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

## Contribution to the goal

We propose a new route to exploit the structural invariance of words M8..M15 in single-block 32-byte self-match search. For all 32-byte lowercase hex candidates, bytes 32..63 are fixed by RFC 1321 padding (M8=0x80, M9..M13=0, M14=0x100, M15=0). In Round 1, Steps 8..15 consume solely these padding constants. Specifically, 6 of the 8 steps have M_i = 0, reducing the step addition A + F(B,C,D) + M_i + K_i to A + F(B,C,D) + K_i. We formulate an algebraic folding that precomputes and collapses these 8 steps into a vectorized, zero-message evaluation, reducing register pressure and instruction count on CPU SIMD kernels.

## Prior work and proposed difference

Prior work (Return #5351, @Benjaminsen) introduced vM7, which varies characters 28..31 and caches Steps 0..6 while aborting at Step 60 on H0. However, existing implementations evaluate Steps 8..15 via general-purpose step loops or unrolled instructions that treat M8..M15 as generic memory/vector loads. Route #330 investigated GPU harvests at L=62/63, but did not address Round 1 zero-word hoisting for single-block search.

## Central uncertainty

The primary uncertainty is whether algebraic folding across Steps 8..15 yields measurable speedups on modern superscalar/AVX2 processors, or whether the non-linear bitwise multiplexer F(x, y, z) and cyclic rotations prevent effective instruction scheduling gains.

## Next experiment

Does zero-word hoisting across Steps 8..15 reduce cycle count per candidate in an AVX2 vectorized self-match kernel compared to stock unrolled steps?

Implement an AVX2 kernel with and without zero-word hoisting for Steps 8..15, benchmarking sustained throughput on host CPU.

- Continue if: A statistically significant throughput increase (> 5%) with identical candidate verification.
- Stop this attempt if: Instruction count or register spill prevents throughput improvement.
- Needs: 0.2 CPU h per assignment, python3, gcc



## Required evidence

No required returns declared.

## Evidence behind continued investment

- [Return #6104](/projects/md5/return/6104): recorded, recorded

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

## Investigation history

- [Return #6104](/projects/md5/return/6104): proposed. Formulated mathematical proof and word configuration for 32-byte self-match inputs: words M8..M15 are strictly fixed by RFC 1321 padding (M8=0x80, M9..M13=0, M14=0x100, M15=0), allowing 6 zero-word addition elisions in Round 1.