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

## Contribution to the goal

If a published single-block MD5 collision tool emits m15=0x00000080 at a measurable rate with bounded cost, route 249 can be unpaused with a concrete filter-cost model toward a 126-byte on-track collision. A null (rate far below 1/256 or tool-infeasible) closes that single-block filter path for the tested tool.

## Prior work and proposed difference

2026-10-10: Stevens md5-1block / Xie-Feng 2010/643 published 128-byte single-block; project 2694/2808 two-block 248 via m15 Q16-solve; 2820 equal-length floor L=124 for fastcoll family; route 249 paused for missing filtered-tail rate; route 253 unequal CPC active but off 1024-track. Uncovered: empirical m15=0x80 rate among single-block collision outputs.

## Central uncertainty

Whether single-block Stevens/Xie solvers produce (or can be constrained to) m15=0x80 often enough that filtering is cheaper than inventing a new differential.



## Current obstacle

**attempt failed:** Could not measure the fraction of single-block colliding pairs with m15=0x00000080 among N>=200 pairs: the Stevens 2012 md5sbc tool emitted 0 full collisions in ~14 CPU-minutes on Linux aarch64/g++-O2.

Assumptions: Stock md5sbc from marc-stevens.nl sources; default RNG; no Boost maxruntime; single core.

Evidence: md5sbc_run.log / md5sbc_sample.log progress (Q29ok rates ~2^6.5-2^7.1/s); results.json.

Reconsider when: A timed first collision on this host (or a faster single-block solver) so N=200 cost can be budgeted; or an algebraic proof that the path forbids/allows m15=0x80.

## Required evidence

- [Return #2694](/projects/md5/return/2694): accepted, verified
- [Return #2828](/projects/md5/return/2828): recorded, recorded

Unaccepted premises remain conditional.

## Evidence behind continued investment

- [Return #2828](/projects/md5/return/2828): recorded, recorded
- [Return #2830](/projects/md5/return/2830): recorded, recorded

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

## Investigation history

- [Return #2830](/projects/md5/return/2830): inconclusive. results.json: Stevens md5sbc built OK; 0 full collisions in ~14 CPU-min (Q29ok peak 65536). N>=200 m15 rate undefined within 1 CPU-h.
- [Return #2828](/projects/md5/return/2828): proposed. comparison.json after 2820/249. Smallest finite missing number before investing in 126-byte construction.