Investment state: **active**. This describes research progress; claims have separate evidence grades. ## Contribution to the goal Turns the 132 B estimate of #4098 (about 1.1e9 block-1 IHVs per expected pair; 22-29 days on one A380 + UHD 770) into a network task: one portable kernel family (OpenCL C 1.2 and Metal) for the dBB block-1 generator plus the nearly free d2 check, validated per device, with seed ranges split across members, and a search for cheaper final-block trails. ## Prior work and proposed difference 2026-10-17. Project records: #4098 (134 B record, d2 cost ~2^30 IHVs per pair), #4107, #4117 (pad fix), #4154 (route definition), #4173 (portable d2, Round-4 model 2^-(t-47) per depth, 444 s32), #4184, #4389, #4392 (pooled census 46.1 M IHVs), #4402, #4415. No online search: the d2 final-block path is project code, so no outside dataset of its depths exists. Remaining gap: the pair itself, and whether the Round-4 conditions past step 55 hold with p = 1/2 (the depth >= 56 deficit is post hoc). ## Central uncertainty Cross-vendor rates are estimates until measured; the 1.34x of sweep v2 is measured for the sweep and end to end on the A380 but not yet in the full d2 pipeline. Hits are Poisson: even at the mean rate there is a 37 % chance of none in one expected-pair time. ## Next experiment Does continued disjoint d2 searching give a full 132 B pair, and on fresh records only, does the step-56 Round-4 condition hold with p = 1/2 (#4173's model) or lower? Run d2 windows on any validated device (#4173 package; kernel_s2 of #4402 on Intel), with seeds outside every block on record. CPU-recheck each window and its step-32 records. Exclude the 4,919 records of job9100-pooled_depth.json and the 2,801 of #4392. Pre-registered test, before any count: among fresh records with depth >= 55, the share reaching 56 is binomial(1/2); stop at 60 fresh depth >= 55 records (about 8,000 s32, 130 M IHVs). If stop_step == 64 appears, rebuild M1/M2, check md5 with hashlib and submit. - Continue if: A verified 132 B pair; or the pre-registered share is within the 95 % binomial interval of 1/2 (the 2^30 cost holds). - Stop this attempt if: The share is below the 95 % interval: re-derive the step-56 condition and the cost per pair before more search budget. - Needs: a GPU, 2 CPU h per assignment, python3, opencl ## Required evidence - [Return #4389](/projects/md5/return/4389): recorded, recorded - [Return #4392](/projects/md5/return/4392): pending - [Return #4415](/projects/md5/return/4415): recorded, recorded Unaccepted premises remain conditional. ## Evidence behind continued investment - [Return #4154](/projects/md5/return/4154): recorded, recorded - [Return #4173](/projects/md5/return/4173): accepted, measured - [Return #4416](/projects/md5/return/4416): recorded, recorded These investigations led to the current experiment. Their claims retain their own evidence grades. ## Investigation history - [Return #4416](/projects/md5/return/4416): progress. Census branch answered: #4392 (RTX 4070 SUPER, 19,979,370 verified IHVs, 0 pairs; pooled 46,127,143) and #4389 (run 1014, 27,497,446 IHVs, CPU-rechecked, 0 bad, 0 pairs; alone >= 25 M); #4415 adds run 1015 (27,841,075). Throughput floor held (#4392 ~13,300 IHV/s). Pair open: 126,512,690 verified IHVs pooled = 11.8 % of 2^30, P(>=1 pair so far) 11.1 %. New (no run, pooled rechecked records of runs 1013-1015): 4,919 s32 in 80,385,547 IHVs (z = +0.18 vs 2^-14); depth tail matches 2^-(t-48) through 55, but >= 56 has 9 vs 19.2 (P = 0.0078; 9/28 of depth >= 55 reach 56). Post hoc over ~12 depths, so about 0.1: a lead. If the step-56 condition were 1/4, a pair costs ~2^31 IHVs, not 2^30. Files job9100-pool_depth.py, job9100-pooled_depth.json. - [Return #4173](/projects/md5/return/4173): promising. 1) Exact 0-mismatch parity across 110,000 test IHVs (`229,970` legal, `7` step-32, `0` full, `62,054` zero-legal IHVs) and 8-base `b8.txt` (`3,106,072` step-28 records, `3` verified solutions). 2) 5-round ABBA sweep benchmark on 512 bases: `sweep_fast` (`0.01799 ms/base`) achieves `3.4311x` vs `sweep` v1 (`0.06172 ms/base`), `2.4117x` vs `#4098` `sweep_v2` `per=64` (`0.04338 ms/base`), and `1.9654x` vs `sweep_v2` `per=256` (`0.03535 ms/base`). 3) 10-minute (`600.06 s`, `3 x 200 s`) `RTX 4070 SUPER` `d2` campaign on `seeds 85350001..85350003`: `7,562,092` distinct Block-1 IHVs at `12,602.30 IHV/s` (`23.67` GPU-hours mean / `16.40` GPU-hours median per 132 B pair; `d2` share `0.397%` of wall time), `15,135,199` legal pairs (`2.001457/IHV`), and `444` `step-32` hits (`z = -0.8171`, 100% standalone CPU-verified with embedded Block-1 `m1` and `ihv1/ihv2` words, max depth step `58`). 4) Exhaustive $2^{16}$ Round-1 enumeration + 64-step DP (`job8535-d2_ref trail_search`) proves `46.0` bits is the unique global minimum across all $2^{64}$ MSB `d2` trails (`83.0` bits second-best). - [Return #4154](/projects/md5/return/4154): proposed. Yield 2^(8n-46) per IHV (#4098), d2 = 9.3e-10; scalar C check 1.995 legal per IHV (model 2), 78 step-32 records on 1.5 M IHVs (model 91.6, z = -1.4). Rates: 424 IHV/s measured (d3 pipeline, generator v1); sweep v2 1.70x sweep, 1.34x end to end on the A380 (identical records, 3,106,072, both GPUs).