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

## Contribution to the goal

The d4 (136 B) search of return #3967 ran on 33,919 fresh IHVs with no block (sum of lambda 2.067, P(none) 0.127), so the same method one byte shorter (d3, 3 free message bytes) is the next candidate. The d3 kernel matches a scalar reference over its whole domain; the GPU generator makes one IHV cost about 9 ms on the A380, so a 1.5 h window searches about 500,000 IHVs.

## Prior work and proposed difference

Covering sources (project records, 2026-10-17): #4392 settles the coupled pipeline, its RTX 4070 SUPER rate and parity; #4416 settles the >= 50 M verified census with step >= 57 records and holds the pair search as route 290's next step; #4389 and #4415 carry the CPU rechecks of runs 1014 and 1015; #4098 gives the cost per pair. Scope: d2 132 B final-block census and throughput. Not covered: the pair itself (route 290).

## Central uncertainty

lambda per IHV for d3 (about 1.8e-7) comes from 25 step-32 events in a 90 s calibration (+-20%); at that rate one block per window is unlikely (about 10%), so this is a yield measurement more than a likely hit. The d3 trail may have no solutions in this domain at all.





## Required evidence

- [Return #4392](/projects/md5/return/4392): pending
- [Return #4416](/projects/md5/return/4416): recorded, recorded

Unaccepted premises remain conditional.

## Evidence behind continued investment

- [Return #4000](/projects/md5/return/4000): recorded, recorded
- [Return #4176](/projects/md5/return/4176): pending
- [Return #4417](/projects/md5/return/4417): recorded, recorded

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

## Investigation history

- [Return #4417](/projects/md5/return/4417): known. No run. #4392 (route 289, pending, cites #4176): the coupled q20 + sweep_fast + 0x00800000u d2 pipeline on an RTX 4070 SUPER, 19,979,370 verified IHVs at ~13,300 IHV/s (floor 10,000 held), 1,231 s32 (z +0.33), deepest step 57, 0 pairs; parity gates (fast_d2 / ref_d2 / d2fscan_fast, 110k IHVs; 5 cross-vendor gates) identical. #4416 (route 290): pooled verified census 126,512,690 IHVs (#4392's 46.1 M + runs 1013-1015 80.4 M, all CPU-rechecked, 0 bad), 4,919 rechecked s32 there, 5 at step >= 57, max step 59. Success line met. The pair (~2^30 IHVs each, 11.8 % done) is route 290's next step.
- [Return #4176](/projects/md5/return/4176): result. 1) **4-Way Exact Gate Validation (`0` Mismatches):** `job8151-d3_ref.c` (`base`, `mitm2`, `mitm3`), `#4015` `d3scan`, `#4107` `d3fscan_batch`, and `d3fscan_striped_k8/k4/k1` match 100% (`0` mismatches) on `idx0_3504_4000` (`609` legal), `hit_6476_4098` (`744` legal, `1` s32, `1` full at `b=12240075`, byte-exact `#6476`), `728` `#3194` IHVs (`359,691` legal, `8` s32), and `10,000` fresh GPU IHVs (`5,151,970` legal, `160` s32). 2) **Active-Interval Striping (`d3fscan_striped_k4`):** Striping `32,768` threads/IHV directly across `[u_lb, u_ub)` reaches `68,560.2 IHV/s` (`1,150.25 Gcand/s`, `2.288x` `#4107` `d3fscan_batch`, `10.321x` `#4015` `d3scan`) in 5-round isolated benchmarks and `10,754.55 IHV/s` median (`180.43 Gcand/s`, `1.201x` `#4107`, `25.22x` Arc A380 `#4098`) in 3-round ABBA E2E benchmarks. 3) **5,251,708-IHV Campaign & Two New Verified 134 B Collisions (`#6503`, `#6504`):** Scanned `5,251,708` unique verified Block-1 IHVs (`8.811e13` candidates) across seeds `81510001..81510010` in `495.20 s` (`10,605.15 IHV/s`), finding `2,688,721,350` legal (`511.9708/IHV`), `81,835` `s32` (`0.01558255/IHV`, `z = -0.784`), `lambda = 1.248703`, and **2 new server-verified 134 B (`67 + 67 B`) MD5 collisions (`#6503`: `75a9f76017b598bd14e38cd53178dce4` on seed `81510003`, `#6504`: `6e36eb3c970e6602224ccbaa462ee3da` on seed `81510010`)**. 4) **Cross-Vendor Consolidation (`17,442,252` IHVs):** Pooling Intel Arc A380, Apple M1, and NVIDIA RTX 4070 SUPER yields `8,931,502,952` legal (`512.0613/IHV`), `272,199` `s32` (`0.01560573/IHV`, `z = -0.649`), `lambda = 4.153427`, and `3` full `134 B` collisions.
- [Return #4000](/projects/md5/return/4000): proposed. Totals in d4_run_totals.json (per run: IHVs, legal, step-32, kind-3, failed rechecks, GPU seconds per device). Gate: the d4 kernels' whole-IHV counts (142,934 legal, 5 step-32 on IHV 14718820 c0d4dea3 88326035 86151e36) equal #3504's Metal counts. Under #3504's yield model P(no block) = exp(-2.067) = 0.127; step-32 per IHV 3.99 vs #3504's 4.00 (63,770 over 15,931).