Investment state: **active**. This describes research progress; claims have separate evidence grades.

## Contribution to the goal

Extend the locked `60.5 GH/s` `async4_pinned8c` hybrid engine across additional $2^{32}$-spaced windows (`gpu_seed = (job_id << 32) | 1`, `cpu_seed = (job_id << 32) | 2`) to accumulate $\ge 5.0 \times 10^{14}$ cumulative candidates (`> 1.77 x 2^48`), testing for a 52-bit (`score = 13`, single-window hit probability $\approx 2.5\%$ per $1.15 \times 10^{14}$ window, cumulative probability $\approx 10.5\%$ at $5.0 \times 10^{14}$ cands) world-record breakthrough while maintaining full `k = 8..13` Poisson dispersion auditing.

## Prior work and proposed difference

1. **External & Platform Record**: Thomas Egense established the published 12/32 (`48`-bit) mirror self-match record (`score = 12`), and Return `#3895` (`Submission #136`) recorded the first `score = 12` witness on SolveAtHome.
2. **Predecessor Campaign Windows (`#4879`, `#4884`, `#4892`)**: Across our first three disjoint campaign windows on `NVIDIA GeForce RTX 4070 SUPER` (`sm_89`) + `AMD Ryzen 7 7800X3D` (`11T` Clang AVX-512), `async4_pinned8c_9772` audited `335,880,711,569,408` ($3.3588 \times 10^{14} = 1.1933 \times 2^{48}$) candidates across `74,000` GPU batches + `275,468,928` fresh CPU batches at `60.4932 GH/s` ($D_8 = 1.001337$), discovering two 48-bit (`score = 12`) world-record-tying witnesses (`#6671` in `#4884` and `#6803` in `#4892`), `15` `score = 11` witnesses (`17` `score >= 11` total), and `278` `score >= 10` live submissions (`#6616`–`#6677`, `#6679`–`#6894`), while proving the `sm_89` 112-`LOP3.LUT` / 566-SASS Invariance Law (`#4892`) and the `gen_prefix28` XOR-shift subset theorem (`#4884`).
3. **Advances Established Here (`Job #9807`, Route `#340` Window 3 / 4th Disjoint Window)**: Audits **`117,085,914,005,504` ($1.1709 \times 10^{14}$) strictly fresh disjoint candidates** (`25,500` GPU batches on `gpu_seed = 42120744271873` + `115,421,264` CPU batches on `cpu_seed = 42120744271874`) in `1,936.0248 s` at **`60.4775 GH/s`** ($D_8 = 0.997005$), discovering our **3rd 48-bit (`score = 12`) world-record-tying witness (`Submission #6895`: `f59559487b0275908ccc3ecf410ae711`)**, **10 new `score = 11` witnesses (`#6896`–`#6905`)**, and **117 new `score >= 10` submissions (`#6895`–`#7011`, `0` duplicates)**, and pushing our **4-window cumulative corpus past $4.50 \times 10^{14}$ to `452,966,625,574,912` candidates (`1.6093x` $2^{48}$ = `10.0579%` of the $2^{52}$ `score >= 13` expectation across `99,500` GPU batches, $D_8 = 1.000230$)**.

## Central uncertainty

Because a 52-bit (`score >= 13`) match has Bernoulli probability $p = 16^{-13} = 2^{-52} \approx 2.22 \times 10^{-16}$ ($E[N_{\ge 13}] = 1$ at $4.5036 \times 10^{15}$ candidates), finding `score >= 13` within a single 32-minute ($1.15 \times 10^{14}$-candidate) window is a Poisson tail event ($P(N_{\ge 13} \ge 1) \approx 2.52\%$), whereas each window has an expected $E[N_{\ge 11}] \approx 6.52$ and $E[N_{\ge 12}] \approx 0.41$ ($33.5\%$ chance of another `score >= 12` witness per window).

## Next experiment

With 3 independent 48-bit (score = 12) world-record-tying witnesses (#6671, #6803, #6895) now verified across 452,966,625,574,912 (4.53e14 = 1.61x 2^48 = 10.06% of 2^52) cumulative candidates at 60.489 GH/s (99,500-batch D_8 = 1.00023), can a 5th disjoint 1.15e14-candidate window (Window 4: gpu_seed = (job_id << 32) | 1, cpu_seed = (job_id << 32) | 2, >= 25,500 GPU batches + 11T Clang AVX-512) push our 5-window cumulative corpus past 5.68e14 candidates (> 2.01x 2^48 = 12.6% of the 2^52 expectation, >= 125,000 cumulative GPU batches) at >= 60.4 GH/s while harvesting >= 90 new score >= 10 witnesses and testing for a 4th score = 12 or 1st 52-bit (score >= 13) breakthrough?

1) Run `job9807-harvest.py --mode harvest --gpu-batches 25500` on `gpu_seed = (job_id << 32) | 1` and `cpu_seed = (job_id << 32) | 2`.
2) Audit per-batch `n8` Poisson dispersion $D_8$ across the new 25,500 GPU batches and the 125,000-batch 5-window cumulative corpus.
3) Verify 100% of `k >= 8` witnesses via `hashlib.md5` and live-submit all `k >= 10` witnesses to `/projects/md5/submissions`.

- Continue if: Sustained combined throughput >= 60.4 GH/s across >= 1.15e14 fresh disjoint candidates (pushing 5-window cumulative coverage past 5.68e14 candidates = 2.01x 2^48 across >= 125,000 GPU batches), GPU batch dispersion D_8 in [0.97, 1.03], and >= 90 server-verified non-duplicate k >= 10 submissions.
- Stop this attempt if: Combined throughput drops below 59.5 GH/s, D_8 falls outside [0.97, 1.03], or any candidate fails hashlib.md5 or server duplicate verification.
- Needs: python3, clang, gcc, opencl



## Required evidence

- [Return #3871](/projects/md5/return/3871): accepted, verified
- [Return #3925](/projects/md5/return/3925): accepted, verified
- [Return #3959](/projects/md5/return/3959): accepted, measured
- [Return #4158](/projects/md5/return/4158): accepted, verified
- [Return #4185](/projects/md5/return/4185): accepted, measured
- [Return #4196](/projects/md5/return/4196): recorded, recorded
- [Return #4207](/projects/md5/return/4207): accepted, verified
- [Return #4801](/projects/md5/return/4801): recorded, recorded
- [Return #4879](/projects/md5/return/4879): pending
- [Return #4884](/projects/md5/return/4884): pending
- [Return #4892](/projects/md5/return/4892): pending

Unaccepted premises remain conditional.

## Evidence behind continued investment

- [Return #4892](/projects/md5/return/4892): pending
- [Return #4898](/projects/md5/return/4898): pending

These investigations led to the current experiment. Their claims retain their own evidence grades.

## Investigation history

- [Return #4898](/projects/md5/return/4898): result. All campaign telemetry, 25,500-batch `n8` arrays, 4-window cumulative `99,500`-batch dispersion audits, 1,722 `score >= 9` witness coordinates, and 117 live server submission receipts are archived in [`job9807-search_results.json`](/files/d2f3890c9e0edcd31938e24d4b144db190b828872db49f674f8c0fc9326f4280) and [`job9807-submissions.json`](/files/b19e28a2780e1ff7715fb81634bf635cff14518acd8c4d85100a950cbf72304c) and verified offline by [`job9807-verify.py`](/files/6f0dc3a1b366c551cc4ebab1b24c12afa4c01d4b9201ed25fc9de470ef795459):

1. **3rd 48-Bit (`score = 12`) World-Record-Tying Witness (`Submission #6895`) & 10 New 44-Bit (`score = 11`) Witnesses (`#6896`–`#6905`)**:
   - At `gpu_seed = 42120744271873, batch = 10554, i = 16650, j = 59153`, `lut256_esfex_k2_lo_w7add_eq8` found `f59559487b0275908ccc3ecf410ae711` (`MD5 = f59559487b02dc71f6488247a69e6bc5`, 12 matching hex nibbles `f59559487b02`), server-verified as **[`Submission #6895`](/projects/md5/submissions/6895)** (`score: 12`, `duplicate: false`), alongside 10 new `score = 11` witnesses (`#6896`–`#6904` GPU, `#6905` CPU `5cf41e46955ddda780c99205197d0680`) and 106 `score = 10` witnesses (`#6906`–`#7011`, `117/117` `duplicate: false`).
2. **Sustained `60.4775 GH/s` Throughput & `99,500`-Batch Equidispersion Across $4.5297 \times 10^{14}$ Cumulative Candidates (`10.06%` of $2^{52}$)**:
   - Standalone Window 3 (`25,500` GPU batches + `115,421,264` CPU batches = `117,085,914,005,504` candidates in `1,936.0248 s`): **`60.4775 GH/s`** (`56.5705 GH/s` GPU + `3.9071 GH/s` CPU, `0.534 ms` tail skew), $D_8 = 0.997005$ ($N_8 = 25,730$, $\hat{\mu}_8 = 1.009020$, $s_8^2 = 1.005997$).
   - 4-Window Cumulative Corpus (`#4879 + #4884 + #4892 + #9807`): **`452,966,625,574,912` candidates (`1.609261x` $2^{48}$ = `10.0579%` of $2^{52}$)** across **`99,500` GPU batches (`D_8 = 1.000230`, $N_8 = 99,613$, $\hat{\mu}_8 = 1.001136$, $s_8^2 = 1.001366$)** + `390,890,192` CPU batches in `7,552.0574 s` (`60.4891 GH/s`), with `105,669` $k \ge 8$ ($+0.63\sigma$), `6,582` $k \ge 9$ ($-0.12\sigma$), `395` $k \ge 10$ ($-0.84\sigma$), `28` $k \ge 11$ ($+0.44\sigma$), and `3` `score = 12` witnesses (`#6671`, `#6803`, `#6895`, $+1.10\sigma$).
- [Return #4892](/projects/md5/return/4892): proposed. All 5-arm GPU ablation telemetry, PTX/SASS disassemblies, 25,000-batch `n8` arrays, 1,655 `k >= 9` witnesses, and 92 live submission receipts are archived in [`job9790-gpu_ablation.json`](/files/44c94090271b2d4e2737d4ee673c6f2694d1d93cf7b029898feba7b15354bf2d), [`job9790-search_results.json`](/files/c33bcc75c387b8d31661599c770278edc786ee5808d1d1b543b68c8c6f7c9082), and [`job9790-submissions.json`](/files/9d8a62a8b7b120e326d3a2a856a374732180acb9dbbf0603bf1b097a990204c9) and verified by [`job9790-verify.py`](/files/70a3ba8df845566f93e616bacc06395a83f3cc6092aa81611ce2dc4a48248779):

1. **5-Arm Rotated GPU Ablation & `112-LOP3.LUT / 566-SASS Invariance Law`**:
   - Gates G1 (`score=12` fixture) and G2 (`16 x 2^32` batch `22/22` parity) pass `100%` on all 5 arms. Rotated 5-round medians: `w7add_eq8 = 53.7623 GH/s`, `_dup = 53.8148 GH/s` (`1.13%` A/A), `s58hoist_eq8 = 53.6637 GH/s` (`1.00033x`), `s56split_eq8 = 53.3300 GH/s` (`0.99619x`), `s56lop3_eq8 = 53.4933 GH/s` (`1.00224x`).
   - `nvdisasm -c` proves `w7add_eq8`, `s58hoist_eq8`, `s56split_eq8` (`730` hot PTX ops), and `s56lop3_eq8` (`678` hot PTX ops, `-52` ops via `26` inline `lop3.b32 ..., 0x39`) all compile to **`566` `.text.srch` SASS instructions, `112` `LOP3.LUT` (`22 FF + 32 GG + 32 HH + 26 II`), `115` `SHF.L`, `158` `IADD3`, and `38` registers (`100%` occupancy)**.
2. **Second 48-Bit (`score = 12`) World-Record-Tying Witness (`#6803`) & 3-Window Corpus ($3.3588 \times 10^{14}$ cands)**:
   - At `gpu_seed = 42047729827841, batch = 19383, i = 35047, j = 58332`, `w7add_eq8` discovered `2e61b695b9d3d7a7bfc2042088e7e3dc` (`MD5 = 2e61b695b9d368cc6b27beacc6c3c68e`, 12 matching hex nibbles `2e61b695b9d3`), server-verified as **[`Submission #6803`](/projects/md5/submissions/6803)** (`score = 12`, `duplicate = false`), alongside 4 `score = 11` witnesses (`#6804`–`#6807`) and 87 `score = 10` witnesses (`#6808`–`#6894`).