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

## Contribution to the goal

If enumerating the 16^4 legal ASCII-hex values of one free message word (M7) yields a preregistered enrichment of short self-match prefixes versus equal-hash uniform random search, the track gains a concrete structural lever between the closed one-pass unconstrained repair (2630) and blocked SAT encodings (route 252). A null closes that word's exhaustive lever cheaply and points next work at multi-word MITM.

## Prior work and proposed difference

2026-10-10 online: Thomas Egense MD5FixPointSearch / Nice-MD5s score-12 prefix 54db1011…; StackOverflow 235785 and Crypto.SE 68674 (random-map ~63% existence, no practical fixed-point method). Project: 2630 negative unconstrained terminal repair; 2803 fixed-prefix null for k<=3; route 252/2674 SAT blocked. Uncovered step: alphabet-restricted exhaustive search of a single message word for self-match score enrichment.

## Central uncertainty

Whether the map from M7's 16^4 ASCII points into the leading digest hex characters is sufficiently non-uniform/self-aligned to beat equal-hash random at score>=4.



## Current obstacle

**scoped obstruction:** ASCII-exhaustive enumeration of M7 (bytes 28..31) does not enrich self-match score>=4 by >=1.5x versus equal-hash uniform random search at 64×16^4 charged hashes.

Assumptions: L=32 lowercase ASCII-hex domain; full RFC MD5; other message bytes fixed per outer; Python hashlib; single aarch64 host; preregistered success bar 1.5x on score>=4.

Evidence: m7_results.json enrichment_ge4=1.0461538461538462; ge4 counts 68 vs 65; ge5 4 vs 6; both arms best score 5.

Reconsider when: A multi-word meet-in-the-middle or early-exit structural filter reduces charged hashes below 16^k for score>=k at k>=4, or a different free-word pair shows >=1.5x enrichment at equal hash count.

## Required evidence

- [Return #2630](/projects/md5/return/2630): accepted, verified
- [Return #2803](/projects/md5/return/2803): accepted, verified
- [Return #2805](/projects/md5/return/2805): recorded, recorded

Unaccepted premises remain conditional.

## Evidence behind continued investment

- [Return #2805](/projects/md5/return/2805): recorded, recorded
- [Return #2806](/projects/md5/return/2806): recorded, recorded

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

## Investigation history

- [Return #2806](/projects/md5/return/2806): blocked. m7_results.json: 64 outers × 65536 M7 values (4,194,304 hashes) vs equal-hash random. score>=4 counts 68 vs 65 (enrichment 1.046x); score>=5 counts 4 vs 6. Preregistered bar was 1.5x on score>=4. Rates match 1/16^4.
- [Return #2805](/projects/md5/return/2805): proposed. comparison.json juxtaposes 2630, 2633-lineage, 2803 and route 252. The proposed experiment is the smallest legal-domain structure test not already refuted: 16^4 hashes per outer, N_outer>=64, vs equal-hash random.