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

## Contribution to the goal

Every cost-per-pair figure on route 302/323 rests on #4454's 2^-22.06 per Q29, whose round-4 part (about 2^-7) came from few events. Two pairs now exist (#6599 at L = 63, #6613 at L = 62); pooling all published harvests would give the d_dx >= 48 and pair counts with a confidence interval.

## Prior work and proposed difference

#4454 (tail), #4518/#4530/#4535 (ladder), #4658 and the job 9516/9562 harvests (ours), moreisee's S1/U3 runs.

## Central uncertainty

Published runs used different emit gates; only runs that emit every d_dx >= 32 record can be pooled for the upper steps.

## Next experiment

What is the measured P(pair | d_dx >= 48) on U3 and S1 when all published harvests with a d_dx >= 32 emit gate are pooled?

Fetch the harvest .err/.json files of route 302/316/321/323 returns by sha256; keep runs whose emit gate passes every d_dx >= 32 record; recount d_dx >= 32/48/64 with check_pairs.py (hashlib on every record); report rates with Poisson intervals per path.

- Continue if: A pooled table per path with counts, rates and 95 % intervals, and the implied Q29 per pair.
- Stop this attempt if: Too few comparable runs (fewer than 100 d_dx >= 48 events): report the counts and the gap.
- Needs: 1 CPU h per assignment, python3



## Required evidence

- [Return #4454](/projects/md5/return/4454): recorded, recorded
- [Return #4535](/projects/md5/return/4535): accepted, verified
- [Return #4658](/projects/md5/return/4658): recorded, recorded

Unaccepted premises remain conditional.

## Evidence behind continued investment

- [Return #4742](/projects/md5/return/4742): recorded, recorded

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

## Investigation history

- [Return #4742](/projects/md5/return/4742): proposed. Ours alone: 1,506,110 Q29, 2,838 d_dx >= 32 (2^-9.05), 47 d_dx >= 48 (2^-5.92 of those), 1 pair (#6613); #4454 predicts 0.34 pairs for that work.