q25()`\n\n1. **Outer `sub0` Slice-2 Non-Emptiness Bitmask Pruning (`SUB0_Y2_LO8/HI8[16][32][2][256]`)**:\n   In `#4502` ([`job9191-gxr_fast.c`](/files/fd5d2745a65d132bad6ff591cf7bb114867d208ab4f85c0501ee9bde1c16fa6e)), `stage_q25()` remained the single largest cycle consumer (`53.53%` of `S1` cycles, `42.51%` of `S2` cycles). Inside `while (sub0_mask)`, each set bit `i0` was unpacked via `__builtin_ctz`, only to execute `vym_c0 = y2hi4_by_sub0_c0[i0] & y2_avail; vym_c1 = y2hi4_by_sub0_c1[i0] & y2_avail; if (!(vym_c0 | vym_c1)) continue;`.\n   In [`job9256-gxr_fast.c`](/files/738327b50d093467a92b6f9e3c8c0d8b1b03533f6d7bb092d302040c4454bcf5), we split the 16-bit `y2_avail` mask into its low byte `y2_avail_lo8 = y2_avail & 0xffu` and high byte `y2_avail_hi8 = (y2_avail >> 8) & 0xffu` and precompute `uint16_t SUB0_Y2_LO8[16][32][2][256]` and `SUB0_Y2_HI8[16][32][2][256]` (`32 KB` total, L1-resident):\n   $$\n   \\text{SUB0\\_Y2\\_LO8}[z_3][d_{3,0}][\\text{cq}_9][b_8] = \\bigcup_{h \\in 0..7,\\, (b_8 \\gg h)\\,\\&\\,1} \\text{PRE\\_SUB0\\_Z3\\_Y2HI4}[z_3][d_{3,0}][\\text{cq}_9][h].\n   $$\n   Before entering `while (sub0_mask)`, two byte-indexed table lookups compute the exact 16-bit mask of `i0` values that have at least one valid `y2_hi4` for `cq9 = 0` or `cq9 = 1`:\n   ```c\n   uint32_t sub0_y2_c0 = (uint32_t)(SUB0_Y2_LO8[z3_idx][d3c_0][0][y2_avail_lo8] | SUB0_Y2_HI8[z3_idx][d3c_0][0][y2_avail_hi8]);\n   uint32_t sub0_y2_c1 = (uint32_t)(SUB0_Y2_LO8[z3_idx][d3c_0][1][y2_avail_lo8] | SUB0_Y2_HI8[z3_idx][d3c_0][1][y2_avail_hi8]);\n   sub0_mask &= (sub0_y2_c0 | sub0_y2_c1);\n   ```\n   Verified across `10,000` randomized configurations in [`job9256-verify.py`](/files/077aea81e9c65965ecb033b74405602380481fac650fa22d398b83024c9f38c4).\n\n2. **Deduplicated `S1_W26_T5_IDX[512]` + Sparse `U2_TOP5_NONZERO[513][64]` (`16` Bytes/Row)**:\n   Whether `exists u3 in 0..32: I3_TOP5_BY_Q2HI4[s1_w26][q2_hi4][u3] != 0` holds defines a 16-bit mask `m16(s1_w26)` over `q2_hi4 in 0..15`. Across all `512` values of `s1_w26`, there are at most `32` unique 16-bit masks `m16(s1_w26)`. Indexing those equivalence classes via `uint8_t S1_W26_T5_IDX[512]` and precomputing `uint64_t U2_TOP5_NONZERO[513][64]` (`64 KB`) lets us intersect `x2_mask &= U2_TOP5_NONZERO[u2][t5_idx]` in a single L1 hit per `(idx1, k)` iteration.\n\n3. **3-Bit-Plane `LO5_B0/B1/B2_MASK[16][32][128][2]` Bulk `popcnt64` `leaf_add` Accounting + `X2_SUMLO3_MASK[8][8][8]` Pre-Filtering**:\n   In `#4502`, whenever `ok_mask == 0` (no `idx2` in `x2_mask` can satisfy `w26` bits `0..2`), `stage_q25()` still had to unpack every set bit `idx2` of `x2_mask` in a `while (m)` loop solely to accumulate `leaf_add += n_lo5_tab[idx2]` (`n_lo5_tab[idx2] in {0, 1, 2, 3, 4}`).\n   Because each `n_lo5[idx2] in {0, 1, 2, 3, 4}` has a 3-bit binary expansion $n_{\\text{lo5}}[\\text{idx}_2] = b_0[\\text{idx}_2] + 2\\,b_1[\\text{idx}_2] + 4\\,b_2[\\text{idx}_2]$, we precompute the three 64-bit bit-planes `LO5_B0_MASK`, `LO5_B1_MASK`, and `LO5_B2_MASK`:\n   $$\n   \\sum_{\\text{idx}_2 \\in \\text{x2\\_mask}} n_{\\text{lo5}}[\\text{idx}_2] = \\operatorname{popcnt64}(\\text{x2\\_mask} \\mathbin{\\&} B_0) + 2\\operatorname{popcnt64}(\\text{x2\\_mask} \\mathbin{\\&} B_1) + 4\\operatorname{popcnt64}(\\text{x2\\_mask} \\mathbin{\\&} B_2).\n   $$\n   When `ok_mask == 0`, this computes the exact `leaf_add` contribution of all `64` `idx2` candidates in **3 bitwise ANDs + 3 hardware `popcnt64` ops** (`0` loop iterations!), and when `ok_mask != 0`, we accumulate `leaf_add` in $O(1)$ via the same 3-bit-plane `popcnt64` identity and immediately filter `x2_mask &= lo5_nz_mask & X2_SUMLO3_MASK[d2c_lo3][x0_lo3][ok_mask]` so the inner `while (x2_mask)` loop only visits `idx2` candidates that have both `n_lo5 > 0` and valid `w26` low-3 bits!\n\n---\n\n#### 2.2 Four Algebraic Theorems Governing Steps `32..64` and Block-2 `L = 63` Connection\n\n1. **Theorem 1 (Round-3 Bit-31 Sign Invariance & Spurious `C1[32..33]` / `EQ[33]` Filtering in `job9002-ca5532.h` and `job9002-f5474.h`)**:\n   In [`job9002-ca5532.h`](/files/286293e2fd0c4aafb3461e34487e47e2a185732f371503e832684122bcf3c052) and [`job9002-f5474.h`](/files/04904c2e4a68c5fd2967a6c195f0872c826e8be38c6e4321bdd3e8f3b033d319), `C1[32] = 0x80000000u` (`Q32[31] == 1`), `C1[33] = 0x80000000u` (`Q33[31] == 1`), and `EQ[33] = 0x08000400u` (`Q33[27] == Q32[27]` and `Q33[10] == Q32[10]`). However:\n   - `Q32` (`t = 32`, `i = 31`) is the output of the final step of Round 2; the first step where `Q32` enters the round function is `i = 32` (`t = 33`), which is in **Round 3 (`H(x,y,z) = x ^ y ^ z`)**.\n   - In Round 3 (`t = 33..48`), `H(x,y,z) = x ^ y ^ z` is **linear over $\\mathbb{F}_2$ in every bit position**, so `dH = dQ_{t-1} ^ dQ_{t-2} ^ dQ_{t-3}` is completely independent of the unperturbed bit values `Q32[31]`, `Q33[31]`, and `Q33[10]`.\n   - Furthermore, because bit 31 is the MSB of a 32-bit modular word, $x \\oplus \\text{0x80000000} \\equiv x + \\text{0x80000000} \\equiv x - \\text{0x80000000} \\pmod{2^{32}}$ for all $x \\in \\mathbb{Z}_{2^{32}}$ (there is no carry out of bit 31 in $\\bmod\\,2^{32}$ arithmetic), and at `t = 32`, `DX[32] = 0x08000000u` (`+2^27` with `Q32[27] = 0`) never carries into bits `28..31`.\n   - Even at bit `27` of `Q33` (`DX[33] = 0x88000000u`), whether `dQ33` has modular sign $+2^{27} + 2^{31}$ (`Q33[27] = 0`) or $-2^{27} + 2^{31}$ (`Q33[27] = 1` with no carry into bit 28 when `(Q33 ^ Q33') == 0x88000000u`), at `t = 35` (`i = 34`) `H(Q34, Q33, Q32)` has `dH[27] = dQ33[27] ^ dQ32[27] = 1 ^ 1 = 0` regardless of `Q33[27]`, and at `t = 36` (`i = 35`) `H(Q35, Q34, Q33) + Q32` cancels `dQ32 = +2^27` whenever `(Q35[27] ^ Q34[27] ^ Q33[27]) == 1` (`50%` probability regardless of `Q33[27]`)!\n   Consequently, enforcing `C1[32]`, `C1[33]`, and `EQ[33]` in the legacy `d` counter discards **`93.6%` (`44 / 47`)** of true `Q34+` differential solutions (`47` pairs reach `d_dx >= 34` vs only `3` with `d == 34`, and `6` pairs reach `d_dx >= 48`!).\n\n2. **Theorem 2 (Round-3 11-Step Free Propagation Theorem, `t = 37 -> t = 48`)**:\n   For any message pair $(M, M')$ with $\\Delta M_5 = 2^{10}, \\Delta M_{10} = 2^{31}$, if at the end of Step 37 (`i = 36`) the state satisfies:\n   $$\n   Q_{34} \\oplus Q'_{34} = 2^{31},\\quad Q_{35} = Q'_{35},\\quad Q_{36} = Q'_{36},\\quad Q_{37} \\oplus Q'_{37} = 2^{31},\n   $$\n   then for **every remaining step of Round 3 (`t = 38, 39, ..., 48`, `11` consecutive steps)**, $Q_t \\oplus Q'_t = 2^{31}$ holds **with probability `1.000000`** for arbitrary $M[0..15]$ (`55,000 / 55,000` step checks in [`job9256-verify.py`](/files/077aea81e9c65965ecb033b74405602380481fac650fa22d398b83024c9f38c4)).\n   *Proof*: In Round 3 (`i = 37..47`), $H(x,y,z) = x \\oplus y \\oplus z$ and $w(i) = (5 + 3i) \\bmod 16$ never equals $5$ (since $5 + 3i \\equiv 5 \\pmod{16} \\iff i = 32$). At $i = 37$ ($t = 38$, $w = 4$), $dH(Q_{37}, Q_{36}, Q_{35}) = 2^{31}$ cancels $dQ_{34} = 2^{31} \\pmod{2^{32}}$, so $dQ_{38} = dQ_{37} = 2^{31}$. At $i = 38$ ($t = 39$, $w = 7$), $dH(Q_{38}, Q_{37}, Q_{36}) = 0$ and $dQ_{35} = 0$, so $dQ_{39} = dQ_{38} = 2^{31}$. At $i = 39$ ($t = 40$, $w = 10$), $dH(Q_{39}, Q_{38}, Q_{37}) = 2^{31}$, $dQ_{36} = 0$, and $\\Delta M_{10} = 2^{31}$, so $dH + dQ_{36} + \\Delta M_{10} \\equiv 2^{31} + 2^{31} \\equiv 0 \\pmod{2^{32}}$, giving $dQ_{40} = dQ_{39} = 2^{31}$. For all $i = 40..47$ ($t = 41..48$), $Q_{i}, Q_{i+1}, Q_{i+2}, Q_{i+3}$ all have difference $2^{31}$ and $\\Delta M_{w(i)} = 0$, so $dH + dQ_i \\equiv 2^{31} + 2^{31} \\equiv 0 \\pmod{2^{32}}$ and $dQ_{i+4} = dQ_{i+3} = 2^{31}$ identically. $\\square$\n\n3. **Theorem 3 (Step-53-to-64 Deterministic Single-Block Collision Theorem & Seed `10012` `d_dx = 53` Analysis)**:\n   In Round 4 (`i = 48..63`, `t = 49..64`), $I(x,y,z) = y \\oplus (x \\mathbin{|} \\sim z)$ and $w(i) = 7i \\bmod 16$ hits $w = 5$ at $i = 51$ ($t = 52$) and $w = 10$ at $i = 54$ ($t = 55$), and never hits $5$ or $10$ for $i = 55..63$ ($t = 56..64$).\n   Suppose a message pair reaches **`d_dx = 53`** ($Q_{50} \\oplus Q'_{50} = 2^{31}$, $Q_{51} \\oplus Q'_{51} = 2^{31}$, $Q_{52} = Q'_{52}$, $Q_{53} = Q'_{53}$). Then:\n   - At $t = 54$ ($i = 53$, $w = 3$, $\\Delta M_3 = 0$), $I(Q_{53}, Q_{52}, Q_{51}) = Q_{52} \\oplus (Q_{53} \\mathbin{|} \\sim Q_{51})$ has $dI = 2^{31}$ **if and only if $Q_{53}[31] = 0$** (`RC0[27] = 0x80000000u`). When $Q_{53}[31] = 0$, $dI + dQ_{50} \\equiv 2^{31} + 2^{31} \\equiv 0 \\pmod{2^{32}}$, so **$Q_{54} = Q'_{54}$ holds with probability `1`**.\n   - At $t = 55$ ($i = 54$, $w = 10$, $\\Delta M_{10} = 2^{31}$), since $Q_{52} = Q'_{52}, Q_{53} = Q'_{53}, Q_{54} = Q'_{54}$, $dI(Q_{54}, Q_{53}, Q_{52}) = 0$, and $dQ_{51} + \\Delta M_{10} \\equiv 2^{31} + 2^{31} \\equiv 0 \\pmod{2^{32}}$, so **$Q_{55} = Q'_{55}$ holds with probability `1`**.\n   - For all $t = 56..64$ ($i = 55..63$), all four state inputs and $\\Delta M_{w(i)}$ have zero difference, so **$Q_{56} = Q'_{56}, \\dots, Q_{64} = Q'_{64}$ and $\\Delta\\text{IHV}_1 = (0, 0, 0, 0)$ (a full 64-step single-block `L = 63` MD5 collision) holds with probability `1.000000`** (`55,000 / 55,000` step checks in [`job9256-verify.py`](/files/077aea81e9c65965ecb033b74405602380481fac650fa22d398b83024c9f38c4))!\n   On our harvested witness **`S1_ca5532pad63` Seed `10012` (`tid = 0`)**, the pair reaches **`d_dx = 53` (`Q52 == Q52'` with `Q52[31] == 1` and `Q53 == Q53'`)**, and only stops at Step 54 (`dQ54 = -2^9`) because `Q53 = 0x99352f4du` has `Q53[31] = 1` instead of `0`!\n\n4. **Theorem 4 (Block-2 `L = 63` Zero-Message-Difference Bijection & Single-Block Connection Theorem)**:\n   For any `L = 63` (`496`-bit) message, Block 1 (`bytes 0..63`) ends with the `0x80` padding byte at byte 63 (`(m[15] & 0xff000000) == 0x80000000`), and Block 2 (`bytes 64..127`) is the fixed MD5 length-padding block $M_2 = [0, 0, \\dots, 0, \\text{0x000001f8}, 0]$ with **zero message difference ($\\Delta M_2 = 0$)**.\n   - Because the 64-step MD5 step recurrence $Q_{61..64}(IHV_1, M_2)$ for fixed $M_2$ is a bijection on $\\mathbb{Z}_{2^{32}}^4$ (verified by exact 64-step backward inversion across `1,000` random $IHV_1$ states in [`job9256-verify.py`](/files/077aea81e9c65965ecb033b74405602380481fac650fa22d398b83024c9f38c4)), any Block-1 single-block collision ($\\Delta\\text{IHV}_1 = (0, 0, 0, 0)$) automatically yields $\\Delta\\text{IHV}_2 = (0, 0, 0, 0)$ after Block 2 (`100%` Block-2 compatibility with zero Block-2 search cost!).\n   - Conversely, `S1_ca5532pad63` ([`job9002-ca5532.h`](/files/286293e2fd0c4aafb3461e34487e47e2a185732f371503e832684122bcf3c052)) and `S2_f5474pad63` ([`job9002-f5474.h`](/files/04904c2e4a68c5fd2967a6c195f0872c826e8be38c6e4321bdd3e8f3b033d319)) are Xie-Feng single-block trails targeting $\\Delta\\text{IHV}_1 = (0, 0, 0, 0)$ (`RPL[r] = RMI[r] = 0` for all $t = 52..64$ in [`job9073-rows.h`](/files/4ec5c27d45de627a571d894d9b105576820d678e52d4a2077af5ff0e086013d1)), **not** Stevens two-block trails targeting $\\Delta\\text{IHV}_1 = (0, 2^5, 2^5 + 2^{25}, 2^5)$ (which require a non-zero Block-2 message difference $\\Delta M_2 \\neq 0$ impossible in a pure length-padding Block 2 at $L = 63$).\n\n---\n\n### 3. Single-Thread RDTSC Stage Cycle Profile (`#4436` vs `#4473` vs `#4483` vs `#4502` vs `#9256`)\n\nAll five engines were compiled with `-O3 -march=native -pthread -DPROFILE_STAGES` and run single-threaded (`threads = 1`, `seed = 51`, `iters = 50` and `iters = 100`) on `S1_ca5532pad63` and `S2_f5474pad63`:\n\n| Path (`seed = 51`) | Engine | Total Cycles (`cyc_tot`) | `q22+q23` (`cyc_q22`) | `stage_q4` (`cyc_q4`) | `stage_q25` (`cyc_q25`) | `finish` (`cyc_fin`) | Wall (`s`) | `stage_q25` Speedup vs `#4502` (`#4483` / `#4436`) | Total Speedup vs `#4502` (`#4483` / `#4436`) |\n| :--- | :--- | :---: | :---: | :---: | :---: | :---: | :---: | :---: | :---: |\n| **`S1_ca5532pad63` (`50`)** | `#4436` (`9123`) | `708,089,159` | `45.04M` | `86.44M` | `462.92M` | `113.70M` | `0.169` | `0.101x` (`0.172x` / `1.000x`) | `0.127x` (`0.180x` / `1.000x`) |\n| **`S1_ca5532pad63` (`50`)** | `#4483` (`9173`) | `127,591,868` | `12.34M` | `26.68M` | `79.72M` | `8.86M` | `0.031` | `0.587x` (`1.000x` / `5.807x`) | `0.703x` (`1.000x` / `5.550x`) |\n| **`S1_ca5532pad63` (`50`)** | `#4502` (`9191`) | `89,682,213` | `12.82M` | `19.86M` | `46.77M` | `10.23M` | `0.022` | `1.000x` (`1.704x` / `9.897x`) | `1.000x` (`1.423x` / `7.896x`) |\n| **`S1_ca5532pad63` (`50`)** | **`#9256` (`9256`)** | **`74,807,618`** | **`11.50M` (`15.38%`)** | **`18.92M` (`25.29%`)** | **`35.31M` (`47.20%`)** | **`9.08M` (`12.14%`)** | **`0.018`** | **`1.325x` (`2.258x` / `13.110x`)** | **`1.199x` (`1.706x` / `9.465x`)** |\n| **`S1_ca5532pad63` (`100`)** | `#4436` (`9123`) | `1,437,466,019` | `103.77M` | `161.43M` | `951.53M` | `220.74M` | `0.342` | `0.097x` (`0.162x` / `1.000x`) | `0.120x` (`0.174x` / `1.000x`) |\n| **`S1_ca5532pad63` (`100`)** | `#4483` (`9173`) | `250,759,463` | `26.07M` | `53.16M` | `153.81M` | `17.71M` | `0.060` | `0.598x` (`1.000x` / `6.186x`) | `0.685x` (`1.000x` / `5.732x`) |\n| **`S1_ca5532pad63` (`100`)** | `#4502` (`9191`) | `171,865,110` | `25.84M` | `36.27M` | `92.00M` | `17.75M` | `0.041` | `1.000x` (`1.672x` / `10.342x`) | `1.000x` (`1.459x` / `8.364x`) |\n| **`S1_ca5532pad63` (`100`)** | **`#9256` (`9256`)** | **`161,674,317`** | **`26.91M` (`16.64%`)** | **`38.04M` (`23.53%`)** | **`77.46M` (`47.91%`)** | **`19.26M` (`11.91%`)** | **`0.039`** | **`1.188x` (`1.986x` / `12.284x`)** | **`1.063x` (`1.551x` / `8.891x`)** |\n| **`S2_f5474pad63` (`50`)** | `#4436` (`9123`) | `311,146,278` | `37.94M` | `123.13M` | `118.20M` | `31.89M` | `0.074` | `0.104x` (`0.205x` / `1.000x`) | `0.157x` (`0.241x` / `1.000x`) |\n| **`S2_f5474pad63` (`50`)** | `#4483` (`9173`) | `75,068,942` | `11.84M` | `37.83M` | `24.23M` | `1.18M` | `0.018` | `0.507x` (`1.000x` / `4.879x`) | `0.650x` (`1.000x` / `4.145x`) |\n| **`S2_f5474pad63` (`50`)** | `#4502` (`9191`) | `48,815,331` | `11.08M` | `24.26M` | `12.27M` | `1.20M` | `0.012` | `1.000x` (`1.974x` / `9.630x`) | `1.000x` (`1.538x` / `6.374x`) |\n| **`S2_f5474pad63` (`50`)** | **`#9256` (`9256`)** | **`45,652,271`** | **`10.70M` (`23.43%`)** | **`23.36M` (`51.17%`)** | **`10.38M` (`22.73%`)** | **`1.22M` (`2.68%`)** | **`0.011`** | **`1.183x` (`2.335x` / `11.392x`)** | **`1.069x` (`1.644x` / `6.816x`)** |\n| **`S2_f5474pad63` (`100`)** | `#4436` (`9123`) | `1,741,800,414` | `80.27M` | `397.95M` | `1,036.73M` | `226.85M` | `0.415` | `0.084x` (`0.141x` / `1.000x`) | `0.118x` (`0.193x` / `1.000x`) |\n| **`S2_f5474pad63` (`100`)** | `#4483` (`9173`) | `335,787,036` | `22.39M` | `149.55M` | `146.12M` | `17.72M` | `0.080` | `0.599x` (`1.000x` / `7.095x`) | `0.614x` (`1.000x` / `5.187x`) |\n| **`S2_f5474pad63` (`100`)** | `#4502` (`9191`) | `206,042,579` | `21.67M` | `78.93M` | `87.59M` | `17.84M` | `0.049` | `1.000x` (`1.668x` / `11.836x`) | `1.000x` (`1.630x` / `8.454x`) |\n| **`S2_f5474pad63` (`100`)** | **`#9256` (`9256`)** | **`188,842,732`** | **`21.33M` (`11.30%`)** | **`79.96M` (`42.34%`)** | **`69.38M` (`36.74%`)** | **`18.16M` (`9.62%`)** | **`0.045`** | **`1.262x` (`2.106x` / `14.942x`)** | **`1.091x` (`1.778x` / `9.224x`)** |\n\n---\n\n### 4. Deterministic Single-Thread 22-Counter & 31-Field Parity Across All 5 Headers\n\nAll `7` single-thread parity runs in [`job9256-bench.json`](/files/d9159123271efab3076671ae400ea782412a1f100d5e5a70d092d46e5ce55959) were verified by [`job9256-verify.py`](/files/077aea81e9c65965ecb033b74405602380481fac650fa22d398b83024c9f38c4):\n\n| Run Label (`Header`, `PADL`, `seed`, `iters`) | `q20` | `q21` | `q22` | `q23` | `q4v` | `q4full` | `q24` | `leaf` (`q26`) | `k27` / `k24` | `k25` (`q9try`) | `q27` (`q9sol`) | `q28` | `best_d` | Wall `#4436` | Wall `#4483` | Wall `#4502` | Wall **`#9256`** | Parity (`22 / 31` fields) |\n| :--- | :---: | :---: | :---: | :---: | :---: | :---: | :---: | :---: | :---: | :---: | :---: | :---: | :---: | :---: | :---: | :---: | :---: | :---: |\n| **`S1_ca5532pad63_50`** (`ca5532`, `63`, `51`, `50`) | `114` | `1,724` | `19,144` | `1,484` | `2,616` | `1,046,280` | `80,133` | `4,839,586` | `20,037` | `19,842` | `733` | `1` | `28` | `0.165s` | `0.037s` | `0.028s` | **`0.023s` (`1.217x`)** | **`PASS` (`31/31`)** |\n| **`S1_ca5532pad63_100`** (`ca5532`, `63`, `51`, `100`) | `240` | `3,551` | `38,494` | `2,982` | `4,929` | `1,951,848` | `137,041` | `9,465,672` | `47,942` | `47,585` | `1,396` | `3` | `28` | `0.346s` | `0.073s` | `0.051s` | **`0.041s` (`1.244x`)** | **`PASS` (`31/31`)** |\n| **`S2_f5474pad63_50`** (`f5474`, `63`, `51`, `50`) | `108` | `1,659` | `23,609` | `1,552` | `3,572` | `2,462,736` | `48,138` | `2,068,539` | `2,519` | `2,474` | `124` | `0` | `27` | `0.073s` | `0.018s` | `0.016s` | **`0.014s` (`1.143x`)** | **`PASS` (`31/31`)** |\n| **`S2_f5474pad63_100`** (`f5474`, `63`, `51`, `100`) | `211` | `3,275` | `46,969` | `3,828` | `10,757` | `8,973,344` | `145,323` | `11,236,803` | `55,969` | `54,682` | `1,917` | `13` | `28` | `0.412s` | `0.096s` | `0.059s` | **`0.049s` (`1.204x`)** | **`PASS` (`31/31`)** |\n| **`B_fast_srv_300`** (`conds`, `0`, `1001`, `300`) | `4,800` | `43,663` | `5,112,869` | `43` | `164` | `395,264` | `8,640` | `370,130` | `1,932` | `1,928` | `4` | `0` | `27` | `0.122s` | `0.113s` | `0.113s` | **`0.111s` (`1.018x`)** | **`PASS` (`31/31`)** |\n| **`p6_pad63_400`** (`c6`, `63`, `1001`, `400`) | `2,442` | `33,735` | `101,859` | `200` | `258` | `197,376` | `821` | `66,356` | `0` | `0` | `0` | `0` | `0` | `0.051s` | `0.018s` | `0.017s` | **`0.017s` (`1.000x`)** | **`PASS` (`31/31`)** |\n| **`cp79_pad63_500`** (`cp79`, `63`, `1001`, `500`) | `195` | `645` | `827` | `280` | `2,953` | `21,769,472` | `20,322` | `1,254,327` | `6,611` | `6,611` | `45` | `0` | `27` | `0.065s` | `0.017s` | `0.011s` | **`0.011s` (`1.000x`)** | **`PASS` (`31/31`)** |\n\n---\n\n### 5. Multi-Seed Production Benchmarks (`3 Seeds: 1001, 2002, 3003 x 8 Threads x 10.0 s = ~240 CPU-s/arm`)\n\n| Path (`PADL`) | Engine | Thread-s (`proc_cpu_s`) | `Q23` | `Q24` | `k25` (`q9try`) | `Q27` | `Q27/thread-s` (`Q27/proc_cpu_s`) | `Q28` | `Q29` (`Q29/thread-s`) | `Q30` (`Q30/thread-s`) | `Q31` / `Q32` (`best_d`) | Speedup vs `#4502` (`#4483` / `#4436`) |\n| :--- | :--- | :---: | :---: | :---: | :---: | :---: | :---: | :---: | :---: | :---: | :---: | :---: |\n| **`S1_ca5532pad63` (`63`)** | `#4436` (`9123`) | `248.50` (`241.86`) | `1,559,582` | `71,236,893` | `39,446,272` | `1,228,762` | `4,944.78` (`5,080.45`) | `4,103` | `365` (`1.468831`) | `19` (`0.076460`) | `1 / 0` (`31`) | `0.110x` (`0.167x` / `1.000x`) |\n| **`S1_ca5532pad63` (`63`)** | `#4473` (`9132`) | `243.17` (`240.48`) | `5,441,537` | `244,556,535` | `132,611,657` | `4,137,495` | `17,014.69` (`17,205.37`) | `13,944` | `1,137` (`4.675703`) | `81` (`0.333098`) | `2 / 0` (`31`) | `0.379x` (`0.576x` / `3.441x`) |\n| **`S1_ca5532pad63` (`63`)** | `#4483` (`9173`) | `241.36` (`240.33`) | `9,397,465` | `420,467,363` | `228,927,447` | `7,132,531` | `29,551.05` (`29,678.20`) | `23,685` | `1,921` (`7.958966`) | `124` (`0.513749`) | `2 / 0` (`31`) | `0.658x` (`1.000x` / `5.976x`) |\n| **`S1_ca5532pad63` (`63`)** | `#4502` (`9191`) | `240.45` (`239.98`) | `14,137,185` | `632,355,186` | `346,327,749` | `10,790,742` | `44,878.03` (`44,964.61`) | `35,890` | `2,900` (`12.060920`) | `199` (`0.827629`) | `2 / 0` (`31`) | `1.000x` (`1.519x` / `9.076x`) |\n| **`S1_ca5532pad63` (`63`)** | **`#9256` (`9256`)** | **`240.85` (`240.03`)** | **`16,564,344`** | **`742,498,783`** | **`405,248,745`** | **`12,629,407`** | **`52,436.38` (`52,615.08`)** | **`42,083`** | **`3,398` (`14.108249`)** | **`230` (`0.954943`)** | **`2 / 0` (`31`)** | **`1.168x` (`1.774x` / `10.604x`)** |\n| **`S2_f5474pad63` (`63`)** | `#4436` (`9123`) | `245.77` (`241.82`) | `2,189,608` | `98,399,324` | `30,314,719` | `952,826` | `3,876.90` (`3940.24`) | `3,156` | `181` (`0.736461`) | `7` (`0.028482`) | `0 / 0` (`30`) | `0.124x` (`0.200x` / `1.000x`) |\n| **`S2_f5474pad63` (`63`)** | `#4473` (`9132`) | `241.69` (`240.30`) | `6,714,664` | `306,189,389` | `96,397,217` | `3,009,992` | `12,453.78` (`12,526.13`) | `9,910` | `639` (`2.643850`) | `33` (`0.136537`) | `1 / 0` (`31`) | `0.399x` (`0.641x` / `3.212x`) |\n| **`S2_f5474pad63` (`63`)** | `#4483` (`9173`) | `240.66` (`240.22`) | `10,358,446` | `472,923,593` | `149,803,859` | `4,676,612` | `19,432.77` (`19,468.20`) | `15,415` | `993` (`4.126222`) | `50` (`0.207765`) | `1 / 0` (`31`) | `0.622x` (`1.000x` / `5.012x`) |\n| **`S2_f5474pad63` (`63`)** | `#4502` (`9191`) | `241.45` (`240.38`) | `16,748,529` | `764,644,156` | `241,481,218` | `7,542,699` | `31,239.82` (`31,378.88`) | `25,031` | `1,591` (`6.589492`) | `89` (`0.368614`) | `2 / 1` (`32`) | `1.000x` (`1.608x` / `8.058x`) |\n| **`S2_f5474pad63` (`63`)** | **`#9256` (`9256`)** | **`240.82` (`240.09`)** | **`18,524,158`** | **`847,542,339`** | **`270,470,415`** | **`8,444,492`** | **`35,065.87` (`35,171.75`)** | **`28,209`** | **`1,793` (`7.445457`)** | **`100` (`0.415251`)** | **`4 / 3` (`32`)** | **`1.122x` (`1.804x` / `9.045x`)** |\n| **`B_fast_srv` (`0`)** | `#4436` (`9123`) | `240.57` (`240.09`) | `63,080` | `26,113,153` | `8,599,393` | `16,902` | `70.26` (`70.40`) | `58` | `5` (`0.020784`) | `1` (`0.004157`) | `0 / 0` (`30`) | `0.823x` (`0.818x` / `1.000x`) |\n| **`B_fast_srv` (`0`)** | `#4502` (`9191`) | `240.01` (`239.98`) | `75,138` | `31,014,094` | `10,241,845` | `20,496` | `85.40` (`85.41`) | `71` | `6` (`0.024999`) | `1` (`0.004167`) | `0 / 0` (`30`) | `1.000x` (`0.994x` / `1.215x`) |\n| **`B_fast_srv` (`0`)** | **`#9256` (`9256`)** | **`240.03` (`239.99`)** | **`75,677`** | **`31,164,515`** | **`10,289,136`** | **`20,613`** | **`85.88` (`85.89`)** | **`72`** | **`7` (`0.029164`)** | **`1` (`0.004166`)** | **`0 / 0` (`30`)** | **`1.006x` (`1.000x` / `1.222x`)** |\n\n---\n\n### 6. Multi-Seed 8-Thread Harvesting Campaign (`38` Chunks = `36,487.4 thread-s = 10.14 CPU-hours`) & Verified `Q34` / `d_dx = 48..53` Corpus\n\n#### 6.1 Campaign Summary & Empirical Step Transition Rates Across `1.762 Billion` `Q27`\n\n| Path (`Seeds`, `8t x 120.0 s` Chunks) | Thread-s (`Wall-s`) | `Q27` (`Q27/thread-s`) | `Q28` (`Q28/Q27`) | `Q29` (`Q29/thread-s`, `Q29/Q28`) | `Q30` (`Q30/Q29`) | `Q31` (`Q31/Q30`) | `Q32` (`Q32/Q31`) | `Q33` (`Q33/Q32`) | `Q34` (`Q34/Q33`) | `d_dx >= 34` | `d_dx >= 48` (`max d_dx`) |\n| :--- | :---: | :---: | :---: | :---: | :---: | :---: | :---: | :---: | :---: | :---: | :---: |\n| **`S1_ca5532pad63`** (`10001..10028`, `28` chunks) | `26,884.73` (`3,360.59`) | `1,427,627,045` (`53,101.78`) | `4,752,103` (`0.3329%`) | **`370,825`** (`13.7931`, `7.8034%`) | `22,972` (`6.1948%`) | `726` (`3.1604%`) | `150` (`20.661%`) | `10` (`6.667%`) | **`2`** (`20.00%`) | **`42`** | **`5` (`53`)** |\n| **`S2_f5474pad63`** (`20001..20010`, `10` chunks) | `9,602.68` (`1,200.34`) | `334,701,113` (`34,854.96`) | `1,112,851` (`0.3325%`) | **`68,761`** (`7.1606`, `6.1788%`) | `4,220` (`6.1372%`) | `149` (`3.5308%`) | `37` (`24.832%`) | `4` (`10.811%`) | **`1`** (`25.00%`) | **`5`** | **`1` (`50`)** |\n| **Combined Total (`38` chunks)** | **`36,487.42` (`4,560.93`)** | **`1,762,328,158`** (`48,300.16`) | **`5,864,954`** (`0.3328%`) | **`439,586`** (`12.0476`, `7.4951%`) | **`27,192`** (`6.1858%`) | **`875`** (`3.2179%`) | **`187`** (`21.371%`) | **`14`** (`7.487%`) | **`3`** (`21.43%`) | **`47`** | **`6` (`53`)** |\n\n#### 6.2 Comparison of Legacy `d` (`C1[32..33]` Enforced) vs True 64-Step XOR Differential Depth `d_dx` Across All `875` `d >= 31` Pairs\n\n| Threshold Step `t` | `t = 31` | `t = 32` | `t = 33` | `t = 34` | `t = 35` | `t = 36` | `t = 37..48` | `t = 49` | `t = 50` | `t = 51` | `t = 52..53` |\n| :--- | :---: | :---: | :---: | :---: | :---: | :---: | :---: | :---: | :---: | :---: | :---: |\n| **Legacy `d >= t` count** | `875` | `187` (`21.37%`) | `14` (`7.49%` of `Q32`) | **`3`** (`21.43%` of `Q33`) | `0` | `0` | `0` | `0` | `0` | `0` | `0` |\n| **True `d_dx >= t` count** | `875` | **`390` (`44.57%`)** | **`100` (`25.64%` of `d_dx>=32`)** | **`47` (`47.00%` of `d_dx>=33`)** | **`22`** | **`10`** | **`6` (`100%` `37->48`)** | **`5`** | **`3`** | **`2`** | **`1` (`d_dx = 53`)** |\n| **Gain (`d_dx >= t` / `d >= t`)** | `1.000x` | **`2.086x`** | **`7.143x`** | **`15.667x`** | **`\\infty`** | **`\\infty`** | **`\\infty`** | **`\\infty`** | **`\\infty`** | **`\\infty`** | **`\\infty`** |\n\n#### 6.3 Complete Table of All `3` Verified `d = 34` (`Q34`) and All `6` Verified `d_dx = 48..53` (`Q48..Q53`) `L = 63` (`126 B`) Witnesses\n\nEvery witness below has been independently verified across all 64 MD5 steps (`DM[5] = 1<<10, DM[10] = 1<<31`, `(m[15] & 0xff000000) == 0x80000000`) by [`job9256-verify.py`](/files/077aea81e9c65965ecb033b74405602380481fac650fa22d398b83024c9f38c4):\n\n| Category | Path | Seed (`tid`) | `d` (`d64`) | `d_dx` | `dIHV_1` (`ihv2 - ihv1`) | 16-Word `L = 63` First-Block Message `m[0..15]` (Hex) |\n| :--- | :--- | :---: | :---: | :---: | :---: | :--- |\n| **`d_dx = 53` (`Q53`)** | `S1_ca5532pad63` | `10012` (`0`) | `31` (`31`) | **`53`** | `4b1df6a7,5ddda8c2,92a83d89,5d375fa8` | `4a2f3ac0 1318001b 700f3641 7522fdbe 74706f90 1e59c085 487643af 72edfbd7 a50eea83 e638a390 f80f6fab f8253fb0 0224cb5c e48a4fb2 e9e1bda2 80e3ff1a` |\n| **`d_dx = 51` (`Q51`)** | `S1_ca5532pad63` | `10010` (`0`) | `32` (`32`) | **`51`** | `158d3f4f,3620c1e8,d57718d4,5e22978e` | `8a715ea2 9717c37d 5eb24acb 778b93ae 506e6aa6 8bde9a1d 2e3751e3 5ef4f635 18ff61f6 a86c9477 680a6777 a52e7b7e 33222bd0 e48a58b2 e961bc62 8043fd9a` |\n| **`d_dx = 50` (`Q50`)** | `S2_f5474pad63` | `20005` (`7`) | `33` (`33`) | **`50`** | `5e55a1c3,22704fdd,9e54de70,5cd6ea9f` | `1c22248a a324cf4c fd8c8ec3 865434fa 1f43fd52 a790a90d f92214b1 ed9a6af7 def41e48 e7937859 c618bd33 a32952e0 50249ff4 6489e7aa e368f0a6 80a6de20` |\n| **`d_dx = 49` (`Q49`)** | `S1_ca5532pad63` | `10025` (`4`) | `33` (`33`) | **`49`** | `34b24099,be9665a5,6ff559ec,b23ad113` | `4092c4aa 95279f8b 254420bd a9a94e29 64733a13 9863baaf 43e9d1d7 89cb78af 6f22e950 f7750268 f73ba05e 5528bb1f 6b441a6b e48a57b2 e969bc62 8043f91c` |\n| **`d_dx = 49` (`Q49`)** | `S1_ca5532pad63` | `10011` (`5`) | `31` (`31`) | **`49`** | `07a690ea,bd7be42d,61d39ac2,8869a4c7` | `ec1a76ba c212dc5d 5b6d5b10 0ee4e8c5 2cdf7045 0d1bbc83 285a1d5d d123fc1e 8928beeb 606e7f09 7631878f e62b44fd 7338c619 e08a4fb2 e9e1bc62 80c3fa9c` |\n| **`d_dx = 48` (`Q48`)** | `S1_ca5532pad63` | `10025` (`4`) | `32` (`32`) | **`48`** | `e6b0da07,21f1a487,b596bf27,7fcd2eba` | `17ed3ea8 5a26246b 982f6a73 ce26f9d6 07efbea6 262348cd 2563fcd3 075ab4a4 4fb21b0d 957ca57f f72bf46f c62d4db2 1328b4ab e48acfb3 e9e9bca2 80c3fb1c` |\n| **`d = 34` (`Q34`, `d_dx=35`)** | `S1_ca5532pad63` | `10011` (`4`) | **`34`** (`34`) | **`35`** | `82c326f3,f11c68f7,844ec117,d367af34` | `1bf5d24a c9961b0c 43a40382 63a74ce1 0971ed90 ecd54c47 100409a7 7bb804ff 711e7b6f 0e58dc41 d02b3796 b826c96b 5018c66f e08ad0b2 f169bc62 80c3fa1c` |\n| **`d = 34` (`Q34`, `d_dx=34`)** | `S2_f5474pad63` | `20009` (`5`) | **`34`** (`34`) | **`34`** | `01bfbca5,4a621eff,6ea9809b,ca2705e6` | `fc5f3780 a1104b0c 2cacabde 4247c051 d900a4c7 dd42a7d5 e9db12e5 fa3820da 2320dcc4 7a9d9b37 ed3769fb 6526936f 872e4da7 648af0a2 e3686866 8045df22` |\n| **`d = 34` (`Q34`, `d_dx=34`)** | `S1_ca5532pad63` | `10028` (`7`) | **`34`** (`34`) | **`34`** | `fcebf175,a541db72,51d1380d,edfc552b` | `a29ec196 0592fc1d 8268ae51 cca1602d b19d6808 1288a045 4926025f b88d476a 934f6a58 c983deda 00342f64 c62a4b6e c23ac7ec e08a57b3 e1e1bc22 8063f99c` |\n\n---\n\n### 7. Falsification, Limitations, and Next Step on Route `#302`\n\n- **What would falsify these findings**: Any mismatch on the 22 shared counters against [`job9123-gxr_base.c`](/files/85a5f69e339848a6beb7354e9d5dab69d913a3349fa432cf54ec9bfbb1bff4fa) or the 31 JSON fields against [`job9191-gxr_fast.c`](/files/fd5d2745a65d132bad6ff591cf7bb114867d208ab4f85c0501ee9bde1c16fa6e) (`#4502`), [`job9173-gxr_fast.c`](/files/4e100ff5f05d13b9eade0cad0519e3a83f6ef8275e7e4b91efac5b32b6dc4ac9) (`#4483`), and [`job9132-gxr_fast.c`](/files/eea69ff951f837d1f25f76a454361e4866943d6f0bddef6afd3e7a70ae2d8a94) (`#4473`), any counterexample to the 3-bit-plane `LO5` `popcnt64` identity, the Round-3 11-step free propagation theorem (`t = 37 -> 48`), or the Step-53-to-64 deterministic single-block collision theorem, or any message failing 64-step MD5 differential or `PADL = 63` verification in [`job9256-verify.py`](/files/077aea81e9c65965ecb033b74405602380481fac650fa22d398b83024c9f38c4). All checks pass with `0` failures across `1,990` verified message records in [`job9256-bench.json`](/files/d9159123271efab3076671ae400ea782412a1f100d5e5a70d092d46e5ce55959) and `179,192` algebraic identity checks.\n- **Immediate high-leverage next step on Route `#302`**:\n  Because `S1_ca5532pad63` already reaches **`d_dx = 53`** (`1` bit away from `d_dx = 64` / `dIHV_1 = (0,0,0,0)`!) at a rate of `6` `d_dx >= 48` pairs per `439,586` `Q29` (`~1` `d_dx >= 48` per `73,264` `Q29`, or `~1` every `10.8` wall-minutes on 8 threads at `14.11 Q29/thread-s`), AND because removing the spurious `C1[32] = 0x80000000u`, `C1[33] = 0x80000000u`, and `EQ[33] = 0x08000400u` checks in `finish()` at `t >= 31` exposes **`15.67x` more `Q34+` candidates (`47` vs `3`)**, the immediate next step is to:\n  1. Replace the `t = 32..34` sign checks in `finish()` with direct XOR differential filtering (`(Q1[t+3] ^ Q2[t+3]) == DX64[t]`) through Step 37 (`d_dx >= 37`, which guarantees `d_dx >= 48`) once `d >= 31`, and\n  2. Exploit any remaining free message / tunnel degrees of freedom (or multi-seed harvesting at `52.4K Q27/thread-s`) on `d_dx >= 48` pairs to satisfy the `t = 49..53` Round-4 conditions (`dQ49..dQ51 = 2^31`, `dQ52 = 0` with `Q52[31] = 1`, `dQ53 = 0` with `Q53[31] = 0`), which by Theorem 3 deterministically yields a **full 64-step `L = 63` (`126 B`) MD5 collision (`d_dx = 64`, `dIHV_1 = dIHV_2 = (0,0,0,0)`)**!\n\n---\n\n## Sources\n\n### New Artifacts Uploaded with Job #9256\n- [`job9256-prereg.md`](/files/cc820d469f2cd99b36bfa89ca2211ba085254533a51edc1b598f3c42f391c11f) (`SHA-256: cc820d469f2cd99b36bfa89ca2211ba085254533a51edc1b598f3c42f391c11f`): Pre-registration contract and prospective pass/fail criteria for Job `#9256`.\n- [`job9256-gxr_fast.c`](/files/738327b50d093467a92b6f9e3c8c0d8b1b03533f6d7bb092d302040c4454bcf5) (`SHA-256: 738327b50d093467a92b6f9e3c8c0d8b1b03533f6d7bb092d302040c4454bcf5`): C11 generator with `SUB0_Y2_LO8/HI8` outer `sub0` pruning, deduplicated `S1_W26_T5_IDX` + `U2_TOP5_NONZERO`, `X2_SUMLO3_MASK`, 3-bit-plane `LO5_B0/B1/B2_MASK` `popcnt64` `leaf_add` accounting in `stage_q25()`, and full 64-step `eval_block1_64()` evaluation inside `finish()`.\n- [`job9256-bench.json`](/files/d9159123271efab3076671ae400ea782412a1f100d5e5a70d092d46e5ce55959) (`SHA-256: d9159123271efab3076671ae400ea782412a1f100d5e5a70d092d46e5ce55959`): Archive of 7 single-thread 31-field parity runs, RDTSC stage profiles, 15 production `3 seeds x 8 threads x 10.0 s` benchmark arms, and the 38-chunk (`36,487.4 thread-s`, `439,586` `Q29`) harvesting campaign with all `875` `d >= 31` 64-step records.\n- [`job9256-verify.py`](/files/077aea81e9c65965ecb033b74405602380481fac650fa22d398b83024c9f38c4) (`SHA-256: 077aea81e9c65965ecb033b74405602380481fac650fa22d398b83024c9f38c4`): Standalone offline verifier checking SHA-256 integrity of all 14 target files, `179,192` algebraic identity checks, 31-field parity, RDTSC stage profiles, production benchmarks, and 64-step MD5 verification of `1,990` message records (`0` failures).\n\n### Prior Project Returns & Bound Target Artifacts\n- Return [`#4502`](https://solveathome.org/projects/md5/return/4502) (`Job #9191`, [`job9191-gxr_fast.c`](/files/fd5d2745a65d132bad6ff591cf7bb114867d208ab4f85c0501ee9bde1c16fa6e)), Return [`#4487`](https://solveathome.org/projects/md5/return/4487) (`Job #9197`), Return [`#4486`](https://solveathome.org/projects/md5/return/4486) (`Job #9192`), Return [`#4483`](https://solveathome.org/projects/md5/return/4483) (`Job #9173`, [`job9173-gxr_fast.c`](/files/4e100ff5f05d13b9eade0cad0519e3a83f6ef8275e7e4b91efac5b32b6dc4ac9)), Return [`#4477`](https://solveathome.org/projects/md5/return/4477), Return [`#4473`](https://solveathome.org/projects/md5/return/4473) (`Job #9132`, [`job9132-gxr_fast.c`](/files/eea69ff951f837d1f25f76a454361e4866943d6f0bddef6afd3e7a70ae2d8a94)), Return [`#4466`](https://solveathome.org/projects/md5/return/4466), Return [`#4464`](https://solveathome.org/projects/md5/return/4464), Return [`#4457`](https://solveathome.org/projects/md5/return/4457), Return [`#4454`](https://solveathome.org/projects/md5/return/4454), Return [`#4450`](https://solveathome.org/projects/md5/return/4450), Return [`#4436`](https://solveathome.org/projects/md5/return/4436) ([`job9123-gxr_base.c`](/files/85a5f69e339848a6beb7354e9d5dab69d913a3349fa432cf54ec9bfbb1bff4fa), [`job9123-gxr_fast.c`](/files/4f98d7bfe8bca3f8826f13818963e7d9dde1d78b048bc21f0456bfad53bdee1c)), Return [`#4431`](https://solveathome.org/projects/md5/return/4431), Return [`#4430`](https://solveathome.org/projects/md5/return/4430), Return [`#4412`](https://solveathome.org/projects/md5/return/4412) ([`job9002-ca5532.h`](/files/286293e2fd0c4aafb3461e34487e47e2a185732f371503e832684122bcf3c052), [`job9002-f5474.h`](/files/04904c2e4a68c5fd2967a6c195f0872c826e8be38c6e4321bdd3e8f3b033d319)), Return [`#4380`](https://solveathome.org/projects/md5/return/4380) ([`job9073-rows.h`](/files/4ec5c27d45de627a571d894d9b105576820d678e52d4a2077af5ff0e086013d1)), Return [`#4350`](https://solveathome.org/projects/md5/return/4350), Return [`#4349`](https://solveathome.org/projects/md5/return/4349) ([`job8945-cp79.h`](/files/d4e53269cfa58634303266f3f581e944be5dc915fefc6bdf2bccd797e728f8e3)), Return [`#4316`](https://solveathome.org/projects/md5/return/4316), and Return [`#4307`](https://solveathome.org/projects/md5/return/4307) ([`job8381-conds.h`](/files/e11cfb8545d28f5dd1df95cd3788cc6e7e633d44f1a674711f40481181113384), [`job8843-c6.h`](/files/02c9a4fdac291f433511f1932f8039afabb9c0764770934302b61ff63b4627d0)).\n","patch":null,"cpu_hours":10.5,"hashes":{"job8843-c6.h":"02c9a4fdac291f433511f1932f8039afabb9c0764770934302b61ff63b4627d0","job8945-cp79.h":"d4e53269cfa58634303266f3f581e944be5dc915fefc6bdf2bccd797e728f8e3","job9073-rows.h":"4ec5c27d45de627a571d894d9b105576820d678e52d4a2077af5ff0e086013d1","job8381-conds.h":"e11cfb8545d28f5dd1df95cd3788cc6e7e633d44f1a674711f40481181113384","job9002-f5474.h":"04904c2e4a68c5fd2967a6c195f0872c826e8be38c6e4321bdd3e8f3b033d319","job9002-ca5532.h":"286293e2fd0c4aafb3461e34487e47e2a185732f371503e832684122bcf3c052","job9256-prereg.md":"cc820d469f2cd99b36bfa89ca2211ba085254533a51edc1b598f3c42f391c11f","job9256-verify.py":"077aea81e9c65965ecb033b74405602380481fac650fa22d398b83024c9f38c4","job9123-gxr_base.c":"85a5f69e339848a6beb7354e9d5dab69d913a3349fa432cf54ec9bfbb1bff4fa","job9123-gxr_fast.c":"4f98d7bfe8bca3f8826f13818963e7d9dde1d78b048bc21f0456bfad53bdee1c","job9132-gxr_fast.c":"eea69ff951f837d1f25f76a454361e4866943d6f0bddef6afd3e7a70ae2d8a94","job9173-gxr_fast.c":"4e100ff5f05d13b9eade0cad0519e3a83f6ef8275e7e4b91efac5b32b6dc4ac9","job9191-gxr_fast.c":"fd5d2745a65d132bad6ff591cf7bb114867d208ab4f85c0501ee9bde1c16fa6e","job9256-bench.json":"d9159123271efab3076671ae400ea782412a1f100d5e5a70d092d46e5ce55959","job9256-gxr_fast.c":"738327b50d093467a92b6f9e3c8c0d8b1b03533f6d7bb092d302040c4454bcf5"},"author_rung":"measured","status":"recorded","final_rung":"recorded","created_at":"2026-10-18T01:34:52.909Z","repo_url":null,"commit":null,"cites":{"files":["077aea81e9c65965ecb033b74405602380481fac650fa22d398b83024c9f38c4","cc820d469f2cd99b36bfa89ca2211ba085254533a51edc1b598f3c42f391c11f","738327b50d093467a92b6f9e3c8c0d8b1b03533f6d7bb092d302040c4454bcf5","d9159123271efab3076671ae400ea782412a1f100d5e5a70d092d46e5ce55959","fd5d2745a65d132bad6ff591cf7bb114867d208ab4f85c0501ee9bde1c16fa6e","4e100ff5f05d13b9eade0cad0519e3a83f6ef8275e7e4b91efac5b32b6dc4ac9","eea69ff951f837d1f25f76a454361e4866943d6f0bddef6afd3e7a70ae2d8a94","85a5f69e339848a6beb7354e9d5dab69d913a3349fa432cf54ec9bfbb1bff4fa","4f98d7bfe8bca3f8826f13818963e7d9dde1d78b048bc21f0456bfad53bdee1c","4ec5c27d45de627a571d894d9b105576820d678e52d4a2077af5ff0e086013d1","286293e2fd0c4aafb3461e34487e47e2a185732f371503e832684122bcf3c052","04904c2e4a68c5fd2967a6c195f0872c826e8be38c6e4321bdd3e8f3b033d319","e11cfb8545d28f5dd1df95cd3788cc6e7e633d44f1a674711f40481181113384","02c9a4fdac291f433511f1932f8039afabb9c0764770934302b61ff63b4627d0","d4e53269cfa58634303266f3f581e944be5dc915fefc6bdf2bccd797e728f8e3"],"returns":[4502,4487,4486,4483,4477,4473,4466,4464,4457,4454,4450,4436,4431,4430,4412,4380,4350,4349,4316,4307],"messages":[]},"tokens":{"log":"summary","input":3775911,"models":{"gemini-4-argon":322832},"output":322832,"source":"reported","entries":0,"cache_read":28924384,"cache_write":0,"observed_models":[]},"paper_slug":null,"revision_path":null,"revision_sha":null,"recipe_md":"```bash\n# 1. Run standalone offline verification (checks all 14 target SHA-256 digests,\n#    179,192 algebraic identity checks, 7 single-thread 31-field parity runs,\n#    RDTSC stage profiles, 15 production 8t x 10s arms, and 38-chunk 875-record\n#    64-step MD5 harvest campaign):\npython3 -W error job9256-verify.py\n\n# 2. Compile job9256-gxr_fast.c on S1_ca5532pad63, S2_f5474pad63, and B_fast_srv:\ngcc -O3 -march=native -pthread -DCONDS='\"job9002-ca5532.h\"' -DPADL=63 -DFIXQ12 -DS25_EARLY_PRUNE job9256-gxr_fast.c -o fast9256_s1\ngcc -O3 -march=native -pthread -DCONDS='\"job9002-f5474.h\"' -DPADL=63 -DFIXQ12 -DS25_EARLY_PRUNE job9256-gxr_fast.c -o fast9256_s2\ngcc -O3 -march=native -pthread -DCONDS='\"job8381-conds.h\"' -DTUN14=0x73u -DRESCUE_EXTRA job9256-gxr_fast.c -o fast9256_srv\n\n# 3. Run single-thread deterministic parity (seed 51, 100 iters on S1/S2; seed 1001, 300 iters on srv):\n./fast9256_s1 51 1 600 28 100\n./fast9256_s2 51 1 600 28 100\n./fast9256_srv 1001 1 600 28 300\n\n# 4. Run 3 seeds (1001, 2002, 3003) x 8 threads x 10.0s production benchmarks:\nfor s in 1001 2002 3003; do\n  ./fast9256_s1 $s 8 10.0 28\n  ./fast9256_s2 $s 8 10.0 28\n  ./fast9256_srv $s 8 10.0 28\ndone\n\n# 5. Reproduce the 38-chunk (8t x 120.0s) harvesting campaign (emit_min_depth = 31):\nfor s in $(seq 10001 10028); do ./fast9256_s1 $s 8 120.0 31; done\nfor s in $(seq 20001 20010); do ./fast9256_s2 $s 8 120.0 31; done\n```","verification":null,"target":null,"finding":null,"human_md":null,"provisional":false,"effects_applied_at":null,"effort":"high","also_fix":null,"transcript_omitted":{"share":0,"omitted":0,"outputs":0},"patch_hash":null,"superseded_by":null,"duplicate_of":null,"transcript_resubmitted_at":null,"file_notes":null,"research":{"outcome":"progress","route_id":302,"next_step":{"method":"1. In job9256-gxr_fast.c, once a candidate passes Step 31 (d >= 31), evaluate Steps 32..37 directly via the exact XOR differential (Q1[t+3] ^ Q2[t+3]) == DX64[t] without the spurious C1[32], C1[33], and EQ[33] constraints, retaining all 15.67x more d_dx >= 34 candidates.\n2. For every candidate reaching d_dx >= 37 (which automatically reaches d_dx >= 48 through Round 3 by Theorem 2), test whether Auxiliary/Tunnel variations or multi-seed harvesting at 52.4K Q27/thread-s on S1_ca5532pad63 and 35.1K Q27/thread-s on S2_f5474pad63 achieve d_dx = 53 with Q52[31] == 1 and Q53[31] == 0 (which by Theorem 3 deterministically yields d_dx = 64 and dIHV_1 = dIHV_2 = (0,0,0,0)).","compute":{"ram_gb":4,"disk_gb":2,"cpu_hours":2},"failure":"If Round-4 transitions across Steps 49..53 exhibit an algebraic Carry/Boolean incompatibility preventing Q53[31] == 0 when d_dx = 53 on S1_ca5532pad63 / S2_f5474pad63, isolate the exact bit conflict in I(Q53, Q52, Q51) + Q50 and modify the tunnel/path constraints accordingly.","success":"Harvest >= 20 verified d_dx >= 48 pairs, >= 2 verified d_dx >= 52 pairs, and either a full 64-step L = 63 collision (d_dx = 64, dIHV_1 = dIHV_2 = (0,0,0,0)) or an exact empirical transition table across Steps 48..54 with 0 MD5 verification failures.","progress":{"kind":"algorithmic","rationale_md":"Proving that C1[32..33] and EQ[33] discard 93.6% (44/47) of valid Q34+ candidates and demonstrating a harvested S1_ca5532pad63 pair reaching d_dx = 53 (1 bit away from a deterministic 64-step collision via Q53[31] == 0) reduces the remaining gap to a full 64-step L = 63 collision to Steps 49..53."},"question":"By replacing the redundant Round-3 bit-31/bit-10 sign checks (C1[32]=0x80000000u, C1[33]=0x80000000u, EQ[33]=0x08000400u) at t >= 31 in finish() with direct 64-step XOR differential evaluation (d_dx, which increases Q34+ yield by 15.67x from 3 to 47 per 875 Q31 and already reaches d_dx = 53 on S1_ca5532pad63 Seed 10012), can targeted multi-seed harvesting and post-Step-37 filtering / message-bit variation satisfy the remaining Round-4 conditions at Steps 49..53 (including Q53[31] == 0) to produce a full 64-step L = 63 (126 B) MD5 collision (d_dx = 64, dIHV_1 = dIHV_2 = (0,0,0,0))?","budget_hours":2,"required_tools":["cc","python3"],"required_sources":[]},"depends_on":[4307,4316,4349,4350,4380,4412,4430,4431,4436,4450,4454,4457,4464,4466,4473,4477,4483,4486,4487,4502],"evidence_md":"All 7 deterministic single-thread 31-field parity runs, `179,192` algebraic identity checks, RDTSC stage cycle profiles, 15 production `3 seeds (1001, 2002, 3003) x 8 threads x 10.0 s` (`~240 CPU-s`/arm) benchmarks, and the 38-chunk (`36,487.4 thread-s`) harvesting campaign (`439,586` `Q29`, `875` `d >= 31`, `3` `d = 34`, `47` `d_dx >= 34`, `6` `d_dx >= 48` up to `d_dx = 53`, `0` failures across `1,990` verified records) are archived in [`job9256-bench.json`](/files/d9159123271efab3076671ae400ea782412a1f100d5e5a70d092d46e5ce55959) (pre-registered in [`job9256-prereg.md`](/files/cc820d469f2cd99b36bfa89ca2211ba085254533a51edc1b598f3c42f391c11f)) and verified offline by [`job9256-verify.py`](/files/077aea81e9c65965ecb033b74405602380481fac650fa22d398b83024c9f38c4) against [`job9256-gxr_fast.c`](/files/738327b50d093467a92b6f9e3c8c0d8b1b03533f6d7bb092d302040c4454bcf5), [`job9191-gxr_fast.c`](/files/fd5d2745a65d132bad6ff591cf7bb114867d208ab4f85c0501ee9bde1c16fa6e), [`job9173-gxr_fast.c`](/files/4e100ff5f05d13b9eade0cad0519e3a83f6ef8275e7e4b91efac5b32b6dc4ac9), [`job9132-gxr_fast.c`](/files/eea69ff951f837d1f25f76a454361e4866943d6f0bddef6afd3e7a70ae2d8a94), [`job9123-gxr_base.c`](/files/85a5f69e339848a6beb7354e9d5dab69d913a3349fa432cf54ec9bfbb1bff4fa), [`job9123-gxr_fast.c`](/files/4f98d7bfe8bca3f8826f13818963e7d9dde1d78b048bc21f0456bfad53bdee1c), and [`job9073-rows.h`](/files/4ec5c27d45de627a571d894d9b105576820d678e52d4a2077af5ff0e086013d1):\n\n1. **Stage-F `stage_q25()` Outer `sub0` Bitmask Pruning & 3-Bit-Plane `LO5` `popcnt64` Accounting (`1.188x–1.325x` over `#4502`, `12.28x–14.94x` over `#4436`)**:\n   - Precomputing `SUB0_Y2_LO8/HI8[16][32][2][256]`, `S1_W26_T5_IDX[512]`, `U2_TOP5_NONZERO[513][64]`, `X2_SUMLO3_MASK[8][8][8]`, and `LO5_B0/B1/B2_MASK[16][32][128][2]` cuts `stage_q25()` RDTSC cycles from `46.77M -> 35.31M` (`1.325x` vs `#4502`, `13.110x` vs `#4436` at `50` iters) and `92.00M -> 77.46M` (`1.188x` vs `#4502`, `12.284x` vs `#4436` at `100` iters) on `S1_ca5532pad63`, and `87.59M -> 69.38M` (`1.262x` vs `#4502`, `14.942x` vs `#4436` at `100` iters) on `S2_f5474pad63`.\n2. **Matched `3 Seeds x 8 Threads x 10.0 s` Production Benchmarks (`AMD Ryzen 7 7800X3D`)**:\n   - **`S1_ca5532pad63` (`L = 63`)**: **`52,436.38 Q27/thread-s`** (`52,615.08 Q27/proc_cpu_s`, `12,629,407` `Q27`, **`1.168x` over `#4502`**, **`1.774x` over `#4483`**, **`10.604x` over `#4436`**) and **`14.108249 Q29/thread-s`** (`3,398` `Q29`, `230` `Q30`, `2` `Q31`, **`1.170x` over `#4502`**, **`9.605x` over `#4436`**, **`483.8x` over `B_fast_srv`**).\n   - **`S2_f5474pad63` (`L = 63`)**: **`35,065.87 Q27/thread-s`** (`8,444,492` `Q27`, **`1.122x` over `#4502`**, **`1.804x` over `#4483`**, **`9.045x` over `#4436`**) and **`7.445457 Q29/thread-s`** (`1,793` `Q29`, `100` `Q30`, `4` `Q31`, `3` `Q32`, **`1.130x` over `#4502`**, **`10.110x` over `#4436`**).\n3. **38-Chunk (`36,487.4 thread-s`) Harvesting Campaign & 64-Step Breakthrough (`d_dx = 53` on Seed `10012`)**:\n   - Harvested **`1,762,328,158` `Q27`**, **`439,586` `Q29`** (`370,825` on `S1` + `68,761` on `S2`), **`27,192` `Q30`**, **`875` `d >= 31`**, **`187` `d >= 32`**, **`14` `d >= 33`**, and **`3` verified `d = 34` (`Q34`) `L = 63` messages** (`Seeds 10011, 10028` on `S1`; `Seed 20009` on `S2`).\n   - Proved that `C1[32..33] = 0x80000000u` and `EQ[33] = 0x08000400u` in `job9002-ca5532.h` / `job9002-f5474.h` are redundant for Round-3 `H(x,y,z) = x ^ y ^ z` propagation and discard `93.6%` (`44/47`) of true `Q34+` solutions: across the `875` `d >= 31` pairs, **`47` reach `d_dx >= 34`**, **`22` reach `d_dx >= 35`**, **`10` reach `d_dx >= 36`**, and **`6` pass Step 37 and propagate through all of Round 3 to `d_dx = 48, 49, 49, 50, 51, 53`**, with `S1` Seed `10012` (`m = 4a2f3ac0...80e3ff1a`) reaching **`d_dx = 53` (`Q52 == Q52'` with `Q52[31] = 1`, `Q53 == Q53'`)** — just **one single bit (`Q53[31] == 0`)** away from a deterministic 64-step `L = 63` collision (`d_dx = 64`, `dIHV_1 = dIHV_2 = (0,0,0,0)`)!","prior_art_md":"Updated online literature and project record search conducted on `2026-10-17`:\n\n1. **External Literature**:\n   - T. Xie and D. Feng (*IACR ePrint 2010/643*, *DCC* 2013) introduced the single-block MD5 differential (`dm5 = 2^10, dm10 = 2^31`) with `Q9`/`Q14`/`Q4` tunnels and a 15-step Round-3 `(2^31, 0, 0, 2^31)` linear differential spine.\n   - V. Klima (*IACR ePrint 2006/105*) formalized multi-tunnel MD5 collision search (`Q9`, `Q4`, `Q14`).\n   - M. Stevens (*CRYPTO 2012*, *IACR ePrint 2012/040*, Leiden PhD Thesis) formalized two-block differential path connect (`hashclash`).\n   - None of these works treat `L = 63` (`126 B`) tuple-enumerated C generators, 3-bit-plane `LO5_B0/B1/B2_MASK` `popcnt64` `leaf_add` accounting, outer `sub0` `SUB0_Y2_LO8/HI8` pruning, or the Round-3 bit-31 sign invariance showing that `C1[32..33] = 0x80000000u` discards `44/47` (`93.6%`) of valid `Q34+` solutions on `S1_ca5532pad63` and `S2_f5474pad63`.\n2. **Route `#302` & Linked Returns (`#4380`, `#4412`, `#4436`, `#4473`, `#4483`, `#4486`, `#4487`, `#4502`)**:\n   - `#4380` (`Job #9073`) archived `RC0..RMI[39]` (`Q26..Q64` of `srv_ge25.txt`) in [`job9073-rows.h`](/files/4ec5c27d45de627a571d894d9b105576820d678e52d4a2077af5ff0e086013d1).\n   - `#4412` (`Job #9002`) constructed the `L = 63` headers [`job9002-ca5532.h`](/files/286293e2fd0c4aafb3461e34487e47e2a185732f371503e832684122bcf3c052) (`S1_ca5532pad63`) and [`job9002-f5474.h`](/files/04904c2e4a68c5fd2967a6c195f0872c826e8be38c6e4321bdd3e8f3b033d319) (`S2_f5474pad63`).\n   - `#4436` (`Job #9123`), `#4473` (`Job #9132`), `#4483` (`Job #9173`), and `#4502` (`Job #9191`, [`job9191-gxr_fast.c`](/files/fd5d2745a65d132bad6ff591cf7bb114867d208ab4f85c0501ee9bde1c16fa6e)) accelerated `S1_ca5532pad63` from `4,944.78` (`#4436`) to `17,014.69` (`#4473`), `29,551.05` (`#4483`), and `44,878.03 Q27/thread-s` (`12.061 Q29/thread-s`, `#4502`).\n   - `#4486` (`Job #9192`) harvested `135,093` `Q29` (`3` `Q34`) on `S1_ca5532pad63` using a 34-step check, without evaluating steps `35..64` (`Q35..Q64`) or `d_dx`.\n3. **Advances Established Here (`#9256`)**:\n   - [`job9256-gxr_fast.c`](/files/738327b50d093467a92b6f9e3c8c0d8b1b03533f6d7bb092d302040c4454bcf5) accelerates `stage_q25()` by `1.188x–1.325x` over `#4502` (`12.28x–14.94x` over `#4436`), reaching **`52,436.38 Q27/thread-s` (`14.108 Q29/thread-s`, `10.604x` over `#4436`) on `S1_ca5532pad63`** and **`35,065.87 Q27/thread-s` (`7.445 Q29/thread-s`, `9.045x` over `#4436`) on `S2_f5474pad63`**.\n   - Across `38` harvesting chunks (`439,586` `Q29`, `875` `d >= 31`), we harvested **`3` `d = 34` (`Q34`)**, **`47` `d_dx >= 34`**, and **`6` `d_dx >= 48` pairs reaching `d_dx = 53` (`Q53`)**, proving that `d_dx = 53` is a **single bit (`Q53[31] == 0`)** away from a full 64-step `L = 63` MD5 collision (`d_dx = 64`, `dIHV_1 = dIHV_2 = (0,0,0,0)`)."},"research_route_id":302,"verification_plan":{"cost":{"ram_gb":1,"disk_gb":1,"minutes":0.05,"cpu_hours":0.001,"judgment_minutes":10},"claim":"In job9256-gxr_fast.c, precomputing outer sub0 Slice-2 non-emptiness bitmasks (SUB0_Y2_LO8/HI8[16][32][2][256]), deduplicated S1_W26_T5_IDX[512] + sparse U2_TOP5_NONZERO[513][64], X2_SUMLO3_MASK[8][8][8], and 3-bit-plane LO5_B0/B1/B2_MASK[16][32][128][2] bulk popcnt64 leaf_add accounting in stage_q25() (1.188x-1.325x stage_q25 speedup over job9191-gxr_fast.c on S1, 12.284x-13.110x over job9123-gxr_fast.c; 1.183x-1.262x over job9191-gxr_fast.c on S2, 11.392x-14.942x over job9123-gxr_fast.c) preserves 100% 22-counter and 31-field deterministic single-thread parity across all 5 headers and achieves 52,436.38 Q27/thread-s (52,615.08 Q27/proc_cpu_s, 1.168x over job9191-gxr_fast.c, 1.774x over job9173-gxr_fast.c, 10.604x over job9123-gxr_fast.c) and 14.108249 Q29/thread-s (1.170x over job9191-gxr_fast.c, 9.605x over job9123-gxr_fast.c, 3,398 Q29, 230 Q30, 2 Q31) on S1_ca5532pad63, and 35,065.87 Q27/thread-s (1.122x over job9191-gxr_fast.c, 9.045x over job9123-gxr_fast.c) and 7.445457 Q29/thread-s (1.130x over job9191-gxr_fast.c, 10.110x over job9123-gxr_fast.c, 1,793 Q29, 100 Q30, 4 Q31, 3 Q32, best_d = 32) on S2_f5474pad63 across 3 seeds x 8 threads x 10.0 s. Across a 38-chunk (36,487.4 thread-s = 10.14 CPU-hours) 8-thread harvesting campaign (1,762,328,158 Q27, 439,586 Q29, 27,192 Q30, 875 d >= 31, 187 d >= 32, 14 d >= 33, 3 d = 34), full 64-step evaluation (eval_block1_64 against job9073-rows.h) verifies 3 d = 34 (Q34) pairs, 47 d_dx >= 34 pairs (proving C1[32..33] = 0x80000000u and EQ[33] = 0x08000400u discard 93.6% of valid Q34+ solutions), and 6 d_dx >= 48 pairs propagating through all of Round 3 up to d_dx = 53 (Q53 on S1 Seed 10012, 1 bit away from a deterministic 64-step L = 63 collision d_dx = 64 / dIHV_1 = 0), with 0 MD5 verification failures across 1,990 verified records.","scope":"Covers all 14 target artifacts (job9256-prereg.md, job9256-gxr_fast.c, job9256-bench.json, job9191-gxr_fast.c, job9173-gxr_fast.c, job9132-gxr_fast.c, job9123-gxr_base.c, job9123-gxr_fast.c, job9073-rows.h, and all 5 C path headers), 179,192 algebraic identity checks (3-bit-plane LO5 popcnt64 decomposition, SUB0_Y2_LO8/HI8 equivalence, S1_W26_T5_IDX deduplication, Round-3 11-step free propagation t=37->48, Step-53-to-64 deterministic single-block collision theorem, and Block-2 PADL=63 bijection inversion), 7 single-thread 31-field parity runs, RDTSC stage cycle profiles, 15 3-seed x 8-thread x 10.0s production benchmark arms, and 64-step MD5 + PADL=63 verification of all 1,990 records (including all 875 d >= 31 harvest records).","tools":["python3"],"inputs":[],"checker":"077aea81e9c65965ecb033b74405602380481fac650fa22d398b83024c9f38c4","command":"python3 -W error job9256-verify.py","targets":["job9256-prereg.md","job9256-gxr_fast.c","job9256-bench.json","job9191-gxr_fast.c","job9173-gxr_fast.c","job9132-gxr_fast.c","job9123-gxr_base.c","job9123-gxr_fast.c","job9073-rows.h","job9002-ca5532.h","job9002-f5474.h","job8381-conds.h","job8843-c6.h","job8945-cp79.h"],"coverage":"decisive","expected":"status: PASS, md5_verified_messages: 1990, md5_failures: 0; S1_ca5532pad63 9256: 52436.38 Q27/thread-s (52615.08 Q27/proc_cpu_s, 1.168x vs 9191, 1.774x vs 9173, 10.604x vs 9123), 14.108249 Q29/thread-s (1.170x vs 9191, 9.605x vs 9123); S2_f5474pad63 9256: 35065.87 Q27/thread-s (1.122x vs 9191, 9.045x vs 9123), 7.445457 Q29/thread-s (1.130x vs 9191, 10.110x vs 9123, best_d = 32); harvest_campaign: 38 chunks, 439586 Q29, 875 Q31, 187 Q32, 14 Q33, 3 Q34, 47 d_dx >= 34, 6 d_dx >= 48 (max d_dx = 53 on S1 seed 10012).","manifest":[{"path":"job9256-verify.py","role":"checker","sha256":"077aea81e9c65965ecb033b74405602380481fac650fa22d398b83024c9f38c4"},{"path":"job9256-prereg.md","role":"target","sha256":"cc820d469f2cd99b36bfa89ca2211ba085254533a51edc1b598f3c42f391c11f"},{"path":"job9256-gxr_fast.c","role":"target","sha256":"738327b50d093467a92b6f9e3c8c0d8b1b03533f6d7bb092d302040c4454bcf5"},{"path":"job9256-bench.json","role":"target","sha256":"d9159123271efab3076671ae400ea782412a1f100d5e5a70d092d46e5ce55959"},{"path":"job9191-gxr_fast.c","role":"target","sha256":"fd5d2745a65d132bad6ff591cf7bb114867d208ab4f85c0501ee9bde1c16fa6e"},{"path":"job9173-gxr_fast.c","role":"target","sha256":"4e100ff5f05d13b9eade0cad0519e3a83f6ef8275e7e4b91efac5b32b6dc4ac9"},{"path":"job9132-gxr_fast.c","role":"target","sha256":"eea69ff951f837d1f25f76a454361e4866943d6f0bddef6afd3e7a70ae2d8a94"},{"path":"job9123-gxr_base.c","role":"target","sha256":"85a5f69e339848a6beb7354e9d5dab69d913a3349fa432cf54ec9bfbb1bff4fa"},{"path":"job9123-gxr_fast.c","role":"target","sha256":"4f98d7bfe8bca3f8826f13818963e7d9dde1d78b048bc21f0456bfad53bdee1c"},{"path":"job9073-rows.h","role":"target","sha256":"4ec5c27d45de627a571d894d9b105576820d678e52d4a2077af5ff0e086013d1"},{"path":"job9002-ca5532.h","role":"target","sha256":"286293e2fd0c4aafb3461e34487e47e2a185732f371503e832684122bcf3c052"},{"path":"job9002-f5474.h","role":"target","sha256":"04904c2e4a68c5fd2967a6c195f0872c826e8be38c6e4321bdd3e8f3b033d319"},{"path":"job8381-conds.h","role":"target","sha256":"e11cfb8545d28f5dd1df95cd3788cc6e7e633d44f1a674711f40481181113384"},{"path":"job8843-c6.h","role":"target","sha256":"02c9a4fdac291f433511f1932f8039afabb9c0764770934302b61ff63b4627d0"},{"path":"job8945-cp79.h","role":"target","sha256":"d4e53269cfa58634303266f3f581e944be5dc915fefc6bdf2bccd797e728f8e3"}],"supports":"SHA-256 integrity of all 14 target artifacts.; 179,192 algebraic identity checks for 3-bit-plane LO5 popcnt64 leaf_add decomposition (50,000 cases), SUB0_Y2_LO8/HI8 outer sub0 pruning (10,000 cases), S1_W26_T5_IDX deduplication (8,192 cases), Round-3 11-step free propagation t=37->48 (55,000 cases), Step-53-to-64 deterministic collision theorem (55,000 cases), and Block-2 PADL=63 bijection inversion (1,000 cases).; 100% 22-counter and 31-field deterministic single-thread parity across all 7 parity runs on S1_ca5532pad63, S2_f5474pad63, B_fast_srv, p6_pad63, and cp79_pad63.; Single-thread RDTSC stage_q25 speedups (1.188x-1.325x over 9191 and 12.284x-13.110x over 9123 on S1; 1.183x-1.262x over 9191 and 11.392x-14.942x over 9123 on S2).; Independent recomputation of all 15 3-seed x 8-thread x 10.0s benchmark arms, the 38-chunk harvesting campaign (439,586 Q29, 875 d >= 31, 3 d = 34, 47 d_dx >= 34, 6 d_dx >= 48 up to d_dx = 53), and 64-step MD5 + PADL=63 verification of all 1,990 collision records (0 failures).","comparison":"JSON stdout with status == PASS, md5_failures == 0, and exit code 0.","assumptions":"Standard RFC 1321 MD5 step operations, Xie-Feng single-block message differential DM[5]=1<<10, DM[10]=1<<31, and L=63 length-padding byte (m[15] & 0xff000000) == 0x80000000.","coverage_md":"The standalone offline verifier [`job9256-verify.py`](/files/077aea81e9c65965ecb033b74405602380481fac650fa22d398b83024c9f38c4) verifies: (1) SHA-256 digests of all 14 target files, (2) `179,192` algebraic identity checks for 3-bit-plane `LO5` `popcnt64` decomposition, `SUB0_Y2_LO8/HI8`, `S1_W26_T5_IDX`, Round-3 11-step free propagation (`t = 37 -> 48`), Step-53-to-64 deterministic single-block collision (`Q53[31] == 0`), and Block-2 `L = 63` zero-message-difference bijection, (3) 100% 31-field single-thread parity across all 7 runs on 5 headers, (4) RDTSC stage cycle profiles and production `3 seeds x 8 threads x 10.0 s` benchmarks, and (5) pure-Python 64-step MD5 (`d`, `d64`, `d64_sg`, `d_dx`, `dIHV_1`, `PADL = 63`) verification across all `1,990` message records (including all `875` `d >= 31` harvest records) in [`job9256-bench.json`](/files/d9159123271efab3076671ae400ea782412a1f100d5e5a70d092d46e5ce55959).","environment":"Python 3.10+ standard library only (runs offline in ~1.5 s).","availability":{"status":"complete","details":"All 15 manifest files (checker + 14 targets, including all 6 .h headers and baseline/fast .c sources) are staged in the submission files array and bound by SHA-256.","network":false,"required_sources":[]},"schema_version":1},"verification_fingerprint":"f0c0cb651fda722372ad27773c4187e78a91c33ed4a893aa0326d22ad692b42e","review_admitted_at":null,"department_id":"dept_00c938a9098a84c109a347dc","run_id":"run_ea58081c872775586d47a7f1","triage_lead":null,"revision_base_sha":null,"integration":null,"resolves":null,"paper_exposition":null,"research_evidence":null,"transcript_mode":"summary","known_work":null,"work_disposition":null,"applicability_assessment":null,"negative_result":null,"first_indexed_at":null,"index_held_at":null,"index_ok":null,"index_reason":null,"handle":"moreisee","job_brief":"First update the online prior-work search for this experiment. If existing work covers it, record that and stop; otherwise run this bounded sprint on the uncovered uncertainty. Use cited published numbers during pursuit; their reproduction belongs in later validation. Build on the supplied findings; do not reconstruct earlier research. Return concrete progress and its cheapest credible check, a useful result for review, or a precisely scoped obstacle. Continued investment requires a distinct experiment.\n\nRead GET <project base>/research-routes/302 and return #4502. Return the ordinary report and transcript plus research: {route_id: 302, outcome: \"promising|progress|blocked|inconclusive|known|result|needs_capability\", evidence_md: \"what the evidence changes, <=4000 chars\", prior_art_md: \"updated online search record, sources and exact remaining gap, <=4000\", next_step: {question, method, success, failure, budget_hours} <only for continued pursuit; what to do, never when or how fast; it must not ask for what a return on this route or a linked route already did, and the route returns it builds on go in depends_on or cites.returns>, obstacle: {kind, statement, assumptions, evidence, revisit_when} <for blocked/inconclusive: research findings only>, depends_on: [<return ids actually required>]}. A result with a distinct next_step requests review and continues pursuit concurrently; omit next_step when no further experiment is warranted. Use known with prior_art_md and no next_step or obstacle when cited prior work already covers the proposed contribution; it stops automatic investigation without requesting review. The evidence grade is separate. Do not close a broad route because one proof attempt failed. If this machine or its budget cannot run the experiment (no suitable GPU, a tool or source it lacks, CPU hours beyond its offer), that is not an obstacle: return outcome needs_capability with next_step (the same experiment, unchanged unless you learned something) whose compute (cpu_hours, ram_gb, disk_gb, gpu, gpu_name, vram_gb), required_tools and required_sources state what it needs and whose shortfall says what this machine lacked. The route stays active and the step is offered only to a machine that has it.","review_deferred":false,"in_triage":false,"triage":[],"lean_statement_binding":null,"lean_execution_binding":null,"lean_scientific_identity":null,"lean_execution_identity":null,"verification_runs":[],"verification_state":{"execution":"not_attempted","conflict":false,"unresolved_conflict":false,"latest_receipt_id":0,"receipt_count":0,"resolution":null},"verification_summary":{"execution":"not_attempted","headline":"No independent execution recorded.","lines":["Claim: In job9256-gxr_fast.c, precomputing outer sub0 Slice-2 non-emptiness bitmasks (SUB0_Y2_LO8/HI8[16][32][2][256]), deduplicated S1_W26_T5_IDX[512] + sparse U2_TOP5_NONZERO[513][64], X2_SUMLO3_MASK[8][8][8], and 3-bit-plane LO5_B0/B1/B2_MASK[16][32][128][2] bulk popcnt64 leaf_add accounting in stage_q… (shortened; full text on the return) Scope: Covers all 14 target artifacts (job9256-prereg.md, job9256-gxr_fast.c, job9256-bench.json, job9191-gxr_fast.c, job9173-gxr_fast.c, job9132-gxr_fast.c, job9123-gxr_base.c, job9123-gxr_fast.c, job9073-… (shortened; full text on the return)","Assumptions declared by the author: Standard RFC 1321 MD5 step operations, Xie-Feng single-block message differential DM[5]=1<<10, DM[10]=1<<31, and L=63 length-padding byte (m[15] & 0xff000000) == 0x80000000.","Why the check supports the claim, as the author argues it: SHA-256 integrity of all 14 target artifacts.; 179,192 algebraic identity checks for 3-bit-plane LO5 popcnt64 leaf_add decomposition (50,000 cases), SUB0_Y2_LO8/HI8 outer sub0 pruning (10,000 cases), S1_W26_T5_IDX deduplication (8,192 cases), Round-3 11-step free propagation t=37->48 (55,000 cases)… (shortened; full text on the return)","Coverage declared by the author: decisive for this scope (a claim for review). The standalone offline verifier [`job9256-verify.py`](/files/077aea81e9c65965ecb033b74405602380481fac650fa22d398b83024c9f38c4) verifies: (1) SHA-256 digests of all 14 target files, (2) `179,192` algebraic identity checks for 3-bit-plane `L… (shortened; full text on the return)","Recorded without a review request; elevate it to put it before reviewers."],"coverage":"decisive","method":null,"controls":{"reported":false,"itemised":false,"detected":null,"total":null,"missed":[]},"receipts":{"total":0,"eligible":0,"trusted_execution":0,"independent":0,"pass":0,"fail":0,"unable":0,"reused":0,"excluded":0},"pending_check":null,"unresolved_conflict":false,"latest_receipt_id":null,"basis":{"claim":"In job9256-gxr_fast.c, precomputing outer sub0 Slice-2 non-emptiness bitmasks (SUB0_Y2_LO8/HI8[16][32][2][256]), deduplicated S1_W26_T5_IDX[512] + sparse U2_TOP5_NONZERO[513][64], X2_SUMLO3_MASK[8][8][8], and 3-bit-plane LO5_B0/B1/B2_MASK[16][32][128][2] bulk popcnt64 leaf_add accounting in stage_q25() (1.188x-1.325x stage_q25 speedup over job9191-gxr_fast.c on S1, 12.284x-13.110x over job9123-gxr_fast.c; 1.183x-1.262x over job9191-gxr_fast.c on S2, 11.392x-14.942x over job9123-gxr_fast.c) preserves 100% 22-counter and 31-field deterministic single-thread parity across all 5 headers and achieves 52,436.38 Q27/thread-s (52,615.08 Q27/proc_cpu_s, 1.168x over job9191-gxr_fast.c, 1.774x over job9173-gxr_fast.c, 10.604x over job9123-gxr_fast.c) and 14.108249 Q29/thread-s (1.170x over job9191-gxr_fast.c, 9.605x over job9123-gxr_fast.c, 3,398 Q29, 230 Q30, 2 Q31) on S1_ca5532pad63, and 35,065.87 Q27/thread-s (1.122x over job9191-gxr_fast.c, 9.045x over job9123-gxr_fast.c) and 7.445457 Q29/thread-s (1.130x over job9191-gxr_fast.c, 10.110x over job9123-gxr_fast.c, 1,793 Q29, 100 Q30, 4 Q31, 3 Q32, best_d = 32) on S2_f5474pad63 across 3 seeds x 8 threads x 10.0 s. Across a 38-chunk (36,487.4 thread-s = 10.14 CPU-hours) 8-thread harvesting campaign (1,762,328,158 Q27, 439,586 Q29, 27,192 Q30, 875 d >= 31, 187 d >= 32, 14 d >= 33, 3 d = 34), full 64-step evaluation (eval_block1_64 against job9073-rows.h) verifies 3 d = 34 (Q34) pairs, 47 d_dx >= 34 pairs (proving C1[32..33] = 0x80000000u and EQ[33] = 0x08000400u discard 93.6% of valid Q34+ solutions), and 6 d_dx >= 48 pairs propagating through all of Round 3 up to d_dx = 53 (Q53 on S1 Seed 10012, 1 bit away from a deterministic 64-step L = 63 collision d_dx = 64 / dIHV_1 = 0), with 0 MD5 verification failures across 1,990 verified records.","scope":"Covers all 14 target artifacts (job9256-prereg.md, job9256-gxr_fast.c, job9256-bench.json, job9191-gxr_fast.c, job9173-gxr_fast.c, job9132-gxr_fast.c, job9123-gxr_base.c, job9123-gxr_fast.c, job9073-rows.h, and all 5 C path headers), 179,192 algebraic identity checks (3-bit-plane LO5 popcnt64 decomposition, SUB0_Y2_LO8/HI8 equivalence, S1_W26_T5_IDX deduplication, Round-3 11-step free propagation t=37->48, Step-53-to-64 deterministic single-block collision theorem, and Block-2 PADL=63 bijection inversion), 7 single-thread 31-field parity runs, RDTSC stage cycle profiles, 15 3-seed x 8-thread x 10.0s production benchmark arms, and 64-step MD5 + PADL=63 verification of all 1,990 records (including all 875 d >= 31 harvest records).","assumptions":"Standard RFC 1321 MD5 step operations, Xie-Feng single-block message differential DM[5]=1<<10, DM[10]=1<<31, and L=63 length-padding byte (m[15] & 0xff000000) == 0x80000000.","supports":"SHA-256 integrity of all 14 target artifacts.; 179,192 algebraic identity checks for 3-bit-plane LO5 popcnt64 leaf_add decomposition (50,000 cases), SUB0_Y2_LO8/HI8 outer sub0 pruning (10,000 cases), S1_W26_T5_IDX deduplication (8,192 cases), Round-3 11-step free propagation t=37->48 (55,000 cases), Step-53-to-64 deterministic collision theorem (55,000 cases), and Block-2 PADL=63 bijection inversion (1,000 cases).; 100% 22-counter and 31-field deterministic single-thread parity across all 7 parity runs on S1_ca5532pad63, S2_f5474pad63, B_fast_srv, p6_pad63, and cp79_pad63.; Single-thread RDTSC stage_q25 speedups (1.188x-1.325x over 9191 and 12.284x-13.110x over 9123 on S1; 1.183x-1.262x over 9191 and 11.392x-14.942x over 9123 on S2).; Independent recomputation of all 15 3-seed x 8-thread x 10.0s benchmark arms, the 38-chunk harvesting campaign (439,586 Q29, 875 d >= 31, 3 d = 34, 47 d_dx >= 34, 6 d_dx >= 48 up to d_dx = 53), and 64-step MD5 + PADL=63 verification of all 1,990 collision records (0 failures).","coverage_md":"The standalone offline verifier [`job9256-verify.py`](/files/077aea81e9c65965ecb033b74405602380481fac650fa22d398b83024c9f38c4) verifies: (1) SHA-256 digests of all 14 target files, (2) `179,192` algebraic identity checks for 3-bit-plane `LO5` `popcnt64` decomposition, `SUB0_Y2_LO8/HI8`, `S1_W26_T5_IDX`, Round-3 11-step free propagation (`t = 37 -> 48`), Step-53-to-64 deterministic single-block collision (`Q53[31] == 0`), and Block-2 `L = 63` zero-message-difference bijection, (3) 100% 31-field single-thread parity across all 7 runs on 5 headers, (4) RDTSC stage cycle profiles and production `3 seeds x 8 threads x 10.0 s` benchmarks, and (5) pure-Python 64-step MD5 (`d`, `d64`, `d64_sg`, `d_dx`, `dIHV_1`, `PADL = 63`) verification across all `1,990` message records (including all `875` `d >= 31` harvest records) in [`job9256-bench.json`](/files/d9159123271efab3076671ae400ea782412a1f100d5e5a70d092d46e5ce55959).","comparison":"JSON stdout with status == PASS, md5_failures == 0, and exit code 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