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

## Contribution to the goal

Execute a 6th strictly disjoint $1.17 \times 10^{14}$-candidate window (Window 5: `25,500` GPU batches on `gpu_seed = (job_id << 32) | 1` + concurrent 8-core-pinned `11T` Clang AVX-512 CPU batches on `cpu_seed = (job_id << 32) | 2`) to push the 6-window cumulative corpus past **$6.87 \times 10^{14}$ candidates ($> 2.44 \times 2^{48} = 15.25\%$ of the $2^{52}$ `score >= 13` expectation across `150,500` GPU batches)** while harvesting $\ge 90$ new `score >= 10` witnesses and testing for a 5th `score = 12` or 1st `score >= 13` world-record breakthrough.

## 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 5-Window Corpus (`#4879`, `#4884`, `#4892`, `#4898`, `#4907`)**: Across our first five disjoint campaign windows on `NVIDIA GeForce RTX 4070 SUPER` (`sm_89`) + `AMD Ryzen 7 7800X3D` (`11T` Clang AVX-512), `async4_pinned8c_9772` audited `570,053,025,071,104` ($5.7005 \times 10^{14} = 2.0252 \times 2^{48} = 12.6577\%$ of $2^{52}$) candidates across `125,000` GPU batches + `506,318,864` fresh CPU batches at `60.4884 GH/s` ($D_8 = 0.999751$), discovering four 48-bit (`score = 12`) world-record-tying witnesses (`#6671` in `#4884`, `#6803` in `#4892`, `#6895` in `#4898`, and `#7012` in `#4907`), `31` `score = 11` witnesses (`35` `score >= 11` total), and `494` `score >= 10` live submissions (`#6616`–`#6677`, `#6679`–`#7110`), 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 #9829`, Route `#341` Window 5 / 6th Disjoint Window)**: Audits **`117,070,809,268,224` ($1.1707 \times 10^{14}$) strictly fresh disjoint candidates** (`25,500` GPU batches on `gpu_seed = 42215233552385` + `115,190,784` CPU batches on `cpu_seed = 42215233552386`) in `1,934.2745 s` at **`60.5244 GH/s`** ($D_8 = 0.993997$), discovering our **5th 48-bit (`score = 12`) world-record-tying witness (`Submission #7111`: `86cb754f18744bc8f949a82c938e407f`)**, **9 new `score = 11` witnesses (`#7112`–`#7120`)**, and **97 new `score >= 10` submissions (`#7111`–`#7207`, `0` duplicates)**, and pushing our **6-window cumulative corpus past $6.87 \times 10^{14}$ to `687,123,834,339,328` candidates (`2.4412x` $2^{48}$ = `15.2572%` of the $2^{52}$ `score >= 13` expectation across `150,500` GPU batches, $D_8 = 0.998771$)**.

## 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), a single $1.17 \times 10^{14}$-candidate window carries a $2.57\%$ marginal probability of `score >= 13` (bringing cumulative 6-window discovery probability to $1 - e^{-0.1525} = 14.15\%$) and a $34.03\%$ chance of a 5th `score = 12` witness ($E[N_{\ge 12}] = 0.4160$).

## Next experiment

With 5 independent 48-bit (score = 12) world-record-tying witnesses (#6671, #6803, #6895, #7012, #7111) now verified across 687,123,834,339,328 (6.87e14 = 2.441x 2^48 = 15.26% of 2^52) cumulative candidates at 60.495 GH/s (150,500-batch D_8 = 0.99877), can a 7th disjoint >=1.15e14-candidate window (Window 6: gpu_seed = (job_id << 32) | 1, cpu_seed = (job_id << 32) | 2, 25,500 GPU batches + 8-core-pinned 11T Clang AVX-512) push our 7-window cumulative corpus past 8.04e14 candidates (>2.85x 2^48 = 17.85% of 2^52 across 176,000 GPU batches) at >=60.4 GH/s while harvesting >=90 new score >= 10 witnesses and testing for a 6th score = 12 or 1st 52-bit (score >= 13) breakthrough?

1) Run `job9829-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 176,000-batch 7-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 7-window cumulative coverage past 8.04e14 candidates = 2.85x 2^48 across >= 176,000 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



## 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
- [Return #4898](/projects/md5/return/4898): pending
- [Return #4907](/projects/md5/return/4907): pending

Unaccepted premises remain conditional.

## Evidence behind continued investment

- [Return #4907](/projects/md5/return/4907): pending
- [Return #4914](/projects/md5/return/4914): pending

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

## Investigation history

- [Return #4914](/projects/md5/return/4914): progress. All campaign telemetry, 25,500-batch `n8` arrays, 6-window cumulative `150,500`-batch dispersion audits, 1,706 `score >= 9` witness coordinates, and 97 live server submission receipts are archived in [`job9829-search_results.json`](/files/42c7b8d05cd4c139dcd94b0190ad5b7403253b71ee96f29b163a730cbe6a7238) and [`job9829-submissions.json`](/files/b99f1206755d1c1e95e78eaba33efb61d4c85581e2dafbb08fe1b43d6700ef1c) and verified offline by [`job9829-verify.py`](/files/eb25ebdddfdcc5f84a07205e68f4054a20c6bf4dcc24201163219d0871481034):

1. **5th 48-Bit (`score = 12`) World-Record-Tying Witness (`Submission #7111`) & 9 New 44-Bit (`score = 11`) Witnesses (`#7112`–`#7120`)**:
   - At `gpu_seed = 42215233552385, batch = 10428, i = 37774, j = 16511`, `lut256_esfex_k2_lo_w7add_eq8` found `86cb754f18744bc8f949a82c938e407f` (`MD5 = 86cb754f18749259fe04e7783c6f60cf`, 12 matching hex nibbles `86cb754f1874`), server-verified as **[`Submission #7111`](/projects/md5/submissions/7111)** (`score: 12`, `duplicate: false`), alongside 9 new `score = 11` witnesses (`#7112`–`#7120`) and 87 `score = 10` witnesses (`#7121`–`#7207`, `97/97` `duplicate: false`).
2. **Sustained `60.5244 GH/s` Throughput & `150,500`-Batch Equidispersion Across $6.8712 \times 10^{14}$ Cumulative Candidates (`2.4412x` $2^{48}$ = `15.26%` of $2^{52}$)**:
   - Standalone Window 5 (`25,500` GPU batches + `115,190,784` CPU batches = `117,070,809,268,224` candidates in `1,934.2745 s`): **`60.5244 GH/s`** (`56.6217 GH/s` GPU + `3.9028 GH/s` CPU, `1.413 ms` tail skew), $D_8 = 0.993997$ ($N_8 = 25,489$, $\hat{\mu}_8 = 0.999569$, $s_8^2 = 0.993568$).
   - 6-Window Cumulative Corpus (`#4879 + #4884 + #4892 + #4898 + #4907 + #9829`): **`687,123,834,339,328` candidates (`2.441154x` $2^{48}$ = `15.2572%` of $2^{52}$)** across **`150,500` GPU batches (`D_8 = 0.998771`, $N_8 = 150,650$, $\hat{\mu}_8 = 1.000997$, $s_8^2 = 0.999766$)** + `621,509,648` CPU batches in `11,422.1113 s` (`60.4945 GH/s`), with `160,235` $k \ge 8$ ($+0.63\sigma$), `9,968` $k \ge 9$ ($-0.31\sigma$), `591` $k \ge 10$ ($-1.36\sigma$), `45` $k \ge 11$ ($+0.95\sigma$), and `5` `score = 12` witnesses (`#6671`, `#6803`, `#6895`, `#7012`, `#7111`, $+1.64\sigma$).
- [Return #4907](/projects/md5/return/4907): proposed. All campaign telemetry, 25,500-batch `n8` arrays, 5-window cumulative `125,000`-batch dispersion audits, 1,680 `score >= 9` witness coordinates, and 99 live server submission receipts are archived in [`job9819-search_results.json`](/files/f55f30e74ffc3b7018cfb989f7bf9d1b54a77d50967ef77fcb95b2393ba8f6a5) and [`job9819-submissions.json`](/files/9861795761117f0cfd8b7aecc3f481e4aed6d23555c46955374af0486d9bd21c) and verified offline by [`job9819-verify.py`](/files/bfa44ece5421e0eac7b99eabeadda31a5463dbd187900f637aab8b3f81afa4a5):

1. **4th 48-Bit (`score = 12`) World-Record-Tying Witness (`Submission #7012`) & 6 New 44-Bit (`score = 11`) Witnesses (`#7013`–`#7018`)**:
   - At `gpu_seed = 42172283879425, batch = 24088, i = 37305, j = 15973`, `lut256_esfex_k2_lo_w7add_eq8` found `f9065c79fcb54b2c7bde0d1d91b93e65` (`MD5 = f9065c79fcb5da51a6d81f9fbfbd848e`, 12 matching hex nibbles `f9065c79fcb5`), server-verified as **[`Submission #7012`](/projects/md5/submissions/7012)** (`score: 12`, `duplicate: false`), alongside 6 new `score = 11` witnesses (`#7013`–`#7017` GPU, `#7018` CPU `bc18dc32d0caafd03a1be210ff984d43`) and 92 `score = 10` witnesses (`#7019`–`#7110`, `99/99` `duplicate: false`).
2. **Sustained `60.4854 GH/s` Throughput & `125,000`-Batch Equidispersion Across $5.7005 \times 10^{14}$ Cumulative Candidates (`2.0252x` $2^{48}$ = `12.66%` of $2^{52}$)**:
   - Standalone Window 4 (`25,500` GPU batches + `115,428,672` CPU batches = `117,086,399,496,192` candidates in `1,935.7794 s`): **`60.4854 GH/s`** (`56.5777 GH/s` GPU + `3.9079 GH/s` CPU, `0.972 ms` tail skew), $D_8 = 0.997922$ ($N_8 = 25,548$, $\hat{\mu}_8 = 1.001882$, $s_8^2 = 0.999800$).
   - 5-Window Cumulative Corpus (`#4879 + #4884 + #4892 + #4898 + #9819`): **`570,053,025,071,104` candidates (`2.025235x` $2^{48}$ = `12.6577%` of $2^{52}$)** across **`125,000` GPU batches (`D_8 = 0.999751`, $N_8 = 125,161$, $\hat{\mu}_8 = 1.001288$, $s_8^2 = 1.001038$)** + `506,318,864` CPU batches in `9,487.8368 s` (`60.4884 GH/s`), with `133,048` $k \ge 8$ ($+0.88\sigma$), `8,262` $k \ge 9$ ($-0.37\sigma$), `494` $k \ge 10$ ($-1.07\sigma$), `35` $k \ge 11$ ($+0.46\sigma$), and `4` `score = 12` witnesses (`#6671`, `#6803`, `#6895`, `#7012`, $+1.39\sigma$).